Potential for B-Physics Measurements with a Fixed-Target

ISBN 91-628-3661-7 LUNFD6/(NFFL-7173) 1999

Potential for B-physics measurements with a ﬁxed-target proton-collision experiment

Thesis submitted for the degree of Doctor of Philosophy in Physics

Jenny Ivarsson

Department of Physics Lund University Professorsgatan 1 Box 118 SE-221 00 Lund Sweden

Abstract

HERA-B is a high-energy physics experiment at HERA. It is a ﬁxed-target experiment with a forward spectrometer to beneﬁt from the strong boost of beauty hadrons. The main goal of HERA-B is to detect and measure the degree of CP violation in 0 0 exclusive B-decays, with emphasis on the golden decay, B J/ψKS. A computer simulated study on this decay is presented and the accura→cy of the measurement is estimated. Necessary conditions for a detection of CP violation are investigated. Various other channels are reviewed, which can give a sign of CP violation within and beyond the Standard Model. Very high rates are required for measurements of the typically very much suppressed signals. The thesis includes a comparison of the situation with the B-factories and the hadron colliders. HERA-B has a very tight time schedule and physics measurements will be performed even before the detector is completed. In particular, the order of installation of detector parts is determined not only by technical factors but also by the feasibility to measure the b¯b cross- section, which is a crucial parameter in the precision of any B-physics measurements at HERA-B. A thorough study has been performed on the possibilities to measure the b¯b cross-section with a partially equipped detector. The emphasis is placed on the inclusive decay B J/ψX. Studies on double semileptonic decays and Υ decays are also presented. →

Contents

Preface 3

1 B Physics and CP Violation 7 1.1 Heavy-quarksymmetries...... 8 1.2 Openheavyﬂavourproductionanddecay ...... 11 1.3 Heavy-quarkonium production and decay ...... 17 1.4 CPviolationintheStandardModel ...... 18 1.5 Mixingofneutralmesons ...... 22 1.6 ExperimentalobservationofCPviolation ...... 24 1.7 CPviolationbeyondtheStandardModel ...... 32

2 The HERA-B experiment 36 2.1 Requirements...... 37 2.2 VertexDetector...... 38 2.3 Trackingsystem ...... 41 2.4 Particleidentiﬁcationdetectors ...... 45 2.5 Trigger...... 48 2.6 OﬄineSoftware...... 52 2.7 ComparisonwithotherB-physicsexperiments...... 63

3 Optimization for σb¯b measurements 68 3.1 Experimentalandtheoreticalpredictions...... 69 3.2 Theoptimalgeometry ...... 70 3.3 Semileptonicdecays ...... 91 3.4 Υreconstruction ...... 106

4 The golden decay 112 4.1 ExtractingaCPviolationsignature ...... 112 4.2 Thesimulatedeventsample...... 116 4.3 Triggersimulation ...... 116 4.4 Analysisandeﬃciencies ...... 119 4.5 Background...... 125 4.6 B ﬂavourdetermination ...... 127 4.7 The precision of sin 2β ...... 130 iv CONTENTS

5 Summary 135

Acknowledgements 138

A Kalman ﬁlter 141

Bibliography 145 Notice the World

The sun shines on a ﬂower stalk On the path where I do walk On the ﬁeld where startled deer Leap into bush to disappear Each step the scenery’s new I could live for this and this view I could die for this and this vital fear.

Spirited songs of greyish lark Cracklings in the aged bark The humming little ﬂies and bees Whispering wind up in the trees Rustle from leaves on the ground I could live for this and this sound I could die for this and this uniﬁed peace.

There’s a scent I can’t locate But it’s clearer near the lake Deep in the wood it’s more intense like moss that clings to a meadow fence And ﬁr growing close by the well I could live for this and this smell I could die for this and this nuance of sense. 2 CONTENTS

The gentle wind that heats and chills Fondles over grassy hills Caresses too my cheek and hair Dabbed by a wing so weak and fair I touch the nature ceiling I could live for this and this feeling I could die for this and this varying air.

Sweet dynamics of death and birth Complexity engulfs the earth With all its souls that need reﬁll Nature itself is rich in it still A superior beauty reigns too I could live for this and I do I could die for this and I know that I will

Jenny Ivarsson Munich 1995 Preface

Have you ever reflected on the endlessly rich complexity in nature? Have you ever walked in a bright friendly forest in early summer, when the wind rustles quietly in the leaves, little creatures run around in the grass and the sun shines on your skin and finds the way to your amygdala? How can a world which exhibits such complexity be built? If you want to describe it, paint it, make a map of it, you can spend your whole lifetime without getting all the details, because once you notice the little needle, you will soon have to accept that it contains a whole world by itself. I pondered this. In physics books, they talked about atoms, protons and even mysterious things like quarks. In biology, the science of the living things, they talked about cells, that cells build up all this. But that dead and living things must be fundamentally the same, I was certain. The burning question I had during my first years as a thinking teenager was, whether cells were made up of atoms or atoms made up of cells. But I was lucky; I asked this question in a time when the wisdom of other people who had already thought about everything was documented in book after book. There was Democritus from ancient Greece with the idea of something undividable, Rutherford who found that the atom has a nucleus, and Gell-Mann postulating the quarks as the constituents of protons and neutrons. And there were Scheiden and Schwann who in 1838 proposed that the cell was the smallest form of life, and Mendel who got the idea of genes. You just need luck to find a book where both atom and cell are mentioned in the same chapter. The cell has a kernel in which there are chromosomes made up of genes, which in turn are made up of bases, and each base consists of five atoms. This sentence gave me my second scientific revelation (the first was when I understood how the earth can be round when it looks flat). No wonder that nature is so complex when it is constructed of such small building blocks. The number of possible combinations is just incredible. Perhaps you also sometimes wonder about the vast empty sky. When you lift your eyes upwards at night, do you then behold infinity? How can the universe be infinite? And if it is not, what lies beyond? And has the universe existed for an eternity? If not, what was there before? These are a couple of very uncomfortable paradoxes. And then along comes Einstein and tells us that time is relative. This concept is very hard to accept, but if you do, you can get a relieving solution to the space–time paradox. If space is bent in an additional dimension, just like the surface 4 CONTENTS of the earth and time is our perception of the extra dimension, then the universe has no boundary but is still not infinite. In my interpretation, space and time were created from a singularity and questions like ‘before’ or ‘outside’ are irrelevant. The history of the universe can tell us a lot, if not all about the world we are living in. In the beginning, when the available space was very small, everything was very concentrated and the energy available for physics processes enormous. In particle physics we try to reconstruct those processes by building particle accelerators, to achieve high energies concentrated on small spots. Under those conditions a lot of particles are created which do not exist in our normal low temperatures. Early in history, in the Big Bang theory, there existed electrons and positrons, quarks and antiquarks in equal proportions. Conservation laws required balance between them. As the universe expanded it cooled down and some processes became impossible. At a certain threshold pair production was no longer possible and annihilation of matter and antimatter became an irreversible process. Electrons and positrons annihilated and released energy in the form of photons. Light quarks and antiquarks annihilated after 10−4 seconds, the heavier b-quarks and anti-b quarks after 10−9 seconds. If the universe had not expanded and cooled down, the annihilation processes would have continued until there was only energy left, which would have led to a terribly boring world without life or complexity. In the end there was more quarks than antiquarks. How could this happen? All those conservation laws required that there should be equal concentrations of both. I read in a book that some very heavy gauge boson (a force mediator), translated more often to a quark pair than the corresponding antiboson translated to an antiquark pair, although their total decay rates were the same. When the temperature decreased so that the reverse reaction was no longer possible, all of those gauge bosons eventually decayed and we were left with more quarks than antiquarks. I thought this was ingenious, but I was still uneasy. What the author of the popular book had not bothered to tell me was that in fact, some of the symmetry laws must be broken to lead to this decay. In this way, one question brings the other and at this stage you are addicted to knowledge. Then you go to university and learn the mathematical formulas for everything and how all the fantastic world of elementary particles and forces and their interactions can be described with mathematics; and all the time new questions arise, like how the particles get their masses and what happens at even smaller distances, at even higher energies. One of the greatest achievements of the retreating century has been the mathematical formulation of three out of the four different kinds of interactions under the same concept. Those were the electromagnetic, the weak and the strong forces. The fourth force, gravity, has no effect at energies accessible in particle physics laboratories of today. The collected knowledge in particle physics is described by the Standard Model. The asymmetry which is broken and gives an excess of matter over antimatter, is called CP violation. C for charge conjugation and P for parity symmetry. But the Standard Model contribution to CP violation is not enough to account for all the matter–antimatter asymmetry observed in the universe. On the other hand, the size of CP violation is not yet measured, and it will not be known whether the Standard CONTENTS 5

Model is sufficient to explain the CP violation in B decays until it is measured. Eventuallt you reach a point when the world heritage can not tell you more. Then you have to put on your working gloves and contribute yourself. This thesis describes my own attempts to bring the physics knowledge of the world a small unnoticeable step forward. I have been participating in a high-energy physics experiment at DESY, the HERA-B experiment, which uses the 920 GeV proton beam of the HERA accelerator and directs the beam halo particles onto target wires. The high luminosities lead to several interactions per proton bunch crossing and to very high rates. HERA-B is designed to perform b-quark physics, also called beauty physics. Particles with b or anti-b quark constituents are called B hadrons, or beauty hadrons. The energy of the HERA proton beam is enough to produce the heavy B hadrons. A crucial parameter for the HERA-B experiment is the rate of b and anti-b quarks that can be produced, i.e. the b¯b cross-section.The main part of this thesis describes the work and preparation studies I have made for the measurement of the b¯b cross-section at an early stage of HERA-B running and the reconstruction of the so called golden decay of neutral B hadrons. In Chapter 1 I introduce the reader to beauty physics and the role of the HERA-B experiment in this context before describing the experiment in more detail in Chapter 2. Studies on the b¯b cross-section are presented in Chapter 3. A computer simulated study on the golden decay of neutral B mesons is presented in Chapter 4. This study is made to find the possibilities of measuring CP violation in this channel in the HERA-B experiment. The CP reach in the HERA-B experiment depends on some unknown factors: The size of the CP-violating parameter sin 2β. • The b¯b cross-section at HERA-B kinematics. • The hardware and its power for event selection and background reduction. • Reconstruction efficiencies, including pattern recognition, bremsstrahlung cor- • rections and particle identification. The size of sin 2β as it is known today is presented following a study of the reconstruction power of the golden decay using detectors with resolutions and efficiencies of the final technical design. The most crucial point is the b¯b cross-section. This is the motivation to learn about the size of the b¯b cross-section and in turn, the power of the detector. The measurement of the beauty cross-section can be performed during the building phase before the detector is completed. HERA-B has a tight time schedule and needs to achieve as much as possible in as short as possible a time. The computer simulations of the detector are constantly updated in parallel with the evolution of production and installation plans. A chain of scenarios eventually emerges in the real situation and meets with real data. The extensive computer simulated studies on the b¯b cross-section for different detector geometries are treated in Chapter 3. I took part in a σb¯b task force in the spring and early summer of 1997. The goal of the task force was to optimize the detector for the 1998 physics run, with the main emphasis 6 CONTENTS on one of the detector components, the outer tracker. The results were collected in the notes [1] and presented to the advisory committee to the DESY director general (Physics Research Committee) [2]. In the task force I was responsible mainly for vertex reconstruction and computing the final efficiencies. Using the tools developed for the task force, I carried out studies on semileptonic decays of B mesons, which were presented to the Physics Research Committee [3], and together with A. Somov a study on Υ reconstruction. One year later, the conditions for physics in 1998 had changed. This years study on physics options in 1998 concentrated on the calorimeter and the vertex detector. I made the studies on the σb¯b cross-section, assuming that the magnetic field would be switched off during data taking of 1998. The results were collected in notes [4] and presented to the Physics Research Committee. I also made a study on semileptonic decays with this geometry, which became a note [5]. Later I continued the study for the case of a magnetic field and for different configurations of the vertex detector. That work was done to be able to optimize the detector configuration for the early run of 1999 and get another chance of seeing a B. In 1995, before being involved in HERA-B, I was working on the ATLAS Transi- tion Radiation Tracker (TRT). I implemented a modular geometrical structure into a GEANT simulation and studied the electron and pion identifications using polypropylene fibre radiator. This work does not fall within the scope of this thesis. A detailed description can be found in my thesis for the degree of philosophie licentiat [6].

Jenny Ivarsson CERN, 1999 Chapter 1

B Physics and CP Violation

The HERA-B experiment will have access to the system of B hadrons. Because of the large mass of the b-quark there is a rich scope of decays to be studied in this hadron family. The mechanisms of open heavy flavour production at fixed-target experiments have been investigated in Refs.[8] and [9] and are reviewed here. When the mass of a quark Q is much larger than the QCD scale the quark is called a heavy quark and simplifications arise due to the asymptotic freedom of the strong interactions. The Non-Relativistic QCD (NRQCD) approach [10], leads to predictions of heavy-quarkonia production and decay, which can explain the data at the pp¯ colliders very well. At fixed-target experiments, where the heavy quarks are produced close to the threshold, the predicted total production cross-section is consistent with data, but there are some discrepancies in the χ1c/χ2c production ratio and the transverse polarization fraction of the J/ψ, which can not be explained by NRQCD alone. For Υ, the corresponding ratios have not yet been measured, but are expected to be more consistent with theoretical predictions. The presentation on NRQCD and comparisons with data is based on the articles in Ref. [11]. For heavy quarks (m ) there is a spin–flavour symmetry because the Comp- Q →∞ ton wavelength of the heavy quark is much smaller than the QCD scale, ΛQCD.A range of measurements to be performed in the B system will be viewed from the Heavy-Quark Effective Theory (HQET) based on the heavy-quark symmetry. A derivation and detailed review can be found in Ref. [12]. Maybe more importantly, CP violation can be studied in a variety of ways in the B system. CP violation is a small effect. It can be studied only at very high luminosities in high-energy environments, where quark–antiquark composites can be produced. The measurement of CP violation in the B system is the main goal of the HERA-B experiment. The theory of CP violation is well described in Ref. [13]. 8 CHAPTER 1. B PHYSICS AND CP VIOLATION

1.1 Heavy-quark symmetries

The mediators of the strong force, gluons, carry themselves the strong charge, colour. As a consequence, gluons couple to other gluons. The emission and absorption of virtual gluons produce an antishielding effect, so that the strength of the field is magnified at larger distances. At distances of the size of a hadron, Rhad 1fm, the quantum numbers of a quark can not be resolved. This phenomenon is∼called confinement. The coupling constant, which describes the interaction strength, depends on the momentum transfer q:

2 12π αs(q )= , (1.1) q2 (33 2Nf )ln Λ2 − QCD where Nf is the number of interacting quark flavours. In processes with very high momentum transfers, which corresponds to interactions at short distances, the effec- 2 0 tive coupling constant is very small: αs(q ) 0asq . In other words, the constituents of the hadron behave as free par→ticles. This→∞phenomenon is known as asymptotic freedom. For sufficiently large momentum transfers, the strong interaction 2 can be described in terms of a power expansion in αs(q ) according to perturbation theory. Because of confinement, perturbation calculations will always need nonperturbative corrections of non-free quarks and gluons from long distances, for which the coupling constant is not small. The scale which separates the regions of large and small coupling constant is ΛQCD. Strong interactions of systems containing heavy quarks allow some simplifications due to the large momentum transfers at the heavy-quark scale, mQ λQCD,and due to the small Compton wavelength of the quark compared with t≫he size of the hadron: λ R . Q ≪ had Nonrelativistic QCD

For a heavy quark, mQ ΛQCD and the eﬀective coupling constant αs(mQ)issmall due to asymptotic freedo≫m. At length scales comparable to the Compton wavelength of the heavy quark, the strong interactions are described perturbatively. A heavy- quarkonium system (QQ¯)isofsizeλ /α (m ) R .The velocity of the heavy Q s Q ≪ had quarks in the rest frame of the quarkonium, vQ, is small. Hence heavy quarkonium can be treated as a nonrelativistic bound state. In order to exploit the smallness of αs(mQ) and perform perturbation calculations, the scale mQ must be separated from 2 the smaller momentum scales, mQvQ, mQvQ and ΛQCD, that involve nonperturbative physics. mQvQ is the three-momentum of the constituents in the quarkonium rest 2 frame. mQvQ is the kinetic energy of the heavy quark and the scale of binding energies. The Lagrangian for NRQCD is

= + + δ (v2)+O(v4 ) . (1.2) LNRQCD Llight Lheavy L Q

light is the normal relativistic QCD Lagrangian for light constituents. heavy is the nLon-relativistic approximation of the Lagrangian for a heavy quark andLis invariant 1.1. HEAVY-QUARK SYMMETRIES 9 under heavy-quark spin symmetry. δ includes the relativistic correction and breaks the spin symmetry. The size of the Lhigher order terms depends on the momentum scale, mQ, and can be calculated using perturbation series in αs(mQ). The diﬀerential cross-section formula for producing a quarkonium state, H,with four-momentum p~ is factorized as

H dσ(H(p~)) = dˆσQQ¯[n,p~] On , (1.3) n X where the sum runs over all colour and angular-momentum states of the QQ¯ pair. The short-distance factor, σˆ, describes the cross-section to produce the QQ¯ pair. It involves momentum scales of order mQ and larger, and can be calculated perturba- H tively. The long-distance factor, On is proportional to the probability that the QQ¯ pair will form the quarkonium state H plus soft hadrons, whose energies in the

H rest frame are of order mQvQ or smaller. In the non-relativistic approximation the last factor is zero for all states except when the produced pair is already in the colour singlet state H.

Heavy quark effective theory The typical momenta exchanged between heavy and light constituents in a hadron are of order ΛQCD and described nonperturbatively. Distances which can be resolved are of order Rhad. However, the Compton wavelength of the heavy quark is much smaller than that, which means that quantum numbers like flavour and spin of the heavy quark can not be resolved. Only the colour field extends over large distances because of confinement. Relativistic effects vanish as m . Such effects are colour magnetism and Q →∞ spin. The quark is at rest with respect to the hadron as mQ mhad. The effective result is that the heavy quark acts as a static source of colour.→This implies relations ∗ ∗ of heavy mesons like B, D, B , D or heavy baryons like Λb and Λc. The descriptions of these hadrons differ only due to nonperturbative corrections in powers of 1/mQ and perturbative corrections in powers of αs(mQ). For Nh heavy-quark flavours, there is an SU(2Nh) spin–flavour symmetry group, under which the effective strong interactions are invariant. The aim is to rewrite the Lagrangian for a heavy quark, = Q¯(iD m )Q, (1.4) LQ 6 − Q into an expansion of 1/mQ in order to construct a low-energy effective theory, which is called the Heavy-Quark Effective Theory (HQET). A heavy quark has more or less the velocity of the hadron, v, and the momentum can be rewritten as µ µ µ PQ = mQv + k , (1.5) where the residual momentum k is small and is affected by interactions with light degrees of freedom like soft gluons. The quark field can be written as a sum of the large and small component fields hv and Hv:

imQvx imQvx hv(x)=e P+Q(x),Hv(x)=e P−Q(x), (1.6) 10 CHAPTER 1. B PHYSICS AND CP VIOLATION

where P+ and P− are the projection operators: 1 v P = ±6 . (1.7) ± 2

The operator hv annihilates a heavy quark with velocity v. It describes the massless degrees of freedom. Hv creates a heavy antiquark. It corresponds to ﬂuctuations with twice the heavy quark mass, which are the heavy degrees of freedom appearing as corrections to the eﬀective Lagrangian. The derivation of the Lagrangian is well describedinRef.[12].

¯ 1 ¯ 2 gs ¯ µν 2 eff = hviv Dhv + hv(iD⊥) hv + hvσµν G hv + O(1/mQ), (1.8) L · 2mQ 4mQ µ ν µν where [iD ,iD ]=igsG is the gluon field-strength tensor. In the limit mQ , only the first term remains. The second term arises from off-shell residual m→∞otion of the heavy quark. The third term describes the colour-magnetic coupling of the heavy quark spin to the gluon field. Both these terms scale like 1/mQ. This effective Lagrangian reproduces all physics at long distances. It does not account for interactions with hard gluons with virtual momenta of order mQ. Short- distance corrections are calculated in perturbation theory in powers of the running coupling constant, αs(mQ), and thus induce a logarithmic dependence on the heavy- quark mass. One way to test and use HQET is in spectroscopy. The mass of the hadron should be the mass of the heavy quark plus a term which is independent of the flavour (up to corrections). Because of heavy-quark symmetries, hadronic states HQ are classified by quantum numbers of the light degrees of freedom:

2 ¯ ∆m 2 mH = mQ + λlight degrees + + O(1/mQ) . (1.9) 2mQ This predicts that the SU(3) mass splittings should be similar for the B and D systems: m m = λ¯ λ¯ + O(1/m ) Bs − Bd s − d b m m = λ¯ λ¯ + O(1/m ) (1.10) Ds − Dd s − d c The prediction is conﬁrmed experimentally, since m m =(90 3) MeV and Bs − Bd ± mDs mDd =(99 1) [58]. The mass of the P-wave beauty mesons is needed in studies− on same side±tagging (Chapter 4, Section 4.6). The mass has been estimated in Ref. [54] using the measured masses of charmed P-wave mesons. Spin corrections are included in ∆m2 above. They depend only on the spin of the heavy quark and the light degrees of freedom and are the same for D and B as well as for D∗∗ and ∗∗ 2 B . The diﬀerence from the ground-state mesons should be equal up to order 1/mQ. In this way, the mass of B∗∗ was estimated to be around 5.8 GeV (or less depending 2 on the size of the O(1/mQ) corrections). The semileptonic branching ratios and the average number of charm hadrons per B decay (known as charm counting) are other challenges for HQET, as well as lifetime predictions. 1.2. OPEN HEAVY FLAVOUR PRODUCTION AND DECAY 11

b b n (ud) n (ud) d d

u u p (ud) p (ud) - b- b

b- n p, ... d u- u p (ud) b

Figure 1.1: Lowest order contributions to open heavy ﬂavour production. Upper diagrams: gluon–gluon fusion. Lower diagram: quark–antiquark annihilation.

1.2 Open heavy ﬂavour production and decay Heavy-quark production Heavy quarks are predominantly produced in the hard collision of one light parton from each colliding hadron. The two basic processes for heavy-quark production are gluon–gluon fusion (gg QQ¯) and quark–antiquark annihilation (qq¯ QQ¯). In perturbative QCD→the heavy-quark cross-section of two partons (→i, j)isaprod- uct of the scale-dependent parton distribution functions (PDF) and a ﬁnite short- distance cross-section, σˆ. The total cross-section is a sum over all parton types and an integration over the kinematic region:

S 2 2 σQQ¯ = dx1dx2fi(x1,µF )fj(x2,µF )ˆσ(x1,x2,µF ,µR) . (1.11) 2 i,j x1x2S=4mQ X Z This factorized formula is valid for quarks with large masses compared to the hadron 12 CHAPTER 1. B PHYSICS AND CP VIOLATION

masses. The corrections are suppressed by powers of mQ. The PDF, fi and fj are evaluated at the momentum fraction x and the factorization scale µF chosen at the heavy-quark mass. The short-distance cross-section is calculated as a perturbation series in orders of the strong coupling constant, αs(µR). The renormalization scale µR is also chosen at the heavy-quark mass, since sensi- tivities to lower momentum scales are included in the PDF. The leading order (LO) 2 diagrams in Fig. 1.1 are of order αs. The cross-section has been calculated up to or- 3 der αs (NLO), which includes all virtual corrections as well as diagrams with initial- or ﬁnal-state gluon radiation. The uncertainties in the perturbative QCD description of the heavy-quark production include the following.

The heavy-quark mass, m . • Q The size of higher-order corrections. This uncertainty is normally estimated by • varying µF and µR between m/2and2m.

The value of the QCD scale Λ which is strongly correlated to the shape of the • parton densities.

Nonperturbative (long-distance) effects. • It is difficult to measure the cc¯ and b¯b differential cross-sections because, in the confinement process, the heavy quarks lose some of their energy and the one-to- one correspondence between the heavy-quark pair and the heavy hadron is lost. In experiments of limited phase space, measurements of the total cross-section depend on extrapolation using fragmentation functions and are thus very uncertain. The energy dependence of the total b¯b cross-section at fixed-target experiments is displayed in Fig. 1.2. The data has a tendency to fall somewhat above the central theoretical values. This can be explained by nonperturbative effects, which have been found to be size- able when the b¯b pair is produced near threshold, as in HERA-B and the presented fixed-target experiments. The b¯b cross-section at HERA-B energies is discussed in more detail in Chapter 3.

B decays B mesons primarily decay via the spectator diagrams in Fig. 1.3. The spectator diagram in Fig. 1.3b is suppressed by colour conservation, which requires gluon exchanges between the initial and ﬁnal states. The b u transition is Cabbibo suppressed. Charmless decays are therefore rare, with branc→ hing ratios of the order 10−5. Examples of charmless decays are B π+π− and B D X. ∼ → → s The semileptonic decays are of particular interest, since they involve fewer strong- interaction eﬀects and thus fewer hadronic uncertainties. In the heavy-quark limit, there is only one form-factor, which depends only on the momentum transfer to the 1.2. OPEN HEAVY FLAVOUR PRODUCTION AND DECAY 13

1000 bb Production

NLO QCD: πN bb + X 100 pN bb + X

10 / ( nb/nucleon ) σ

1 πN Data: pN Data: E653 E771 E672/E706 E789 WA92 NA10 0.1 200 400 600 800 1000 Beam Momentum / GeV

Figure 1.2: Theoretical calculations at NLO from Ref. [8] of the b¯b cross-section compared with ﬁxed-target data. The dashed curves are the calculated πN cross- section and the solid curves the calculated pN cross-section. The lower limits, central values and upper limits are represented. 14 CHAPTER 1. B PHYSICS AND CP VIOLATION

e µ u c 33xx νe νµ ds b c W u W b c, u d u, d u, d u u a) b)

Figure 1.3: a) External spectator diagram for the decay of B mesons. b) Colour- suppressed spectator diagram.

ℓν¯ system. The rate of the semileptonic decay is described by the hadronic form factor and the amplitude of the electroweak quark transition:

dΓ(B¯ Dℓν¯) → = V 2 2(q2) . (1.12) dq2 | cb| F

Exclusive semileptonic decays of B mesons are studied to extract values of the elements Vcb and Vub of the CKM matrix, which describes the weak transitions between| the| quark|s (1|.20). The heavy-quark symmetry implies relations between form-factors of diﬀerent heavy mesons, because in the limit mQ the form- factor can only depend on the Lorentz boost γ = v v′. Matrix eleme→∞nts of scattering of heavy quarks or decays to other heavy quarks are· all determined by the Isgur-Wise function ξ(v v′),ξ(1) = 1. For example, for the decay of a B¯ meson into a D meson: ·

1 ′ µ ′ ′ µ D(v ) c¯v′ γ bv B¯(v) = ξ(v v )(v + v ) . (1.13) √mB mD | | ·

Additional spin rotation factors appear in the relation between vector mesons and n pseudoscalar mesons. Nonperturbative power corrections (ΛQCD/mQ) are added. n Perturbative corrections of order αs (mQ) are also applied to account for short distance interactions, which do resolve the spin and ﬂavour of the heavy quark. The combined result is that ξ(v v′) is replaced by · (v v′)= (1)[1 ̺ˆ2(v v′ 1) + ...]. (1.14) F · F − · − (1) is calculated using HQET and including power corrections. The slope ̺ˆ2 can be mFeasured experimentally and extrapolations to zero recoil can be made (see Fig. 1.4). In such a way V can be extracted from the semileptonic decay | cb| dΓ(B¯ D∗ℓν¯) → = k 2(v v′) V 2, (1.15) d(v v′) F · | cb| · where k is a kinematic constant. 1.2. OPEN HEAVY FLAVOUR PRODUCTION AND DECAY 15

0.04 ALEPH 0.03

)|Vcb| 0.02 . v v'

F( 0.01

0 1 1.1 1.2 1.3 1.4 1.5 v .v'

′ ′ 2 Figure 1.4: (v v ) Vcb as a function of v v . (1) Vcb corresponds to the intercept of the straightF -lin· e ﬁ| t. The| example is from· theF ALEPH| | Collaboration [14].

Vcb can also be determined from inclusive B decays. HQET applies to the theo|retica| l expressions of the decay widths with the nonperturbative corrections in 2 powers of (ΛQCD/mB) . The determination of Vub depends on form-factors for heavy- to light-meson transitions, where the heavy-qu| | ark symmetry does not help. The ratio V / V can be determined from the inclusive semileptonic decay: | ub| | cb| dΓ(B¯ Xeν¯)= V 2dΓ(ˆ B¯ X eν¯)+ V 2dΓ(ˆ B¯ X eν¯), (1.16) → | cb| → c | ub| → u where dΓ(ˆ B¯ Xqeν¯) denotes the contribution to the total semileptonic rate from the part of the→ weak current where a bottom quark couples to the quark q = c or u. The contribution from dΓ(ˆ B¯ X eν¯) can be isolated by examining the electron → u spectrum dΓ/dEe in the end-point region near the maximum allowed electron energy, since only b u transitions can contribute for E > (m2 m2 )/(2m )[15]. → e B − D B

Bc mesons Among the heavy-quark states, the (¯bc) system takes a particular place. Since top quarks are too heavy to form a stable state, (¯bc) is the only system, composed of two heavy quarks, which can neither decay strongly nor electromagnetically. The study of Bc mesons can increase the understanding of QCD dynamics and important parameters of the electroweak theory. 16 CHAPTER 1. B PHYSICS AND CP VIOLATION

+ Figure 1.5: Some typical Feynman diagrams for the subprocess g + g Bc + b + c¯. The fragmentation-type diagrams a) and b) have cc¯ pairs created on→ the leg of the ¯b. In the recombination-type diagram c) the quark–antiquark pairs are created independently.

The question has been raised whether there is a possibility to observe Bc mesons in HERA-B. The predictions on the total cross-section of Bc production at HERA-B do not give precise information except that it is small [39]. The production of Bc mesons is suppressed relative to other beauty hadrons, because of the hard production of an additional c-quark pair. At HERA-B there is a strong threshold eﬀect because additional pairs of heavy B and D mesons have to be produced. There is an additional suppression in the small probability of the (¯bc) quarkonium state formation. The two ﬁrst diagrams in Fig. 1.5 describe b¯b production and subsequent fragmentation of a ¯b-quark. The fragmentation of a c-jet contributes too, but it is less important than that of a b-jet. The contribution of recombination diagrams of the type depicted in Fig. 1.5c is not negligible at pT values below 10 GeV. According to Ref. [39], σ =0.07 0.08 pb. Bc − On the other hand Ref. [40] presents

σ =0.002 0.09 pb. Bc − The interaction frequency in HERA-B could be as much as 50–60 MHz. In a nominal 7 year of 10 seconds about 100–2300 Bc mesons would then be produced in HERA-B. The Bc mesons can decay via three main processes as is shown in Fig. 1.6, leading to a considerable number of diﬀerent decay products. The HERA-B trigger is a dedicated J/ψ trigger. Therefore it is advantageous to search for Bc in decays to J/ψ. The inclusive decay rate to J/ψ is 20%. The decay mode Bc J/ψπ deserves special attention because all of the three ﬁnal-state particles can be w→ell reconstructed and allow for a mass reconstruction of the Bc meson. They also have a common secondary vertex, which makes the topology very clean. The invariant mass of the lepton pair from the J/ψ supplies an additional constraint on the secondary vertex. 1.3. HEAVY-QUARKONIUM PRODUCTION AND DECAY 17

u, c, l b d, s,ν b b u, c, l c d, s W W ν W d, s, ν b c c d, s, c c u, l a) b) c)

Figure 1.6: The decay of Bc mesons. a) and b) are the semileptonic and nonleptonic spectator decays and c) illustrates nonleptonic weak annihilation.

The branching ratio of this channel is estimated in [39]:

BR(B+ J/ψπ+) 0.2%. c → ≈ Including the branching ratio of J/ψ ℓ+ℓ−, it follows that a maximum of only → one Bc signal event can be expected every second year in HERA-B. This is of course not possible to detect. There are many other channels, which could improve the statistics. The decay mode Bc J/ψℓν has an expected branching ratio of 3% leading to a maximum of seven e→vents per year, which is obviously also too low≈for an observation.

1.3 Heavy-quarkonium production and decay

The NRQCD factorization approach to the production of heavy quarkonium, J/ψ and Υ and higher states describes well the existing data. The quarkonium states can be produced by gluon fusion (Fig. 1.7) or fragmentation of a single parton (Fig. 1.8). The fragmenting parton is produced in a two-to- 2 one process of order αs. The fragmentation contribution dominates at high pT.The cross-section is a product of the heavy-quark pair production at short distance and the formation of the bound quarkonium state at long distance. Concentration is here laid on the J/ψ production, but the description can be generalized to ψ(nS)andΥ(nS) states. In the NRQCD factorization approach, the nonrelativistic Lagrangian heavy L 3 for the heavy-quark system corresponds to the formation of the J/ψ state, S1, through the production of a cc¯ singlet state with the same quantum numbers, de- 3 noted (cc¯1) S1. This type of production is illustrated in Figs. 1.7a and 1.8a. If the velocity of the quarks, vQ, is suﬃciently large, a quark–antiquark pair in a colour-octet state can evolve into a singlet state via electric dipole transition (soft ′ 3 gluon emission). For the J/ψ and J/ψ states, S1, the cross-section is dominated 3 by the production of the colour-octet state (cc¯8) S1 in Fig. 1.8b. This diagram is suppressed at long distance by a factor v4 relative to the colour-singlet-state diagrams Figs. 1.7a and 1.8a. At short distance, on the other hand, the operator for the 18 CHAPTER 1. B PHYSICS AND CP VIOLATION

J/ψ, χ , χ χ 0c χ χ χ χ 1c, 2c 0c, 2c 0c, 2c

a) b) c)

Figure 1.7: Schematic diagrams for the production of J/ψ and Υ in gluon fusion. a) 3 2 and b): Leading-order diagrams of order αs and αs respectively. c): An example of 4 a virtual diagram of order αs. The lowest states can be produced directly as in a) or via the χ1 state produced in a) or the χ0 and χ2 states produced in a), b) and c).

3 2 (cc¯8) S1 state is only of order αs at high pT and αs at low pT, where the production 3 is dominated by gluon fusion. This should be compared with the order αs for the 3 (cc1) S1 state. At high pT the domination of the colour-octet production becomes even more pronounced as the cc¯ pair produced in Fig. 1.8b carries all the momentum of the fragmenting gluon. 3 Also for the χ1c state, P1, the colour-octet production is expected to dominate 3 because of the suppression in αs of (cc¯1) P1 production. Also for the other χic states, the colour-octet production is important. The leading contributions from the 3 nonrelativistic Lagrangian in the NRQCD factorization approach are (cc¯1) Pi and 3 (cc¯8) S1. At fixed target, even after including the colour octet contribution, the predicted ratio χ1c/χ2c is almost one order of magnitude too low, compared to data. Another discrepancy at fixed-target energies, is the fraction of transversely polarized J/ψ, which is predicted to be an order of magnitude larger than the measured fraction. The reason could be not yet understood interactions of the colour-octet pair with soft gluons as it traverses the target in combination with spin symmetry breaking. The total production of J/ψ and Υ includes decays of the higher quarkonia states. In summary, the total production of J/ψ and Υ is dominated at high pT by the process gg g, where the final-state gluon fragments into a heavy-quark pair in a colour-octet→state; g (QQ¯ ). At low p , the process gg (QQ¯ ) dominates. → 8 T → 8 The decays of quarkonia can be formulated using the same nonrelativistic QCD. The two principal decay diagrams are the electromagnetic decay into a lepton pair (Fig. 1.9a) and the hadronic decays (Fig. 1.9b).

1.4 CP violation in the Standard Model

CP is the combined eﬀect of charge conjugation (C) and parity transformation (P). Charge conjugation ﬂips the signs of internal charges, such as the electric charge, the 1.4. CP VIOLATION IN THE STANDARD MODEL 19

ψ′ ψ′ ψ′

−(1) − − QQ QQ(8) QQ(8)

a) b) c)

Figure 1.8: Parton fragmentation into J/ψ and Υ via colour-singlet and colour- octet states: a) leading-order gluon fragmentation via a colour-singlet QQ¯ state; b) Leading-order gluon fragmentation via a colour-octet QQ¯ state; c) example of a real 2 fragmentation diagram at order αs.

u c e,++ µ d c γ* d c d d c e, µ u a) b)

Figure 1.9: a) Electromagnetic decay of quarkonium; b) hadronic decay of quarkonium. 20 CHAPTER 1. B PHYSICS AND CP VIOLATION baryon number and lepton numbers. Under parity operation the space coordinates are reversed so that for example the direction of motion is reversed. The spin is not affected. Parity and charge conjugation are violated by weak interactions. These circumstances are described with the concept of helicity, ~s p~ h = · , (1.17) ~s p~ | || | which describes the direction of the spin relative to the direction of motion. Particles of positive helicity are called right-handed and those of negative helicity left-handed. Experiments show that only left-handed fermions and right-handed antifermions par- ticipate in weak interactions. Whereas P and C are not conserved in weak interactions, the combined operation CP was long thought to be a good symmetry in all types of interactions. Violation of CP symmetry was first discovered in the long-lived neutral K meson. The effect of CP violation is expected to be larger in the system of B mesons. Several independent measurements are needed to determine the nature of CP violation and the access to the B system offers a wide range of decays with different quark transitions. All field theories are automatically invariant under the succession of C, P and T (time reversal) operations because of the requirement that the Lagrangian be hermitian and invariant under Lorentz transformations. One consequence of this CPT theorem is that particles and antiparticles have the same masses and lifetimes. The consequence of CP violation or equally T violation is in very generalized words the sense of a direction of time in the evolution of history. It is believed that, in the early stages of our universe, CP violation resulted in an excess of matter over antimatter, which lead to the observed baryogenesis. The Standard Model prediction is too small to account for the observed baryon asymmetry in the universe. Therefore, measurements of CP violation are of high interest. Owing to its smallness, CP violation is one of the least tested properties of the Standard Model. Exploration of the B system gives access to new sources of CP violation, which will lead to more precise measurements of the CP-violating parameter in the Standard Model. It might also indicate scenarios for CP violation beyond the Standard Model.

Theoretical description Theories within the Standard Model include CP violation in both strong interactions (QCD) and electroweak interactions. If there is CP violation in strong interactions it has been shown experimentally to be very small (see, for example, Refs. [13] and [16] ). In the Electroweak Model the CP violation is incorporated in the CKM (Cab- bibo, Kobayashi, Maskawa) matrix which describes the weak interaction between the quarks, i.e. the ﬂavour-changing charged current interactions:

d′ g L ′ ′ ¯′ µ ′ + int = (¯uL, c¯L, tL)γ sL Wµ + h.c. (1.18) L −√2  ′  bL   1.4. CP VIOLATION IN THE STANDARD MODEL 21

′ Here qL are the left-handed quark doublets. Because of interaction with the Higgs doublet, these are nonphysical ﬁelds, having a non-diagonal mass matrix. The CKM matrix appears when the Lagrangian is written in terms of the mass eigenstates:

dL g µ + int = (¯uL, c¯L, t¯L)γ VCKM sL W + h.c. , (1.19) L −√2   µ bL   where Vud Vus Vub V = V V V (1.20) CKM  cd cs cb  Vtd Vts Vtb   is the unitary CKM matrix. It has nine parameters (the square of the dimension). There are three Euler angles in three dimensions: These are the quark mixing angles. The rest of the parameters are phases. The phases of all the quark fields are arbitrary, unmeasurable quantities. Under i(φ(k)−φ(j)) phase transformation of the quark fields, Vjk is replaced by e Vjk. There are accordingly five unmeasurable phases and only one measurable phase, which is the origin of CP violation in the Standard Model. The CKM matrix is often written in the Wolfenstein parametrization, which is an expansion in powers of λ = Vus =cosθC ,whereθC is the Cabbibo angle known from the mixing of two generatio| ns.|

λ2 3 1 2 λAλ(ρ iη) − λ2 − 4 VCKM λ 1 Aλ2 + O(λ ). (1.21) ≃  2  Aλ3(1− ρ iη) −Aλ2 1  − − −  A, ρ and η are real numbers of order unity as indicated by experiments. V and V | ud| | us| are known to better than 1% accuracy. Vcd and Vcs are known to 10–20%. Vcb is known to 5% accuracy. Hence both λ an| d A| are w| ell|determined experimenta|lly.|

V λ =0.2205 0.0018,A= cb =0.81 0.04. (1.22) ± V 2 ± us

Vub and Vtd are known to 30% accuracy, implying a high uncertainty in ρ and η. | | | | 0 0 Vtd is obtained from B B¯ mixing and Vub from charmless decays of B mesons. The| | phase is accessible as−described below.| | The unitarity condition of the CKM matrix yields the following relations:

V V ∗ =0 (j = k). (1.23) ij ik 6 Among these, the relation

∗ ∗ ∗ VudVub + VcdVcb + VtdVtb = 0 (1.24) 22 CHAPTER 1. B PHYSICS AND CP VIOLATION

b t d b d

± ± B0 B0 B0 t t B0

d t b d b

Figure 1.10: B0 B¯0 mixing. − deserves special attention, since the phases between Vub,Vcd and Vtd are large and can be detected in beauty decays. The condition can be presented as a triangle. 2 2 Below, the sides are rescaled by V V ∗ and ρ¯ = 1 λ ρ, η¯ = 1 λ η. cd cb − 2 − 2 (¯ρ, η¯) η α Vtd λ Vcb

γ β 00.20.40.60.81.0 ρ

The lengths of the two sides are

1 V 1 V R ρ¯2 +¯η2 = ub and R (1 ρ¯)2 +¯η2 = td (1.25) u ≡ λ V t ≡ − λ V cb cb p p and the three angles are V V ∗ V V ∗ V V ∗ α = arg td tb ,β= arg cd cb ,γ= arg ud ub . (1.26) −V V ∗ − V V ∗ − V V ∗ ud ub td tb cd cb The angles are physical quantities and can be measured independently by CP asymmetries in B decays. If CP were conserved, the quark mixing matrix would be real and the triangle collapse to a line.

1.5 Mixing of neutral mesons

Neutral mesons mix via an intermediate state. The description for B0 and B¯0 mesons 0 0 given here can be generalised to other neutral mesons like Bs, K and D and their antistates. Any arbitrary state is a superposition of the ﬂavour eigenstates, which 1.5. MIXING OF NEUTRAL MESONS 23

obeys the time-dependent Schr¨odinger equation d a a i a i = H = M Γ . (1.27) dt b b − 2 b The eigenvectors are the mass eigenstates B = p B q B¯0 , | H i | 0i− (1.28)

B = p B + q B¯0 ; p2 + q2 =1. | Li | 0i | | | |

Solving this for the CP eigenstates g ives 0 1 B (0) = ( BH + BL ) , 2p | i | i (1.29) B¯0(0) = 1 ( B B ) . 2q H L | i−| i

The time evolution of the ma ss eigenstates is given by (1.27)

1 −iMH t − ΓH t BH (t) =e e 2 BH , | i −iM t − 1 Γ t | i (1.30) B (t) =e L e 2 L B , | L i | Li i where Mi 2 Γi are the eigenvalues. The width diﬀerence between the physical states is negligible− compared with the mass diﬀerence: ∆Γ | B | < 10−2. (1.31) ∆mB

From this relation it follows that one can set ΓH =ΓL(= ΓB), while the masses diﬀer 1 1 with a magnitude ∆mB,sothatMH = mB + 2 ∆mB and ML = mB 2 ∆mB .With this notation, −

0 1 −im t − 1 Γ t − i ∆m t i ∆m t B (t) = e B e 2 B e 2 B B +e2 B B 2p | H i | Li 1 (1.32) −imB t − ΓB t 1 0 q 1 0 =e e 2 cosh ∆mB t B + i sin ∆miBt B¯ . 2 p 2 h i The time evolution of B¯0 is determined in a similar way. Studying CP violation, the ratio q/p is of interest. It depends on the oﬀ diagonal elements, M12 and Γ12: q M ∗ i Γ∗ = 12 − 2 12 . (1.33) p M i Γ B 12 − 2 12 Using (1.31) it follows that Γ M and the ratio can be approximated as | 12|≪| 12| q M ∗ 1 Γ 12 1 Im 12 . p ≃−M − 2 M B | 12| 12 To order 10−2 the rate of B0 B¯0 mixing is just a phase, i.e − q 1. (1.34) p ≃

24 CHAPTER 1. B PHYSICS AND CP VIOLATION

∗ The vertices in Fig. 1.10 are proportional to Vtb and Vtd. Therefore q/p can be expressed in terms of the CKM parameters. In the B0 system

q M ∗ (V ∗V )2 V ∗V 12 = tb td = tb td =e−2iβ , (1.35) p ≃− M V ∗V 2 V V ∗ B | 12| | tb td| tb td where β is one of the angles in the famous unitary triangle. In the approximation of quark–hadron duality, the box diagram contributions of Fig. 1.10 are responsible for the nondiagonal element M12 of the mass matrix. The contributions of the light charm and up quarks can be neglected. At high loop momentum, k Λ , which is the case in the B and B systems, the box diagram ≫ QCD s is a good approximation to the Standard Model contribution to M12. The matrix element is roughly proportional to the masses of the two internal quark lines, so that contributions from box diagrams with up or charm quarks are negligible. In lighter systems (K or D), the hadronic uncertainties are large due to contributions from light intermediate states (long-distance contributions). In the Standard Model

G2 ∆m = F η m m2 (B f 2 )S (x ) V V ∗ 2, (1.36) B 6π2 B B W B B 0 t | tb tq| where GF is the Fermi constant, ηB is a QCD correction factor calculated to NLO, fB is the B-decay constant, BB parametrizes the value of the hadronic matrix element, S0(xt) is the electroweak contribution of the top quark and xt is the ratio of the top mass and the W mass, mW .Theq in Vtq stands for the light-quark content in the mixing B (d or s). The world average of the mixing frequency is [18]

∆m =0.480 0.016ps−1 (1.37) B ± ∗ From a measurement of ∆mBd the side VtbVtd of the unitary triangle can be determined. The largest uncertainty comes|from t|he matrix element of the four- quark operator between the meson states, fB√BB. The uncertainty is smaller in the ratio between Bd and Bs mixing:

B f 2 2 ∆mBd mBd Bd Bd Vtd = 2 . (1.38) ∆mB mB BB f Vts s s s Bs

In the Standard Model, Γ12 is related to box diagram s with internal u and c quarks. The width diﬀerence of B0 and B¯0 is proportional to (V V ∗ )2 (Aλ3)2 and cb cd ∼ may be too small to be detected. The width diﬀerence of Bs and B¯s is proportional to (V V ∗ )2 (Aλ2)2, which might be large enough. cb cs ∼ 1.6 Experimental observation of CP violation

Apart from a recent measurement of sin 2β by CDF [17], the only unambiguous measurement of CP violation is in K decays. As explained above, the eﬀect of CP violation is expected to be larger in the B system. The methods of extracting 1.6. EXPERIMENTAL OBSERVATION OF CP VIOLATION 25 the value of the CP-violating parameter in the electroweak model from decays of B mesons will be discussed in the remaining part of this chapter. Three manifestations of CP violation in pseudoscalar mesons can be distinguished: direct CP violation, indirect CP violation and the interference between the two. Direct CP-violation results from interference of decay amplitudes in the weak decays. The CP operation is a charge conjugation combined with parity transformation. For pseudoscalar mesons, this means

CP P (p~) =eiϕP P¯( p~) . (1.39) | i | − i P and P¯ are CP-conjugated states. The phase is unmeasurable and arbitrary. Consider the decays of CP-conjugated pseudoscalar meson states (e.g. B+ and B− or the neutral B mesons) to CP-conjugated ﬁnal states f and f¯. The CP conjugated amplitudes are A = f P = A eiδk eiφk , h |H| i k Xk A¯ = f¯ P¯ =ei(ϕP −ϕf ) A eiδk e−iφk . (1.40) |H| k k X The sum runs over all possible decay diagrams. δi appear in scatterings due to strong interactions. φi are the weak phases that violate CP. The physically meaningful quantity is the absolute value of the ratio between the amplitudes: A¯ =1 Direct CP violation. (1.41) A 6 ⇒

To avoid mixing, it is b est t o observe direct CP violation in the decays of charged mesons. The measurable CP asymmetry is deﬁned as 2 Γ(P + f) Γ(P − f¯) 1 A/¯ A a = → − → = − . (1.42) f + − ¯ 2 Γ(P f)+Γ(P f) 1+ A/¯ A → → If there is only one partial decay amplitude, the pha se is unmeasurable. Inter- ference between at least two diagrams is required. The candidates are found among those nonleptonic decays which receive contributions of the same order from ‘tree’ and ‘penguin’ diagrams, or decays with contributions from penguin diagrams only. The ± ± 0 ∗ −3 contribution of the tree diagram of the decay B K ρ is small, VubVus 10 , which is the same order as the penguin diagram. →Examples of tree-f|orbidden|∼decays are shown in Fig. 1.11. The hadronic uncertainties in direct CP violation are large because of poorly known hadronic matrix elements and strong phase shifts. Direct CP violation has not yet been measured experimentally. Indirect CP violation arises in the mixing of neutral mesons. Because of mixing, P 0 and P¯0 form the mass eigenstates 0 0 ¯0 P1 = p P q P , | i | i− | i (1.43) P 0 = p P 0 + q P¯0 ; p2 + q2 =1. | 2 i | i | i | | | | 26 CHAPTER 1. B PHYSICS AND CP VIOLATION

γ b s, d φ, K 0 q s- b s, d B- s - q * - ρ - - B K , K - -u u

Figure 1.11: Penguin diagrams for some tree-forbidden B decays.

If p = q =1/√2then

CP P 0 = P 0 ,CPP 0 = P 0 , (1.44) | 1 i | 1 i | 2 i −| 2 i which is equal to the CP eigenstates. The physically meaningful probe is

q =1 Indirect CP violation. (1.45) p 6 ⇒

Indirect CP violation ca n b e searched for in semileptonic decays. Decays which are only allowed in the presence of mixing are studied:

Γ(P¯0 ℓ+νX¯ ) Γ(P 0 ℓ−νX) 1 q/p 4 aSL = → − → = −| | (1.46) Γ(P¯0 ℓ+νX¯ )+Γ(P 0 ℓ−νX) 1+ q/p 4 → → | | The value of q/p is to the ﬁrst approximation only a phase (as explained in Section 1.5). The asymmetry (1.46) is of the order 10−3. Flavour eigenstates diﬀerent from the CP eigenstates have been detected in the neutral K mesons [19]. The measured asymmetry was

Γ(K e+ν π−) Γ(K e−ν π+) aK = L → e − L → e =(3.27 0.12) 10−3. (1.47) SL Γ(K e+ν π−)+Γ(K e−ν π+) ± × L → e L → e The measurement in the decay of the KL meson is usually presented in terms of the parameter Re ǫ¯ aK /2, such that K ≃ q 1 2Re ǫ¯ , (1.48) p − ≃− K K

so that q/p K =0.99673 0.00012. It is diﬃcult to relate the asymmetry in terms of fundamen| tal| CKM paramet± ers because the calculation of q/p involves poorly known hadronic matrix elements. | | There exists yet another method to detect CP violation. CP violation in the interference between direct decays and decays via mixing gives access to the phases of the quantities A/¯ A and q/p. In the decay of neutral mesons into CP eigenstates,

A = f P 0 , A¯ = f P¯0 , (1.49) CP |H| CP|H|

1.6. EXPERIMENTAL OBSERVATION OF CP VIOLATION 27 the product q A¯ λ = (1.50) p · A is physically meaningful. This is because all phase convention dependence of q/p cancels against A/¯ A:

λ =1 CP violation. (1.51) 6 ⇒ In this case, interference between partial decays is not necessary and hadronic uncertainties can therefore be minimized. For many B decays it is true that A/¯ A = e2iφ as well as q/p =e−2iβ to ﬁrst approximation. This gives

λ =1, but Im λ = sin(2β 2φ). (1.52) | | − − The actual measurement in an experiment is the time-dependent asymmetry between the number of B0 and B¯0 mesons decaying to the same CP eigenstate:

0 0 Γ(B (tˆ) fCP ) Γ(B¯ (tˆ) fCP ) af (tˆ)= → − → . (1.53) CP Γ(B0(tˆ) f )+Γ(B¯0(tˆ) f ) → CP → CP The asymmetry is only visible after allowing some time for mixing. At an arbitrary time, tˆ, the ﬂavour composition is given by Eq. (1.32). The amplitude of the decay of this B to the ﬁnal state fCP is

0 −im tˆ − 1 Γ tˆ 1 q 1 f B (tˆ) =e B e 2 B A cos ∆m tˆ + iA¯ sin ∆m tˆ CP 2 B p 2 B (1.54) |H| ˆ 1 ˆ −imB t − 2 ΓB t 1 ˆ 1 ˆ = Ae e h cos 2 ∆mBt + iλ sin 2∆mBt i The width is ˆ 1+|λ|2 1−|λ|2 Γ(B0(tˆ) f )= A 2e−ΓB t + cos(∆m tˆ) Imλ sin(∆m tˆ) . → CP | | 2 2 B − B h (1i.55)

In a similar way, the corresponding width for B¯0(tˆ)is

ˆ 1+|λ|2 1−|λ|2 Γ(B¯0(tˆ) f )= A 2e−ΓB t cos(∆m tˆ)+Imλ sin(∆m tˆ) . → CP | | 2 − 2 B B h (1i.56)

Using the last two equations, the measurable asymmetry in (1.53) is calculated as (1 λ 2)cos(∆m tˆ) 2Imλ sin(∆m tˆ) a −| | B − B . (1.57) fCP ≃ 1+ λ 2 | | In the approximation λ =1, | | ∆m a = Imλ sin x t, x = B , (1.58) fCP − d d Γ where ∆mB is the mass diﬀerence between the mass eigenstates of the B mesons, Γ is the inverse lifetime and t is measured in units of the lifetime. 28 CHAPTER 1. B PHYSICS AND CP VIOLATION

± ± bc d d

± 0 J/ψ ± 0 B B KS ± s c ± d s b q c ψ ± KS J/ d ± c a) b)

Figure 1.12: The golden decay. a) The tree diagram and b) the penguin diagrams. The quark in the loop can be either t, c or u.

The Golden Decay

0 0 The decay B J/ψKS oﬀers a very clean measurement of CP violation for four main reasons: →

1. CP violation is expected to be large in B0 B¯0 mixing. − 2. The ﬁnal state is a CP eigenstate.

3. The contamination from penguin diagrams is small.

4. It has a clear signature to pick out from a high combinatorial background.

The last point is explained in Chapter 2. Because of these favourable conditions, the channel is labelled the gold-plated mode for measuring sin 2β. The decay diagrams are depicted in Fig. 1.12. The amplitude of the tree diagram ¯ ∗ 2 4 is proportional to Atree = VcbVcs = Aλ + O(λ ). There are three types of penguin contributions, each with a t-, c-orau-quark in the loop. All penguin diagrams are suppressed due to this loop. The amplitude of ∗ ¯ 4 the t-quark diagram is proportional to VtbVts = Atree + O(λ ). With a c-quark the ¯ − ∗ 4 amplitude is proportional to Atree and with a u-quark to VubVus = O(λ ). Hence all penguin diagrams contribute with the same weak phase as the tree diagram, up to corrections of order λ4 10−3. The hadronic uncertainties are only of that order. ∼0 0 ¯ 0 The CP eigenstate KS is formed from K K mixing. This mixing factor adds to − ∗ the value of λ 0 . The participating amplitudes, Vcs and V have no CP-violating J/ψKS cd phases in the Wolfenstein parametrization up to order λ4 and do not contribute to the imaginary part of λ 0 . The ratio of the decay amplitudes in Fig. 1.12, J/ψKS

¯ ∗ Atree VcbVcs = ∗ , Atree VcbVcs 1.6. EXPERIMENTAL OBSERVATION OF CP VIOLATION 29

b s φ t s- - 0 B s

K S - d

Figure 1.13: Penguin diagram for the decay B¯0 φK0 . → S is also real, giving φ = 0; and using (1.52) and (1.35),

ImλJ/ψK0 = sin(2β 2φ)= sin(2β). (1.59) S − − − Detection of an asymmetry in the golden decay gives a direct measurement of sin 2β of the unitary triangle with hadronic uncertainties of order 10−3.

Other measurements of the angle β Some other B decays which can be used to measure the angles of the CKM unitary 0 0 triangle are B ππ, B DD¯, B φKS and Bs ρKS. →¯0 0→ → → The decay B φKS involves a ﬂavour-changing neutral current in the quark transition b sss¯ .→Since ﬂavour-changing neutral currents are forbidden at tree level in the Standard→ Model, this decay proceeds through the penguin transitions shown in Fig. 1.13. The diagrams with a t and a c quark in the loop contribute with the same phase up to order λ4, whereas the u contribution is of order λ4. Relative to the leading penguin diagram, the penguin with a u quark in the loop contributes with ∗ ∗ the order VubVus / VtbVts 0.03. The deca| y amplitude| | r|≃atio ¯ ∗ Apenguin VtbVts = ∗ Apenguin VtbVts is real and consequently

ImλφK0 = sin(2β 2φ)= sin 2β. (1.60) S − − − The decay B¯0 D∗−D∗+ shown in Fig. 1.14 has a tree diagram contribution of order λ3, which is →the same as for the penguin diagram. The penguin diagram contribution is loop suppressed by an order of 2%. On the other hand, the hadronic matrix elements of penguin operators are usually enhanced, leading to a total suppression of (4–10)%. The hadronic uncertainties are reduced to this order. The problem with a final state composed of two vector mesons is that its different helicity states will have different CP parities and hence different signs of the CP asymmetry. Experiments on other decays to vector mesons show that the longitudinal polarization dominates and the same could be true for this decay. Another B decay with a final state composed of vector mesons, which can be used to measure sin 2β is B¯ J/ψρ0. → 30 CHAPTER 1. B PHYSICS AND CP VIOLATION

d D*- d - b c D*- q - b c c - 0 B c - 0 + B D* - d D*+ - d

Figure 1.14: Tree and penguin diagrams for the decay B¯0 D∗+D∗−. →

d - π d - b u π - q - u b u - B0 - + u B0 π - d π + - d

Figure 1.15: Tree and penguin diagrams for the decay B¯0 π+π−. →

Measurements of the angle α The decay B¯0 π+π− proceeds through the quark decay b uud¯ , as shown in Fig. 1.15. The→tree and penguin diagrams are both of order →λ3, but the penguin diagram is suppressed by the order of 10%. The admixture of penguin contributions leads to λ = 1. These hadronic uncertainties of the order of 10% can be reduced by using iso|spin|6 analysis. To good approximation ¯ ∗ A VubVud −2iγ ∗ =e A ≃ VubVud and Imλ = sin(2β +2γ) = sin(2α). (1.61) ππ −

Measurements of the angle γ Of the three angles of the unitary triangle, the γ angle is the most diﬃcult to measure, because there are no decays with high branching ratios and small penguin contributions, which give direct access to this angle. In a hadronic B factory the angle can be measured in the decay of the Bs meson. In the Bs system the oscillations are fast. The time-dependent asymmetry can only be measured if the mixing parameter xs is not too large compared with the z-resolution of the experiment. 4 In the mixing of Bs mesons q/p is real up to order λ :

∗ q VtbVts = ∗ 1 . (1.62) p VtbV ≃ Bs ts 1.6. EXPERIMENTAL OBSERVATION OF CP VIOLATION 31

- - b u s s ρ - 0 - B K0 Bs s S -u d -s b q u d ρ 0 K0 s- S -u

Figure 1.16: Tree and penguin diagrams for the decay B¯ ρ0K0 . s → S u- b u - 0 - 0 - D B b c D B c- u- u- s K- K- s u-

Figure 1.17: Diagrams for the decays B− K−D0 and B− K−D¯ 0. These diagrams interfere in the case in which the →D0 and D¯ 0 mesons →decay to the same ﬁnal state.

¯ 0 0 The decay Bs ρ KS shown in Fig. 1.16 has a tree contribution of the order of ∗ 3 → VubVud = O(λ ). The hadronic uncertainties are of the order of 10% for the same |reasons|as explained for the B¯0 π+π− decay. Thus → ∗ ∗ ∗ VtbVts VudVub VcsVcd −2iγ λρK0 = = e (1.63) S V V ∗ V V ∗ V V ∗ tb ts ud ub cs cd and ImλρK0 = sin(2γ). (1.64) S − ± ∓ Other examples of decays which measure the γ angle directly are the Bs Ds K decays. → The γ angle can also be measured in direct CP violation using some less straight- forward approaches. A method with small hadronic uncertainties is presented in Ref. [21]. The idea is to measure the asymmetry Γ(B− K−f) Γ(B+ K+f¯) adirect = → − → , (1.65) Γ(B− K−f)+Γ(B+ K+f¯) → → where f is the ﬁnal state of a D or D¯ decay. Thus the two interfering amplitudes needed for accessing the CP asymmetry are the two quark transitions b cus¯ and b cus¯ . The two diagrams are shown in Fig. 1.17. The B− K−D¯→0 decay is co→lour suppressed. To make up for this, the ﬁnal state is chosen→such that D¯ 0 f is Cabbibo allowed whereas the D0 f decay is doubly Cabbibo suppressed.→For the modes f = K+π− and f = Kππ→the two interfering amplitudes are of the same order. Another clean approach is to measure the four B πK decays. This can give an upper limit on sin2 γ [20]. → 32 CHAPTER 1. B PHYSICS AND CP VIOLATION

1.7 CP violation beyond the Standard Model

All CP violation arises from a single phase, which makes the Standard Model picture very predictive. From the single measurement in the K system, all other CP-violating observables can be predicted. Most probably, however, the Standard Model does not describe the whole picture of CP violation. There are several reasons to believe that there is CP violation beyond the Standard Model. First of all because almost any extension of the Standard Model includes additional sources of CP-violating eﬀects. Such models are denoted as new physics. Models like those including FCNC (Flavour Changing Neutral Currents) and supersymmetry introduce a host of new CP violating phases, which are all small. In most models, CP is an approximate symmetry, whereas in the Standard Model, CP is almost maximally violated (as found from the asymmetry measured in the K system). Another strong argument for CP violation beyond the Standard Model comes from cosmology. In the initial state of the expanding universe, baryons and antibaryons were created with a number density comparable to that of photons. As the universe cooled, baryon pair creation could no longer compensate for the annihilation to photons. If CP had been conserved, the annihilation of baryons and antibaryons would have continued until the expansion rate exceeded the annihilation rate and the ﬁnal ratio would have been [22]

n b 10−18 . (1.66) n ∼ γ CP

From the present distribution of matter , the baryon-to-photon ratio in the universe is estimated to be n b =(4 7) 10−10 . (1.67) n − × γ Observed

−8 This corresponds to a baryon–an tibaryon asymmetry of 10 in the early universe. A baryon asymmetry requires baryon-number violation, CP violation and a deviation from thermal equilibrium [23]. The baryon asymmetry could be generated by the decay of a super-heavy particle (for example an X or Y boson or a majorana neutrino) at the GUT scale (1015 GeV). In this case it is very unlikely that the responsible CP- violating processes have any consequences in high-energy physics experiments. The baryon asymmetry could also have been created in the electroweak phase transition. Baryon-number violation in the Standard Model of electroweak interactions is rapid at high temperatures but stops after the phase transition, when the electroweak symmetry is broken into electromagnetism. This happens at a scale of 100 GeV, which is accessible in laboratories. This picture can only explain the observed baryon asymmetry if the Standard Model is extended to account for a phase transition of enough strength and enough CP asymmetries. The Standard Model prediction of the CP asymmetry is many ( 10) orders too small to explain the imbalance between matter and antimatter [24∼]. The so-called ‘strong CP problem’ urges also for extensions to the Standard Model. QCD allows a source of CP violation, but extreme ﬁne-tuning is needed 1.7. CP VIOLATION BEYOND THE STANDARD MODEL 33

- - b c s s ψ - - J/ B φ Bs s -c s -s b q c s φ J/ ψ s- -c

Figure 1.18: Tree and penguin diagrams for the decay B¯ J/ψφ. s → in order that its contribution to the electric dipole moment of the neutron does not exceed the experimental bound. Some mechanism beyond the Standard Model is welcome to explain this situation. The electroweak contribution to the electric dipole moment is strongly suppressed and therefore any detected electric dipole moment of the neutron would be due to strong CP violation. The measurement of the electric dipole moment of the neutron is thus a very interesting probe for CP violation. In summary, CP violation is one of the least tested aspects of the Standard Model and one of the most promising directions in the search for new physics. If the new physics is not too high above the Standard Model scale (i.e. much lower than the GUT scale), deviations from the predictions are expected to be observed in the B system accessible at HERA-B. In the rest of this chapter, various ways to detect non-Standard Model CP violation in HERA-B are investigated. The primary goal in the search for new physics is to look for inconsistencies. Independent measurements of an angle can give different results and the unitarity conditions of the CKM matrix can appear to be broken. An important observation is that the unitary triangle is a natural condition in models with three lepton families. Unless a fourth family is introduced the unitarity of the CKM matrix is still valid. From this assumption it is possible to find information that can tell about the nature of the new physics contribution. Does it for example appear in mixing (∆B = 2) or in decay (∆B = 1) or in both mixing and decay? Are the new sources of CP violation flavour diagonal or due to flavour changing neutral currents, or both? Such information is valuable in order to rule out models and select directions in the construction of theories of new physics.

The Bs system The detection of deviations from the Standard Model prediction requires precision measurements. Attention is drawn to the asymmetry detected in the interference between direct decay and decay via mixing because of the small hadronic uncertainties. A clean method is to search for asymmetries in decay channels where a small CP violation is predicted by the Standard Model. In particular, CP asymmetries in all Bs decays that do not involve direct b u transitions are all the same and approximately zero. → Such a mode is B J/ψφ depicted in Fig. 1.18. It is predicted to have the s → relatively large branching fraction of 0.3% [27]. Combined with the Bs production 34 CHAPTER 1. B PHYSICS AND CP VIOLATION suppression, this decay will occur at roughly the same rate in HERA-B as the golden decay. Also the trigger and reconstruction conditions are similar. The CKM amplitudes contributing to this decay are all real up to order λ4:

∗ q VtbVts = ∗ 1 , (1.68) p VtbV ≃ Bs ts ∗ Atree VcbVcs = ∗ 1 . (1.69) A¯tree VcbV ≃ Bs cs The amplitudes of the penguin diagrams are also real to O(λ4). In addition they are loop suppressed. Therefore, this mode is as clean from hadronic uncertainties as the golden decay. Any CP asymmetry detected in this decay will be a sign of new physics, with practically no Standard Model background.

Measurements involving the golden decay

0 0 New physics can also be found in the golden decay B J/ψKS, which is dominated by the tree contribution. This amplitude is very unlik→ ely to be modified by new physics, since the scale of the latter is expected to be large compared to MW .Onthe other hand, the mixing amplitude can easily be modified. The strong suppression of the Standard Model box diagrams in B B¯ mixing by the fourth order of the weak coupling and small CKM angles allows fo−r large contributions from new physics. This would shift the asymmetries in B decays universally (φ φ + θd). In particular for the golden decay: → Imλ 0 =sin2(β + θd) . (1.70) J/ψKS It is only possible to disentangle the new physics contribution from the Standard Model contribution if the unitarity of the triangle β angle can be constrained by independent measurements on the sides and on other angles (for example sin 2(α + θd)). The β angle in the unitary triangle can be measured in numerous decays. The 0 0 measurement in the golden decay B J/ψKS is extremely clean and in the decay 0 → B φKS it can be measured with a precision of 3%, due to the effect of light qua→rks in the penguin loop. The Standard Model thu±s predicts that the asymmetries measured in those two decays should be equal:

aB→J/ψK0 = aB→φK0 3% . (1.71) S S ± A violation of this equality would be a sign of new physics. New physics in B B¯ 0 − mixing introduces a shift of the same size for the two decays. The B φKS involves a ﬂavour changing neutral current. The leading SM contributions are →penguin diagrams with a suppression by αs and a loop factor. Here extensions to the SM are possible which could lead to larger CP asymmetries [20]:

Imλ 0 =sin2(β + θd + θA) (1.72) φKS 1.7. CP VIOLATION BEYOND THE STANDARD MODEL 35

so that aB→J/ψK0 = aB→φK0 . (1.73) S 6 S Relatively small eﬀects, of order 10% can lead to an observation of such an inequality. Another interesting example is the decay KL πνν¯ of the long-lived K-meson, which also measures the β angle [28]. This decay m→easures the relative phase between K0 K¯0 mixing and the quark transition s dνν¯. In the presence of new physics, there− is no reason for a relation between the→asymmetry in this decay and decays of B mesons.

Semileptonic decays 0 0 New physics contributions to the B B¯ and Bs B¯s mixing matrices could also lead to an observable CP asymmetry −in semileptonic− B decays. This is measured in the decay of a BB¯ pair into equal-signed leptons:

Γ(BB¯ ℓ+ℓ+X) Γ(BB¯ ℓ−ℓ−X) Γ Γ a = → − → =Im 12 = 12 sin φ (1.74) SL Γ(BB¯ ℓ+ℓ+X)+Γ(BB¯ ℓ−ℓ−X) M M 12 12 12 → → −3 In the Standard Model this asymmetry is very small (O(10 )) beca use of the small difference in the decay rates and the small phase difference φ12 between Γ12 and M12. New contributions to B B¯ mixing would change the phase φ but not the relation − 12 Γ12 M12 , since the new physics are only expected to contribute at higher order |[25].|≪| | + 0 The final hadronization states can be any combinations of B , B , Bs,Λb and their conjugates. However, if the flavour content can be determined and neutral mesons selected, the asymmetry is larger at the cost of statistics. Chapter 2

The HERA-B experiment

The HERA-B experiment is a forward spectrometer at the HERA electron-proton collider. The proton beam is directed on a fixed nucleus target whereas the electron beam is passing untouched through the detector. The experiment is primarily designed to detect CP violation in the asymmetry between the fraction of B0 and B¯0 0 decaying to J/ψKS,wheretheJ/ψ decays to a lepton pair. The rate of this signal is suppressed by a factor of 10−11 per inelastic event. Owing to the smallness of the asymmetry and the total reconstruction efficiency of about 10%, the order of 10 000 such golden events are needed for a CP-violation measurement. The proton bunch-crossing rate at HERA is 10 MHz, which is equal to about 1014 bunch crossings per year. Clearly more than one event per bunch crossing is needed for a CP measurement in one or two years. The solution is to put target wires around the beam core in a manner described in fig 2.1. With this configuration four or five Poisson-distributed interactions per bunch crossing can be extracted from the off-momentum protons that are in the halo. This procedure allows HERA-B to operate without interrupting the other experiments around HERA. The final state of the golden decay is a CP eigenstate, which means that it does

Figure 2.1: Schematic view of the halo target, consisting of eight metal ribbons on independently movable forks. The ribbons are about 50 µm wide and 500 µm thick. They are separated along the beam by about 5 cm. 2.1. REQUIREMENTS 37

not determine the flavour of the B meson. The b-quarks can only be produced in pairs (fig 1.1). The B meson under study is therefore always produced together with a B hadron of opposite flavour. This hadron does not normally decay to a CP eigenstate. The most common decay is to the lighter D meson with the subsequent decay to a K meson. Usually those decays are reconstructed and serve as a tag. Exclusive reconstruction has a high quality but poor efficiency. Other possibilities are to determine the charge of the kaon or the lepton accompanying the D meson. Another option is to geometrically reconstruct the decay vertex of the tagging B and count the charges of secondary tracks. Finally the charge of soft pions accompanying the B meson can serve as a tag. Soft pions come from either the decay of an excited B∗∗ meson or from the local charge conservation in the quark fragmentation process. The combination of all these methods will bring the tagging power to the calculation of the precision of the CP measurement. Since the b-quark quantum number is not conserved in weak interactions, the B0 and B¯0 mix to the physical mass eigenstates, which are compounds of B0 and B¯0.If there were no CP violation these compounds would be equal to the CP eigenstates. Because of the mass difference between the mass eigenstates, the asymmetry oscillates with time. The decay time of the B meson has to be measured as the flight distance in the detector. This is the distance between the main vertex at a target wire and a displaced secondary decay vertex. The experimental programme also includes measurements of CP violation in other decay modes like B π+π−, studies on B0 B¯0, B0 B¯0 and D0 D¯ 0 mixing, and → − s − s − properties of the Λb hadron. The matrix element Vcb can be determined from the ∗ semileptonic decay B D ℓνℓ. Rare decays are im→portant to test the Standard Model predictions. The predicted branching ratio of B Kℓ+ℓ− is 5 10−7 and for the decay to a vector meson it is slightly larger: → · BR(B K∗e+e−) 4 10−6 → ≃ · and BR(B K∗µ+µ−) 2 10−6. → ≃ · Because of the small branching ratios of these decays, the trigger must be very selective. Since there are no requirements on the other B in the event, decays with such small branching ratios and two final-state leptons can be detected. Measurements of total and differential cross sections over the entire phase space will be important for testing and developing QCD models. So far, there is only a limited amount of data available on B and Υ production at HERA-B kinematics. Also hadronic decays of B hadrons will be of interest. Charm physics is also included in the experimental programme.

2.1 Requirements

The goal to reconstruct the rare B decays in the environment of a very high track density demands a careful choice on trigger and detector design. In particular a fast readout is required because of the high bunch-crossing rate. 38 CHAPTER 2. THE HERA-B EXPERIMENT

The hardware has to be radiation hard. It will be exposed to 3 107/R2 particles per second, which corresponds to for example 100 krad/yr at a dis·tance R =10cm from the beam. Further downstream the ﬂux is even higher due to secondary interactions in the detector material. For cost reasons and to pay regard to the other experiments around HERA (H1, ZEUS and Hermes), the components have to operate for one year at full rate before they can be replaced. The requirements on precise measurements in the full kinematic region and the proﬁle of the signal put the special requirements on the HERA-B detector:

Large geometrical acceptance. • A ﬁne-granularity tracker with good momentum resolution to observe a narrow • peak of a B meson which is reconstructed from four ﬁnal-state particles.

Reconstruction of multiple secondary vertices at 1 cm from the beam, which • is the mean decay length of the B. At this positio∼n the annual radiation dose is 10 Mrad.

Efficient muon and electron identification. This is particularly important for • the reconstruction of the J/ψ from the golden decay. A J/ψ candidate is selected already at the first triggering stage.

Efficient kaon identification. This concerns in one way the reconstruction of • 0 + − KS π π from the decay of the neutral B in the golden channel, but more pron→ounced the identification and separation of charged kaons of the tagging B in the same event, from the copious production of pions and protons.

2.2 Vertex Detector

The precise reconstruction of multiple displaced vertices relies on the Vertex Detector System (VDS) consisting of seven superlayers of silicon strip detectors, positioned close to the target and starting at 1 cm radius from the beam. The information from the VDS will be used already at the second level trigger. The target wires and the vertex-detector superlayers are placed in a vacuum tank, named the Vertex Vessel in Fig. 2.2. Each superlayer of VDS consists of four quadrants as shown in Fig. 2.3. The quadrants are contained in pot assemblies that can be displaced individually in the radial and lateral directions. Each sector is built up by two double-sided detectors. The principle of the silicon strip detectors is illustrated in Fig. 2.4. The strip pitch is 25 µm and every second strip is read out. Both sides are read out, giving two views per detector module. Each vertex-detector superlayer thus provides four views, 2.5◦, 87.5◦ and 92.5◦,and stand-alone pattern recognition can be performed over most±of the angular range. The resolution of a secondary vertex is about 500 µminthez-direction (along the beam) and 25 µminthexy-projection. The VDS must also determine the impact parameter of tagging particles. The impact-parameter resolution is 25 µm 30 µm/p . ⊕ T 2.2. VERTEX DETECTOR 39

↓↓ ↓↓ ↓ ↓↓

p e+

Vertex Vessel

↑ Magnet TRD ↑ ECAL x RICH Muon System

02468101214161820z[m]

Figure 2.2: The design of the ﬁnalized HERA-B detector as simulated in GEANT [61]. Planes used in the ﬁrst level trigger are indicated by arrows. 40 CHAPTER 2. THE HERA-B EXPERIMENT

Figure 2.3: The geometrical layout and positioning of the silicon vertex-detector superlayers. (The position of the silicon detector belonging to the tracking system is also indicated at z = 206 cm.) The polar angle coverage is 10–250 mrad. There are two double-sided detector modules per quadrant in four stereo angles. 2.3. TRACKING SYSTEM 41

+Vbias

Aluminium

SiO2 22X n+ implantation p-compensation Guard Ring Structure n-type silicon 280 µ m

p+ implantation 25 µ m

Figure 2.4: The principle of a silicon strip detector. Two bias rings surround the active detector region. The protective guard ring structure provides a controlled drop of bias voltage. Every second strip is read out both on the p- and the n-side.

2.3 Tracking system

The HERA-B detector (fig 2.2) is a large-acceptance forward spectrometer covering 10 mrad up to 160 mrad. This corresponds to 90% of the coverage in the centre-of- mass system. For momentum measurements, the tracks are bent horizontally in an inhomogeneous magnetic field. The field integral is 2.2 Tm. The field is produced by a dipole magnet, centered at about 4.5 m from the target. In the bending plane the lateral acceptance reaches out to 250 mrad. The granularity of the tracking system varies with the distance from the beam in order to limit the occupancy and minimize the number of channels. The tracking system is divided in three different technologies depending on the distance from the beam: 1 6 cm. Silicon strip of the same technology as the vertex detector. The spatial • − resolution is 12 µm. The B vertex resolution is σxy =25µm,σz = 500 µm. 6 25 cm. Inner Tracker (IT). Micro-Strip Gaseous Chambers (MSGC) with • Ga−s Electron Multiplier (GEM). The resolution is 80 µm. ∼ > 20 cm. Outer Tracker (OT). Drift tubes in a honeycomb structure. The • spatial resolution is 150–200 µm. ∼ A silicon strip superlayer is placed in front of the magnet, where the track density is very high. This superlayer is referred to as the 8:th and last VDS superlayer. The inner and outer tracker chambers in the magnet will be used for finding the curvature of tracks. The chambers in the field free region between the magnet and 42 CHAPTER 2. THE HERA-B EXPERIMENT

Figure 2.5: The geometry of the MSGC. Two layers are shown forming one superlayer with two stereo angles.

RICH are mainly used for pattern recognition of straight tracks. There are also inner and outer tracker chambers in front of the calorimeter, to extrapolate tracks to clusters in the calorimeter and to the muon system. About half of all tracks in a HERA-B event will be reconstructed in the IT. Four L-shaped MSGC modules with dimension 30 30 cm2 constitute one IT layer around the beam, as shown in Fig. 2.5. Every superl×ayer consists of two or more layers with different strip orientations. The three stereo angles are 0◦ and 5◦. The trigger planes have double layers of each orientation to guarantee full efficiency± . One MSGC is built as a glass box with electrodes on a glass substrate, a 6 mm long drift region and a glass cover coated with a drift cathode. The glass substrate is coated with diamond to prevent accumulation of charges between anode and cathode electrodes. The field becomes stronger near the anodes (as can be seen in Fig. 2.6), causing an avalanche with a gain of 150. The total gain is 3000, separated in two steps to avoid sparks at the anode. For this purpose there is a GEM with a gain of 20 in the middle of the drift region (Fig. 2.6). It is a perforated polyimide foil coated with copper. The coordinate is measured by detecting the centre of gravity of a strip cluster. For radial distances from the beam axis larger than about 20 cm the particle densities are small enough that straw tubes of 5 and 10 mm diameter can be used. The Outer Tracker layers are grouped in thirteen superlayers of which seven belong to 2.3. TRACKING SYSTEM 43

Drift Cathod

3mm

U1 GEM U2

3mm

Anode Cathode

300 µ m 300 µ m

Figure 2.6: The principle of a GEM-MSGC. The particles enter from the glass substrate and exit by the drift cathode.

the magnet tracking (MC01–MC06, MC08) and four to the pattern tracking (PC01– PC04). PC01 and PC04 are also included in the first level trigger. The two large trigger chambers (TC01 and TC02) are also useful for extrapolation to the calorimeter and the muon system after the RICH. Inside all superlayers except MC02, MC04 and MC08, there is an IT superlayer. Each superlayer contains one or two sets of the three stereo angles, 0◦ and 5◦. The pattern-recognition chambers and the trigger chambers have two sets. M±C01 has a sequence 0◦, 5◦,+5◦,0◦ to link track segments found in the vertex detector. MC05 consists only−of a single 0◦ layer because of space restrictions inside the magnet yoke. A single layer is assembled from four folded pocalon foils. The pocalon is coated with gold and copper to increase the conductivity. TC1, TC2 and half of PC1 and PC2 consist of double layers as in Fig. 2.8. The diameter of the honeycomb cells is 5 mm for the innermost sections (shaded in Fig. 2.7) to limit the occupancy and 10 mm for the rest. This size provides a sufficient cell granularity for the first level trigger, which uses only wire hit information. At higher trigger levels and offline reconstruction, the wire information is supplemented by drift-time information. The drift time measures the radial distance of the impact point from the hit wire. The momentum resolution of the tracking is very good. For muons from the golden decay, a Gaussian fit gives [68] ∆p/p =(8.1 0.3) 10−3, which leads to a mass resolution of about 8–10 MeV for B0 J/ψK0±. · → S Inside and directly behind the magnet there are also three additional pad chambers. They are used for a high-pT hadron extension of the trigger. Its primary purpose is the search for B0 π+π− decays. → 44 CHAPTER 2. THE HERA-B EXPERIMENT

Figure 2.7: The geometrical structure of TC2. The sections in the shaded area have 5 mm cells; the rest have 10 mm cells. The proton and electron beam pipes are indicated. An IT superlayer ﬁts in the central hole.

Figure 2.8: The principle of the Honeycomb Drift Chambers: a double layer of the type which are in the trigger chambers. The particles enter from the left.

5/10 mm 25-30 µ m 2.4. PARTICLE IDENTIFICATION DETECTORS 45

γ + K

C 4 F10 Figure 2.9: Schematic picture of the RICH and the principle of particle detection and iden- tiﬁcation.

Photo- Detector

2.4 Particle identiﬁcation detectors

In order to identify charged leptons and kaons, four different detector systems are needed: Ring Imaging Cerˇ enkov Counter (RICH). • Transition Radiation Detector (TRD). • Electromagnetic Calorimeter (ECAL). • Muon detectors with absorbers (muon system). • Behind the magnet and the main part of the tracking system, there is a large Cˇerenkov counter (RICH). The task of the RICH is to separate charged kaons with momenta between a few GeV and about 50 GeV from pions and protons. The main part of the RICH is a big tank of C4F10 gas. When charged particles traverse the tank, they emit Cˇerenkov light, which is reflected against the two mirrors and detected (see Fig. 2.9). The opening angle of the light cone translates to the radius of a reconstructed ring of photon impact points. From the opening angle, the velocity of the particle is determined, which together with momentum information from the tracking system is used for particle identification. The angular resolution that can be obtained by combining a single photon hit with the charged-particle track information −3 is σθ =0.65 10 . The probability of wrong particle identification is below 2%. From the position·of the ring, the slope of the trajectory can be determined. The lepton identification is carried out by the electromagnetic calorimeter, the TRD and the muon system, supplemented by track information. 46 CHAPTER 2. THE HERA-B EXPERIMENT

25 cells/ 4 cells/ 1 cell/ 468 cm module module module 42 modules

624 cm 56 modules

Figure 2.10: The geometry of the ECAL. Inner, middle and outer regions are separated by bold lines. There are holes for the proton and electron beam pipes. The depth of the middle and outer calorimeter is 33 cm (20 radiation lengths). The depth of the inner calorimeter is 13.6 cm (22 radiation lengths).

Readout PMT Scintillator plates

WLS fibres

Figure 2.11: Schematic view of a Shashlik module of the inner calorimeter.

Tungsten plates 2.4. PARTICLE IDENTIFICATION DETECTORS 47

The ECAL is placed 13 m downstream of the target. It is divided in inner, middle and outer sections,∼ with segmentations adjusted to ensure at most 10% occupancy. The overall geometry is illustrated in Fig. 2.10. The modules are sampling plastic scintillator/absorber sandwiches read out by plastic wavelength shifter (WLS) fibres. The fibres run perpendicular to the plates through holes in the module in the ‘Shashlik’ manner (see Fig. 2.11). In the middle and outer calorimeter the absorber is lead. The sizes of the inner, middle and outer modules are 2, 6 and 11 cm, respectively. The impact point of a particle on the ECAL is determined by the centre of gravity of the shower, and the resolutions are 1, 4 and 10 mm respectively, for the inner middle and outer modules, which is sufficient to match the clusters with tracks from the main tracker. A signal in the ECAL is used in the pretrigger. The acceptance of electrons from the golden decay is 68%. The main loss is due to the hole in the centre. In this region there is also no track information. In addition to electron identification, the ECAL is also supposed to measure the energy of photons for bremsstrahlung corrections. The energy resolution of the middle and outer parts is ∆E 9.5% =1% . (2.1) E ⊕ √E At the inner positions where the track density is very high, tungsten-alloy absorbers are used. The resolution of the inner modules is ∆E 17% =1.6% (2.2) E ⊕ √E

The purpose of the TRD is to separate electrons and positrons from hadrons. The TRD modules are placed between the two tracker superlayers in front of the calorimeter in the central region, where the track density is very high and the hadron rejection power of the calorimeter is lower. A charged particle which passes the boundary between two media of different dielectric constants emits transition radiation, due to a change in the phase velocity. The rate has a strong dependence on the Lorentz factor of the particle, γ = E/mc2, which is the basis for the particle separation. Lighter particles emit more transition radiation. The TRD consists of fibre radiator (polypropylene) and straw detector cells. A particle hits on average 36 layers of straws interspaced with 15 mm fibre radiator. The straw diameter is 5 mm. Hadron rejection of a factor of 15 at 98% electron identification efficiency is planned for. Fast and high-precision tracking makes the TRD useful in the trigger. It could possibly be used already at the pretrigger level. The penetrating muons are separated from hadrons using a hadron absorber. Three iron/concrete absorber blocks are alternated with muon chambers to link the muon hits with the tracks in the rest of the tracking system. In the matching, multiple scattering in the absorber has to be taken into account. The HERA-B detector system ends with a sole fourth muon superlayer, to provide clean measurements of track directions after the filter. 48 CHAPTER 2. THE HERA-B EXPERIMENT

12mm 14mm ooo oo Gas inlet Gas outlet 4 cm o o o o o

27 cm, 16 cells

Figure 2.12: Schematic drawing of the pad chamber construction.

Gas pixel chambers are used in the muon system in the high-occupancy region close to the beam pipe (15–33 cm in the y-direction). A pixel cell has a sensitive wire in the centre and four potential wires in the corners. The cells are 9 9mm2 in the first three superlayers and slightly larger in the last superlayer. This×provides an adequate spatial resolution for muons from the main vertex with high momenta and relatively small multiple scattering. The size of a chamber in the outer region is determined by the drift time. It should be small enough to provide a signal within the time between two bunch crossings. The first two superlayers consist each of three double layers of tube chambers with stereo angles 0◦ and 20◦. Tube chambers are wire chambers made from 2 mm aluminium profile. Pad ch±ambers are used in the last two superlayers. They are assembled using aluminium profiles with open cells as shown in Fig. 2.12. Cathodes in the form of copper pad plates are inserted as one of the cell walls. The x-coordinate is defined by the position of the wire and the y-coordinate by the position of the hit pad.

2.5 Trigger

Although the bb¯ cross section has not been measured for HERA-B kinematics, the order of magnitude is expected to be 10 nb while the inelastic cross section is expected to be 13 mb, σ(pN b¯b + X) → 10−6. (2.3) σinelastic ∼ At least one neutral B is formed in as much as 80 % of the cases. The branching ratios of the interesting B decay modes are very small,

BR(B0 J/ψK0 ) BR(J/ψ ℓ+ℓ−) BR(K0 π+π−)=4 10−5. (2.4) → S · → · S → · The signal of a golden event is accordingly suppressed by a factor of 10−11.Ata bunch-crossing rate of 10 MHz, the rate of interesting signals is much less than 1 Hz. 2.5. TRIGGER 49

The mean number of interactions per crossing is about four, leading to 120–200 tracks per event in the detector. These conditions require the trigger to be extremely fast and selective. In total the rate has to be reduced from 10 MHz to less than 100 Hz. The realization is based on a four-level trigger system. Concentration is put here on the J/ψ trigger. This trigger is the one that is most relevant for the golden decay.

0. A pretrigger will select high-ET clusters in ECAL or muons by a pattern after the muon absorber (or hadrons by very high pT tracks in the high-pT chambers). Electron candidates require also coincidences with TC02, in order to suppress photon background. A Region of Interest (RoI) is deﬁned and passed on to the succeeding trigger levels. The processing time of the pretrigger is only about 1 µs. The pretrigger does not reduce the event rate.

1. FLT. In the first level the rate is reduced from 10 MHz to 50 kHz. The maximal time for a decision is 12 µs. The data flow to filter is 150 Gbyte/s. In the tracking processors (TFU), lepton-pair track candidates are followed up to the magnet using ideas from Kalman filtering A. The planes used in the first level trigger for the fast track reconstruction are indicated in Fig. 2.2. Each TFU projects the track to a RoI in the next detector plane and the last TFU in the chain extrapolates the RoI to an imaginary plane in the centre of the magnet at zm = 450 cm. The Track Parameter Units (TPU) reconstruct the kinematics in the main vertex. The input to the TPU is a RoI in TC02 and a RoI at zm.Thex- coordinate at zm is calculated at the centre of the RoI given by the RoI at TC02 and at zm. The strategy is illustrated in Fig. 2.13. The magnetic field is treated as a plane at zm. The momentum of the track is found using a map of the magnetic field. The map contains a number of x-coordinates at z0 and at zm and the momenta of tracks with those coordinates. The momentum of a track with the coordinates (x0,xm) is found by interpolation between the points on the map. In this way, the length of the field the particle has passed is combined with the strength and included in the field map. From the momentum information the pT can be calculated. The Track Decision Unit (TDU) combines tracks into pairs and calculates their invariant masses. In order to reduce the latency, internal calculations are based on look-up ta-

bles. The mass resolution for muons using look-up tables is σmJ/ψ =0.163 0.004 GeV [65]. ± For electrons, the track momentum is compared with the calorimeter energy. A substantial number suﬀer energy losses due to bremsstrahlung. The photons from bremsstrahlung that occur in front of the magnet can be found in the ECAL and the energy and momentum of the electron can be corrected to some extent. 50 CHAPTER 2. THE HERA-B EXPERIMENT

2. SLT. In the second level, the rate is reduced further to 500 Hz. The average latency is about 7 ms. The input rate is 1.8 Gbyte/s. An FLT track refit improves the track parameters about 10 times and computes a χ2. A Kalman filtering technique is used for tracking in all planes of the pattern and trigger chambers. In addition drift-time information is used. The track is first propagated through the x-view and then through the stereo planes with the x-parameter fixed. Tracks are then propagated through the magnet using hits in the tracking devices in front of the magnet (the first Inner Tracker or Outer Tracker superlayer or the last Vertex Detector System (VDS) superlayer) as constraints. The re- fined RoI is followed through the VDS using a Kalman filter in two projections. At second level, multiple-scattering corrections are applied as a momentum- independent constant only dependent on the number of planes the track has passed (including also the wall of the vertex vessel). The vertex quality for two-track triggers is checked. If possible, a cut on the vertex separation will be applied already at this stage. This is the main cut to reduce the immense background from the direct production of J/ψ and other sources of high-pT leptons.

3. TLT. The processing time of the third level is 100 ms.

The third level trigger mainly reduces the rate of the high-pT lepton trigger. In the case that the second level has found a secondary vertex, the event is passed directly to the L4 trigger. In the case that the second level has not found a secondary vertex, the TLT will search for two tracks with high impact parameters and then reconstruct one or two secondary vertices including those tracks. Tracks and vertices are reconstructed using space point reconstruction in the VDS. At the third level, the tracking and vertexing is done with correct treatment of multiple scattering. Particle identiﬁcation can be done at this level. The third and second level trigger algorithms are part of the same executable code running on the same PC farm.

4. L4. In the fourth level trigger, the events are identified and classified. The output of the full event reconstruction is stored on tape for detailed offline analysis like B-flavour tagging and calculation of physical properties. Owing to high track densities and occupancies in the detector, the event reconstruction needs seconds of computing time per event on present high-speed computers. The fourth level farm minimizes the time delays between data taking and physics analysis. The reduction factor is about 2 or 2.5.

An overview of the trigger levels is presented in Table 2.1. 2.5. TRIGGER 51

x TC02 (z00 ,x ) x m-max (z ,x ) mm θ x x m-min z x TC-max Magnet x TC-min

Figure 2.13: Simpliﬁed illustration of the TPU procedure with RoI windows from the TFU.

Table 2.1: Overview of the trigger scheme of HERA-B. Trigger level Pretrigger FLT SLTTLT L4 Input Rate 10 MHz 10 MHz 50 kHz 500 Hz 50 Hz Reduction factor 1/1 1/200 1/100 1/10 1/2.5 Time scale 1 µs12µs 7 ms 100 ms 2–4 s 52 CHAPTER 2. THE HERA-B EXPERIMENT

2.6 Oﬄine Software

Monte Carlo event generation All hardware and software development is dependent on Monte Carlo simulations of a completed detector and its response to an event. The final reconstruction and analysis program will use the filtered data stored on tape to extract the physics parameters. To develop such a program a simulation of the events including a complete detector and complete data processing is desired. The comparison of real data with a fully simulated event is necessary for the understanding of the results. The simulation must include every relevant detail of the chain. The simulation of normal inelastic interactions is done with FRITIOF [57], which handles proton–nucleus collisions and simulates nuclear effects like energy loss and multiple scattering of partons crossing the target nucleus. It generates soft gluon radiation and hard Rutherford parton scattering. In HERA-B there is the possibility to generate samples with minimum-bias or general high-pT inelastic events using FRITIOF with the help of an importance sampling technique [60]. This tool is convenient for the generation of Monte Carlo samples for trigger studies. Heavy-flavour production is not treated by FRITIOF. To date, there is no generator which simulates heavy-flavour production in proton–nucleus collisions. The simulation of this type of interactions is based on PYTHIA [56], which is restricted to the collision of nucleons. The interaction is chosen to be 920 GeV protons on a stationary nucleon, which is either a proton or a neutron with probabilities defined by the target material. The energy used for the production of B or D hadrons and particles strongly correlated with them is subtracted from the beam energy before it is given, in a second iteration, to FRITIOF to simulate the underlying event due to nuclear interactions. The procedure is not quite trivial, if it is to be handled strictly correctly. For example one should not let FRITIOF simulate any reaction with the layer of nucleons, which has already been simulated by PYTHIA. The nucleus to simulate with FRITIOF should be of the target type, but distorted and with a gap after which the projectile proton has changed to, for example, a pion of another direction and energy. The processing of the event in PYTHIA and FRITIOF can in principle not be carried out in sequence. The proton to send to PYTHIA should be one which has suffered multiple scattering and energy loss. It could also have changed its colour or even flavour composition. Moreover, the product particles from PYTHIA should be sent to FRITIOF as well, for simulation of interactions on their way out of the nucleus. None of these effects are simulated, but they are expected to be relatively small. In the first step, PYTHIA is called. Products from PYTHIA which are not correlated with the heavy quarks or the heavy hadrons are removed from the listing to ensure energy conservation. To discover how to select particles from PYTHIA, it is useful to investigate the colour flows. In Fig. 2.14, the two most important processes for open b¯b production are shown. In gluon–gluon scattering (Fig. 2.14a), the two heavy quarks form colour singlets 2.6. OFFLINE SOFTWARE 53

B*0 d d d g ∆∗, ... p u n, p u u u u g b d b g g b d d d d n b d n u u

a) b)

Figure 2.14: Typical colour configuration for open b¯b production. The process is displayed in the CMS frame. The proton enters from the left and the nucleon (a neutron in the examples) from the right. a) Gluon–gluon fusion, gg b¯b. In the example, the invariant masses of the strings are high. b) Quark–antiquark→ annihilation, qq b¯b. In this example, the invariant masses of the strings are small. → with parts of the spectator partons. These colour singlets are treated as strings or as clusters in the fragmentation, depending on their invariant masses. A third colour string is formed by the remnant quark–diquark pair from the two spectators. This string resembles the soft underlying event of the proton–nucleus interaction. In qq¯ annihilation (Fig. 2.14b), a sea quark pair is created by a quark–gluon splitting inside one of the nucleons. The antiquark is annihilated with one of the quarks of the other nucleon to produce the heavy-quark pair. One colour singlet is formed with one of the spectator systems and one of the heavy quarks; another is formed with part of the other spectator system and the other heavy quark. The remnant of the second spectator system forms a colour singlet itself and normally converts directly into a nucleon or a nucleon resonance. In this case there is no third string created between the spectator systems. Colour strings can be locally excited by gluon emission. In rare cases further quark–gluon splittings lead to additional strings and clusters. 70% of all b¯b pairs are created by gluon fusion, which is recognized by the third string. 80% of the cc¯ pairs are created by gluon fusion. In 2–4% of all heavy-flavour production, there are more than three parton-level colour singlets (strings or clusters). The masses of the heavy-quark singlets depend on the energy transferred to the heavy-quark system and on the scattering angle in the parton-parton centre of mass system. When the heavy quark and the corresponding nucleon remnant move in the same direction, the string is short and the invariant mass small. Long strings, appearing when the heavy quark and the corresponding nucleon remnant move in opposite directions, have large invariant masses. As shown in Fig. 2.15, the invariant masses tend to be small. When the invariant mass is small, the singlet is treated as 54 CHAPTER 2. THE HERA-B EXPERIMENT a cluster in the fragmentation. In extreme cases, the clusters can convert directly into heavy-meson resonances, which then take over almost the total available energy. This happens mostly when there is no associated string created as in Fig. 2.14b. Clusters and all their decay products are kept. If both heavy-quark singlets form clusters, the only energy left for FRITIOF is the energy of the associated singlet. As seen in Fig. 2.15, the invariant mass of the associated singlet is often very small, at the level of a few GeV. The FRITIOF generator is not suited to treat such small CMS energies. In these cases, the underlying event from the associated singlets (consisting of a few soft particles) has to be either taken from the PYTHIA event or neglected completely. In the case that the heavy (anti)quark is created in a colour string, the string is boosted to its rest frame. All first-generation fragments which move into the heavy- quark hemisphere are kept with all their decay products. All other fragments are discarded. The remaining particles are boosted back into the lab frame. A little illustration is found in Fig. 2.16. The multiplicity of first-generation fragments is displayed in Fig. 2.17. When only clusters and half-strings are kept, there are mostly only the hadrons containing the heavy quarks left; but in as much as one third of the events, a second cluster, not containing a heavy quark, is kept. Those particles are correlated in their quantum numbers to the flavour content of the leading heavy hadron. To keep them is very important for same-side flavour tagging. Since the ad hoc combination of FRITIOF and PYTHIA can never be fully consistent, a variety of options with different strengths and shortcomings are available [60]. The different simulation techniques can later be compared with data. If a realistic description of the hard-scattering fragments is desired, all fragments from PYTHIA can be kept (full strings). The multiplicity in Fig. 2.17 will then be higher, but there is no energy left for FRITIOF, so the total multiplicity will be an underestimate. The multiplicity obtained using the method of independent fragmentation is also shown in the same figure. When independent fragmentation of the heavy quark is applied, there are fewer events in which the colour singlet has very low invariant mass, leading to a slightly higher multiplicity. In the second step, the FRITIOF generator is called in the fixed-target mode with the original target nucleus and a proton beam with reduced energy. The lab frame is the fixed-target frame used in the PYTHIA event generation. The initial situation, before PYTHIA is called, is (in the lab frame)

EB + MAl P = 0 ,  P E  B ≃ B   where EB is the beam energy (920 GeV) and MAl the mass of the target nucleus. The four momenta of the particles produced in the PYTHIA step are added up, leading to a total lost energy EQ, a total lost longitudinal momentum PQz,anda 2.6. OFFLINE SOFTWARE 55

Figure 2.15: Invariant-mass distribution of parton-level colour singlets for the hard interaction of 920 GeV protons with nucleons, randomly selected from the Al target nuclei, as predicted by PYTHIA with all subprocesses but open heavy-ﬂavour production via two-to-two parton scattering switched oﬀ. Dots represent strings or clusters containing a heavy (anti)quark. Stars represent the additional strings, not containing heavy (anti)quarks. The upper plot presents the distributions for charm production and the lower plot for beauty production. (From Ref. [60].) 56 CHAPTER 2. THE HERA-B EXPERIMENT

Figure 2.16: A string in its rest frame. The fragments which move in the hemisphere of the light (di)quark are discarded. u

total lost transverse momentum PQT . In the lab frame, after the PYTHIA step,

E + M E B Al − Q P = PQT .  E− P  B − Qz   In the ﬁxed-target frame used in the FRITIOF event generation,

M P˜ = 0 .   E˜   The energy E˜ which should be given to FRITIOF can then be calculated. If MQ is the invariant mass of the systems of all particles kept in the ﬁrst step, then

E M 2 E˜ = E E B (E P )+ Q . (2.5) B − Q − M Q − Qz 2M The fixed-target frame used in the FRITIOF event generation does not exactly co- incide with the lab system (because of PQT ). Therefore, energy and momentum conservation requires some final adjustments by appropriate boosts and rotations of the FRITIOF fragments. The decays of the hadrons have also to be treated carefully if special decay channels are desired (like for example B0 J/ψK0 ). The difficult situation appears in → S the decay of neutral mesons, like K0 and B0 and their antiparticles, since they mix 0 0 to their mass eigenstates. The procedure is described here for B J/ψKS, but works equally well for other neutral mesons or any situation when onl→y one of several equal particles decays according to a selected channel. PYTHIA simulates the mixing and decay of the neutral mesons. Care has to be taken to have one meson decaying golden and the other according to the particle decay table in Ref. [58]. To ensure this, the neutral B meson which decays golden 0 0 (B J/ψKS) is picked out. The rest of the particles in the event, including the other→B hadron, are then sent to decay according to their default decay tables. After that, the decay table for neutral B mesons is changed to B0 J/ψK0 .TheB → S 2.6. OFFLINE SOFTWARE 57

Figure 2.17: Multiplicity of daughter clusters formed in the first generation from parton-level colour singlets (colour strings or clusters) containing a heavy quark or antiquark. Upper figure: charm production. Lower figure: beauty production. Three different algorithms for the selection of daughter clusters from those generated by PYTHIA for hard interactions of 920 GeV protons with Al nucleons are displayed. 58 CHAPTER 2. THE HERA-B EXPERIMENT meson is then forced to decay to this channel. Before the decay of the succeeding event it is important to reinstall the default decay table of the neutral B mesons. 0 Long-lived particles, like KS, decay during the simulation of interactions in the detector (GEANT simulation), outside PYTHIA and FRITIOF. Therefore the selec- 0 tion of events, where the KS decays to charged pions, has to be done after or during the GEANT simulation. Apart from open heavy-flavour production, b¯b and cc¯ pairs can also be produced in bound resonances such as bottonium and charmonium. The parton-fragmentation models and the NRQCD factorization approach (Chapter 1, Section 1.3) to predict the production of quarkonia are relatively recent (1995). The quarkonium simulation in PYTHIA is based on the colour-singlet model, where it is assumed that the J/ψ can only be created if the cc¯ pair is produced in a colour-singlet state with the same quantum numbers as the bound quarkonium state. In Fig. 1.7a, the processes implemented in the simulation are depicted. High- pT processes of the types in Fig. 1.7a are included in the Monte Carlo simulation. Divergences at pT 0 in a), when the final state is χ0 or χ2, are cancelled by low-pT diagrams of type b→) and higher order corrections of type c). PYTHIA is intended for application at hadron colliders with high transverse momenta and therefore, low-pT diagrams of types b) and c) are not implemented in the Monte Carlo simulation. The Monte Carlo simulations include instead a cut pˆT > 1 GeV for divergent processes. The production of J/ψ, χ0c, χ1c and χ2c is included by default in PYTHIA. For Υ production, the method PYTHIA provides for direct J/ψ production has been applied. It is adapted to Υ production with a simple heavy-quark substitution. The J/ψ value of the wave function at the origin has been kept. The relative cross sections of the quarkonium states must be controlled by the user. The HERA-B Monte Carlo simulation [60] offers a reweighting procedure to adjust the pT spectra of the quarkonia produced by PYTHIA to the experimentally determined inclusive spectra. The pT spectrum of J/ψ production is adjusted to data from the E789 experiment [45]. The Υ pT spectrum is adjusted to data from the E605 experiment [47]. The distribution of the Feynman scaling variable xF has also been compared with experimental data and found to agree rather well without weighting.

Detector simulation The simulation of the HERA-B detector is handled by a program called HBGEAN [62]. It also creates geometry structures for use in GEANT and provides the digitization routines. The detector as it is implemented in the GEANT simulation is displayed in Fig. 2.2. The target (Figs. 2.1 and 4.7) consists of two sets of four aluminium ribbons at a distance of 2 mm ( 5σ) from the beam and separated by 4 cm along the direction of the beam. The ∼ribbons are 50 µm thick and 500 µmlo∼nginthez-direction. The vertex vessel, containing the target and the vertex detectors, is implemented including a hole for the beam. The beam pipe is an aluminium tube with 500 µm thick walls. Detailed information on the geometry of vertex and tracker planes is 2.6. OFFLINE SOFTWARE 59

x = 0 , y = 0

B/ T 0.8

0.6 By

0.4

0.2 Bx X 10

Bz X 10 -0.2 -200 -100 0 100 200 300 z - z magnet /cm

Figure 2.18: The magnetic field components as a function of z in the centre of the magnet. The z-coordinate is given relative to zmagnet = 450 cm. necessary for track reconstruction. The Monte Carlo simulation of the Vertex VDS, the Outer Tracker Honeycomb Drift Chambers (OT) and the Inner Tracker with a Microstrip Gaseous Chamber technique (IT) is consistent with the geometry specified in Sections 2.2 and 2.3. The simulation of the inhomogeneous magnetic field is based on real measurements [63]. The size of the Bx, By and Bz components as a function of z is shown in Fig. 2.18 for the centre of the magnet (x =0,y= 0). The centre of the field is at z = 450 cm, which is 451–456 cm away from the target stations. In the xz-plane, the dipole magnet has the shape of a circle with a radius of 1.4 m. In GEANT, the particles are traced through the magnetic field using Runge–Kutta methods of the fourth order and a fixed step size.

The high-pT trigger chambers, RICH, TRD, ECAL and muon system are also 60 CHAPTER 2. THE HERA-B EXPERIMENT described in detail. In the digitization, the response from a particle on each traversed cell of various detector parts is simulated. The digitization includes a Gaussian smearing of the Monte Carlo impact points, a double hit resolution and an eﬃciency for a hit to be recorded. For OT the hit eﬃciency is set to 98% and for the MSGC IT it is set to 95%.

Trigger simulation Events including the golden decay have to be selected in an interaction rate of 10 MHz and the final state tracks found among 200 background tracks. The trigger for this task is the J/ψ trigger described in Set∼ion 2.5. The HERA-B first level trigger simulation L1simu, is not compatible with all modules and can only be utilized under certain circumstances. L1simu simulates all the first level trigger electronics, however it does not use look-up tables, which leads to an overestimate of the mass resolution [65]. The following cuts are applied at pretrigger and first level trigger: The momentum is required to be larger than 5 GeV, the transverse momentum larger than 0.5 GeV and the invariant mass larger than 2.75 GeV. For clusters in ECAL in the region close to the beam pipe there is a position-dependent threshold condition:

1 1 E>Ktrig + , (2.6) · R x2 + y3 ! | | p where Ktrig = 750 GeV cm and the distances are measured in cm. The ﬁrst term is proportional to the radia· l distance R to the beam pipe and corresponds roughly to the transverse momentum of the electron. The second term accounts for the bending of particles in the magnetic ﬁeld. Closest to the beam the threshold is about 90 GeV and for distances larger than 200 cm the lower cut of 5 GeV applies. The central tower of the cluster is required to contain at least half of the threshold energy. The program L2simu [66] simulates the second level trigger according to the scheme in Section 2.5. The same algorithms which are developed for the simulation can be used on the second level trigger processing PC farm. The third level trigger algorithms can also be processed on Monte Carlo data.

Reconstruction Reconstruction software which has been utilized for studies presented in this thesis is described here. This software will also run in online mode on the fourth level trigger. The clusterization in ECAL and cluster analysis is performed by the ‘CARE’ software package [67]. In CARE, hit cells with a signal above a cell-dependent threshold are sorted in decreasing order of energy. In this way, the clusterization starts with the central cells. Neighbouring cells are added to the clusters and overlapping clusters are structured to complexes. The complex clusters originate from split-oﬀs from electromagnetic showers or from interacting heavy hadrons. The coordinate of the 2.6. OFFLINE SOFTWARE 61 cluster, presented to other modules in the reconstruction chain, is the conversion point of the particle originating the shower. This point is found from the centre of gravity of the cluster and a correction due to the fact that the released energy is decreasing exponentially with the distance from the shower axis. One of the main tasks for ECAL is pion/electron discrimination. With a full HERA-B detector this is done by comparing the momentum measured in the tracking system with the energy measured in ECAL. Some pion/electron discrimination can also be carried out using information from ECAL alone. This is done in CARE by deﬁning a quantity that describes the shape of the cluster:

#cells β α i=1 ri Ei RPID = , #cells α P i=1 Ei where Ei is the energy released in the cellP i and ri the distance from the centre of the cell to the corrected centre of gravity of the cluster. α and β are parameters which have been optimized in CARE. The lateral size of an electromagnetic shower is limited with a logarithmic dependence on the energy: ln(E/E ) maximum number of radiation lengths = c , ln2

+ − where Ec is the critical energy, at which bremsstrahlung and e e conversion cease to occur. Because of this roughly fixed lateral spreading, the distribution of the RPID quantity will be relatively narrow for electrons. About half of all hadrons also produce a shower in the ECAL. Hadron showers have a more varying and in general larger shower shape. Asking for 90% electron efficiency reduces the hadron rate to about 53–54% in the inner and outer ECAL sections and 35% in the middle ECAL [4]. The particle trajectories are reconstructed using a Kalman filtering technique described in Appendix A. The ranger program [68] provides pattern recognition and track reconstruction in the main tracker (IT and OT). It uses a seed of three hits. The navigation is not trivial in the complicated multiplanar geometry of the tracker planes. Ranger solves this problem by defining a domain at each z-position as all the planes of the combined IT and OT superlayers. The domain is divided into search windows with modules of similar granularity and length belonging to the same window. Since the OT uses drift-time measurements, the resolution is better than the size of the cells and the occupancies of cells reach as much as 20%. This is another challenge for the pattern recognition. For every seed there are normally several candidates. A method called Concurrent Track Evolution solves this problem. Following this strategy, several candidates are tracked in parallel. A track candidate is discarded when the number of faults exceeds a certain value. A fault is for example a missing hit in a plane or a wrong hit. Energy loss in the detector material is accounted for as well as trajectory deflection due to multiple scattering in the Coulomb field of the nuclei. Multiple scattering corrections are applied using a momentum estimate which is given by the track deflection relative to the direction to the target. Ionisation losses are assumed to 62 CHAPTER 2. THE HERA-B EXPERIMENT be negligible. Electrons lose energy via electromagnetic radiation. Bremsstrahlung corrections are applied for losses inside the magnet. The tracks are described by five track parameters taken at a reference z-position z0. The parameters are the impact parameters x0 and y0,theslopestx =tanθx and ty =tanθy and the charge over momentum Q/p. The pattern recognition is done in three phases:

1. The four superlayers between the magnet and the RICH are called the pattern tracker. Here, standalone pattern recognition is performed on straight tracks. In the ﬁrst phase, tracks are found using only the hit information of the 0◦ layers to determine the track parameters x0 and tx.

2. In the second phase, the corresponding vertical track is found using the hit information from all stereo layers. The hits of the vertical track are then combined with those of the xz projection and a three-dimensional track candidate is ﬁtted.

3. The three-dimensional track segments found in the pattern tracker are propagated through the magnet to determine the charge and momentum of the particles. In the magnet propagation Kalman ﬁltering requires also the transport of the covariance matrices. To save time, the ﬁrst successful track candidate is accepted.

The track is then continued upstream through the vertex detector and downstream to the two superlayers behind the RICH and further to the lepton identification devices, ECAL and muon system. This propagation updates the track after the considerable multiple scattering through the RICH. The propagation is particularly important for the particle identification in the RICH, which needs a high precision on the slope estimates. It does not improve the track parameters in the vertex region. The pattern-recognition efficiency in the pattern tracker is 97% for leptons from 0 the golden decay and 93% for pions from the KS. The total pattern-recognition efficiency for the golden decay is (83.9 3.9)% when the J/ψ decays to µ+µ− and (83.0 2.1)% when the J/ψ decays to ±e+e− [68]. ± A full pattern recognition needs matching with VDS pattern recognition. The latter will most probably also be based on Kalman filtering techniques. Until a powerful VDS pattern recognition is available, Monte Carlo events are reconstructed with ideal pattern recognition, which means that hits are assigned to tracks using Monte Carlo information. For vertex reconstruction in the VDS, outside the magnetic field, a vertex package [70] based on a Kalman-filter technique (Appendix A) is available. The vertex package reconstructs vertices outside the magnetic field with or without mass constraints and from an arbitrary number of outgoing tracks. It performs vertex pattern recognition and reconstructs main vertices on target wires. The V0fit program [71] performs vertex reconstruction which requires propagation of track parameters inside the magnetic field, using numerical methods (Runge–Kutta of the fourth order and a variable step size). 2.7. COMPARISON WITH OTHER B-PHYSICS EXPERIMENTS 63

2.7 Comparison with other B-physics experiments

HERA-B is a pioneer experiment in large-acceptance hadron heavy-flavour factories. Earlier experiments like CDF and E789 at Fermilab, which were not optimized for B physics, see only a fraction of the kinematic distribution. CDF and D0 will upgrade and improve the forward acceptance and run with a luminosity of 2 1032cm−2s−1 [37, 38]. · B physics and CP-violation measurements will also be carried out in the next- generation experiments in the hadron environment at LHC at CERN and at the B-factories at SLAC and KEK. For such different kinematic situations, systematic errors are very different and the measurements carried out by experiments at the three types of machine will be quite independent. This situation is very favourable for a thorough check of the Standard Model to come in a few years time. A comparison of the HERA-B with experiments at e+e− machines and pp machines is therefore something very interesting and will be carried out here. Some of the different aspects are summarized in Table 2.2.

SLAC/KEK

KEKB and PEP-II are two very similar asymmetric electron–positron colliders built at KEK (High Energy Accelerator Research Organisation in Japan) and SLAC (Stan- ford Linear Accelerator Center), with the purpose of doing B physics and CP- violation measurements. The challenge for these two experiments is the machines, which need to be asymmetric to be able to measure the relative decay time of the two B mesons. They also need to provide high luminosities in order to provide the needed statistics. (The cross section for b¯b production is only of the order of 1 nb.) PEP-II uses 9 GeV electrons and 3.1 GeV positrons, and KEKB uses 8 GeV electrons and 3.5 GeV positrons. The luminosity is 3 1033 1034cm−2s−1, which is of the same order as at HERA-B. · − The BaBar experiment at SLAC [34, 35] and the BELLE experiment at KEK [36] are both provided with B0B¯0 pairs coherently produced in the decay of the Υ(4S) resonance. Because of the coherence of the initial state, the time-integrated asymmetries are zero. HERA-B can gain statistics by such time integration (see Chapter 4, Section 4.1). The e+e− environment is very clean. This leads to a number of advantages. The trigger and reconstruction efficiencies are larger and the combinatoric problems smaller. The total reconstruction efficiency for BaBar is about 50% while for HERA- B it is about 10% or less. It also means that neutral pions can be reconstructed, 0 which is the final state of about 30% of the KS. The different kinematics also gives 0 access to the J/ψKL channel. BaBar and BELLE need to go to a heavier resonance Υ(5S) in order to study heavier B-mesons like the Bs. They also naturally will not get any Λb hadrons. Same-side tagging is not possible when working at the Υ(4S) resonance, since no B∗∗ Bπ can be produced. → 64 CHAPTER 2. THE HERA-B EXPERIMENT

CERN The high luminosities in HERA-B lead to several interactions per bunch crossing and to rates comparable to the LHC (Large Hadron Collider) scenario. In LHC the bunch-crossing rate is 40 MHz. The centre-of-mass energy in the proton–proton collider will be 14 TeV enabling the production of very heavy particles. For an inelastic cross-section of 70 mb, around 23 minimum-bias events per bunch crossing are expected at the peak∼ luminosity of 1034 cm−2s−1. In an initial stage the luminosity will be 1033 cm−2s−1. Physics is then accessible using more complex signatures such as tau-lepton detection and heavy-flavour tags from secondary vertices and reconstruction of CP eigenstates. The extremely high luminosities and high energies are challenging for detector construction. The challenges are similar to those of HERA-B. An illustrative example is the comparison of radiation levels in Fig. 2.19. Meeting the problems already at the present time, HERA-B can in some sense be seen as a test-bench for future constructions. At the same time, HERA-B profits from developments already made for the LHC detectors. Some examples are the four-level trigger system and the fast electronics. The Transition Radiation Tracker in the ATLAS [31] experiment is very similar to the HERA-B TRD which was designed from experience gained in ATLAS. MSGC is of great importance in CMS [33]. Lots of experience has been gained in HERA-B on such devices. ATLAS and CMS are the two general-purpose experiments planned at LHC. There is also LHCb [32], which is dedicated to measurements of CP violation and rare decays. It does not concentrate on the golden channel. LHCb sees the forward region of the proton–proton collisions while ATLAS and CMS look at the central region. This gives LHCb a better acceptance for b¯b events and a better tagging efficiency. LHCb will operate at the lower average luminosity of 1.5 1032 cm−2s−1,tohave lower occupancies and smaller radiation damage than in the o·ther LHC experiments. About 1012 b¯b pairs per year are expected. Because of the higher energies, the selection is easier compared to HERA-B. For example there are 56 000 golden decays expected to be reconstructed per year, including the flavour tag. LHCb also has better access to the heavier B-mesons like Bs and Bc and to more decay channels. Because of the similar conditions and goals for HERA-B and LHCb, both are designed as forward spectrometers with very much in common. For example, the positioning of the vertex detector, magnetic field, pattern tracker in front of the RICH, trigger chambers and muon system are all the same. It means that not only progress in technology but also software methods like pattern recognition can be profitable for LHCb. Additional components in LHCb are the pile-up veto counter in the vertex region, the extra RICH in front of the magnet (behind a shield) and the scintillating tile hadron calorimeter. The extra RICH is there to detect low-momentum (> 1GeV) tracks that are swept out by the magnetic field. The electromagnetic calorimeter is of the Shashlik type as for HERA-B and the electron pretriggers of the two experiments are based on the same processing units. Also for vertex detector and inner and outer 2.7. COMPARISON WITH OTHER B-PHYSICS EXPERIMENTS 65

Silicon tracker MSGC OTr/ATLAS-Straws

LHC Hera-B

Figure 2.19: The radiation levels in ATLAS/CMS and HERA-B for diﬀerent detector types. The peak luminosity delivered by LHC is 1034 cm−2s−1. It is interesting to note that although the ATLAS/CMS levels are higher, the diﬀerent detectors see the same rate in both experiments, since the HERA-B detectors are closer to the interaction point. A simple 1/r2 dependence of the particle density is assumed, where r is the radial distance from the beam axis. 66 CHAPTER 2. THE HERA-B EXPERIMENT tracker, the same techniques are chosen in HERA-B and LHCb. 2.7. COMPARISON WITH OTHER B-PHYSICS EXPERIMENTS 67

Table 2.2: Comparison of future B experiments on CP-violation measurements in the golden decay, B0 J/ψK0 . The dilution is deﬁned as D =(1 2f),where → S − f is the probability of a wrong tag. ǫtag is the tagging eﬃciency. Numbers are all predictions for the central values of the b¯b cross section and are to be used merely for rough comparisons. For HERA-B a cross section of 24 nb is assumed. CDF II and D0 values are given for the Tevatron luminosity upgrade. CDF III is a proposed detector upgrade. The large number of tagged events and the low tagging dilution for the ATLAS experiment are because same side-tagging has been included in the simulation. Restricting the analysis to opposite side tagging results in a dilution of 0.51 and a sample of 17 000 tagged events. ∼ HERA-B BaBar Belle LHCb Approximate start of data-taking 2000 1999 1999 2005 Centre-of-mass energy 41.6 GeV Υ(4S) Υ(4S) 14 TeV Interactions 40 MHz 12 Hz 12 Hz 30 MHz −6 −3 σb¯b/σtot 1 10 0.28 0.28 6 10 Untagged events/year 900· 800 2300 140· 000 Tagging dilution, D 0.67 0.71 0.80 0.60 D ǫtag 0.45 0.55 0.53 0.37 Tagged· events/year 600 500 1000 56 000 ∆sin2β after one year 0.14 0.11 0.08 0.01 Impact parameter 25 µm 70 µm 60 µm 40 µm Mass resolution (J/ψK0 ,J/ψ µ+µ−) 8MeV 15 MeV 8.3MeV 7MeV S →

ATLAS CMS D0 CDF II CDF III 2005 2005 2000 2000 2000 14 TeV 14 TeV 2TeV 2TeV 2TeV 40 MHz 40 MHz 7.6 MHz 7.6 MHz 7.6 MHz 6 10−3 6 10−3 1 10−3 1 10−3 1 10−3 · · · · · 0.17 0.47 0.28 0.30 500 000 8000 1443 15 000 15 000 0.02 0.05 0.08 0.12 0.08 64 µm 20 µm 25 µm 15 µm

19 MeV 12 MeV 20 MeV 30 MeV Chapter 3

Optimization for σb¯b measurements

The estimates of the b¯b cross section at the HERA-B experiment are based on theoretical predictions and comparisons with a limited number of experimental results. The theoretical uncertainties vary by about a factor of two up or down, mainly due to the choice of the effective b-quark mass, the scale at which the strong coupling constant is evaluated and the parton distribution functions. Among the available data, the E789 [44] and E771 [46] fixed-target experiments with a beam of 800 GeV protons are most relevant for the HERA-B case. The result from E789 falls below the range of the theoretical prediction, whereas the E771 result lies in the larger range. Both experiments have large uncertainties. This situation shows that additional more precise measurements are needed to determine the rate of b¯b production. To gain experience and give feedback to the construction of the experiment, it is of interest to optimize the geometry for physics reach already before the detector is completed. In particular it is of great value to measure the b¯b cross section at an early stage due to its importance in the precision of the CP-violation measurement. Extensive studies have therefore been performed in order to optimize the detector layout in such a way that the b¯b cross section can be measured as early as possible even before the detector is completed. The aspects given here are the VDS and OT geometries and a discussion on the magnetic field on or off. An exhaustive report is found in Refs. [1] and [4]. The inclusive B J/ψX decayisusedasareference channel. Also the double semileptonic decay BB→ ℓ+ℓ−X has been studied, as well as Υ µ+µ−. → → For the Monte Carlo studies, only single interactions have been generated in order to minimize the combinatoric background and maximize the conditions for track reconstruction. With a 10 MHz bunch-crossing rate and 10 MHz interaction rate, the rate for single interactions is 4 MHz. If only nine of ten bunches are filled in HERA, the rate for single interactions is 3 MHz, but the difference in running period for the same amount of statistics is only 80 h per 106 s. 3.1. EXPERIMENTAL AND THEORETICAL PREDICTIONS. 69

3.1 Experimental and theoretical predictions.

In HERA-B the b-quark production is near the threshold, which leads to large perturbative corrections and large uncertainties in the next-to-leading order (NLO) calculations. Soft-gluon emission can occur both from the fusing partons and from the heavy- quark pair. When the heavy-quark pair is produced near threshold (√s 2mQ), the two quarks are at rest with respect to each other and emit soft gluons as→a single particle. Only a heavy-quark pair in a colour-octet state will emit soft gluons. Dif- ferent soft-gluon resummation factors are therefore applied for the singlet and octet part of the Born cross section. With soft-gluon resummation at the next-to-leading logarithmic (NLL) level and all orders of perturbation theory the predictive power is increased. The NLO+NLL b¯b cross section has been calculated for HERA-B conditions (pp at √S =39.2 GeV, corresponding to a beam energy of 820 GeV) [9]. The predicted cross section ranges from 11 nb to 45 nb as the renormalization scale goes from 2mb to mb/2 and the pole mass m goes from 5 to 4.5 GeV. For m =4.75,σ¯ =23 6 nb. This b b bb ± is calculated using a parton distribution set (MRSR2, αs(MZ )=0.119), which has been justified at Tevatron energies by experiment. Choosing another set (MRSR1, αs(MZ )=0.112), the central value is σb¯b =15 3 nb and the lowest value is 8 nb. The NLO+NLL cross section is only calculated±for a proton beam of 820 GeV but the NLO calculations from Ref.[8] suggest an increase of 36–38% when going to 920 GeV. This would put the central values at 31 (with MRSR2) and 20 nb (with MRSR1) and the lowest value explainable by theory is 11 nb. E789 and E771 are two fixed-target experiments at Fermilab which both measured the b¯b cross section in 800 GeV proton-nucleon interactions. The E789 measurement was made with p–Au interactions at 800 GeV beam energy and at xF = 0.05 and pT = 1 GeV, whereas in HERA-B the target is lighter and the phase space much larger ( x < 0.5, i.e. almost the entire range). The integrated b-quark production | F| cross section was obtained by extrapolation over all xF and pT, which is nontrivial since the pT, xF and J/ψ momentum distributions are not well known. The nuclear dependence is also not completely understood. After integration over phase space, E789 obtains a central value below the NLO+NLL calculation, σ(pN b¯b + X)= (6.4 2.2) nb/nucleon (including corrections from updated values of branc→hing ratios). ± The mentioned result does not include insights which have been achieved after the measurement was carried out. The model used by E789 to integrate the cross section is based on the NLO calculations by Nason, Dawson and Ellis [8]. Fragmentation effects have also been taken into account by applying the Peterson function [49], which softens the xF distribution. In hadronic production the fragmentation function decreases the cross section by roughly 20%. However, the nonperturbative effects have turned out to be smaller than previously thought [48], leading to a much harder fragmentation function. Another smaller uncertainty comes from a possible nuclear dependence. In all cross section estimates, as well as in comparisons of data from experiments, a linear dependence on the mass number of the target nucleus is assumed. The E789 experiment uses targets of gold and beryllium to measure the nuclear dependence of 70 CHAPTER 3. OPTIMIZATION FOR σBB¯ MEASUREMENTS

D-meson production by 800 GeV protons [51]. This has given a value 1.02 0.05 of α ± the exponent in σ(A) A at 0.0

3.2 The optimal geometry

In order to do physics at an early stage of the experiment, already during the construction, it is helpful to know which configurations optimize the acceptance. Ab- solutely necessary devices for J/ψ measurements are lepton triggers with any of the lepton identification devices, ECAL or the muon system. The muon pretrigger must be complemented by momentum information which pleads for a magnetic field, while the ECAL measurement would be more precise without bremsstrahlung effects in- duced by the magnetic field. The signal of a B is a detached vertex. This adds the additional requirement of some VDS planes. A sufficient number of OT and IT planes at strategic places would increase the physics potential. Different topics of detector 3.2. THE OPTIMAL GEOMETRY 71

optimization are discussed in this chapter. A single interaction rate of 4 MHz and a running period of 106 s are assumed. Under these conditions, there would be 4800 B J/ψX,whereJ/ψ ℓ+ℓ− and ℓ is either muons or electrons, depending on the→type of trigger. A bac→kground of 6.5 106 direct J/ψ events is to be expected. The number of inelastic events produced dur· ing the same running period is 4 1012. · Magnetic field A magnetic field is necessary for momentum determination with tracking devices. The field will also reduce the low momentum background and hence the occupancies. The ECAL determines the momenta of light particles (electrons) without a magnetic field. For the ECAL, there are some disadvantages with a magnetic field:

The dilution of the pT distribution requires harder cuts to reduce the inelastic • background. There are additional combinatorics due to the charge ambiguity. • Bremsstrahlung dilutes the signal. • The trigger arriving first is the e+e− trigger with a first level trigger decision made on clusters in ECAL alone. The preferred situation for trigger and reconstruction issues is then a scenario without any magnetic field. In the xy-plane, the VDS is divided in four sectors. Only a limited number of VDS modules are available for the early runs. In the initial stage, these must be installed in the first place in favour for alignment studies. Hence, installed sectors must be near to each other. For pattern recognition three or four adjacent superlayers are needed. The result is a design with four superlayers in an L-shape as in Fig. 3.1. 20 ECAL pretrigger boards and 50% of the ECAL readout boards are equipped to match the VDS acceptance as depicted in Fig. 3.2. This numnrt of boards is not available from the first run. The impact points in ECAL of tracks reconstructed in an L-shaped VDS geometry are shown in Fig. 3.3. This distribution is used for deciding in which order the pretrigger boards will be installed. Cells with a high population of reconstructed tracks from J/ψ events are equipped first. The feasibility to reconstruct J/ψ and B J/ψX events with this geometry is studied first and then compared with the fea→sibility when the magnetic field is switched on. ECAL and VDS superlayers are installed complete in the GEANT simulation and sensitive channels selected before the trigger simulation. This procedure makes it practical to study several different configurations. A complete RICH contributes to material and multiple scattering but is not used as a sensitive detector in this study. 2000 B J/ψX and 20 000 direct J/ψ events have been generated with this geometry an→d without any magnetic field. One vertical target wire positioned at z = 6mm and x = 2 mm is simulated. The− first level trigger is simulated according to a distribution of ECAL electronics as in Fig. 3.2 and by applying a cut on the transverse energy component ET and a cut 72 CHAPTER 3. OPTIMIZATION FOR σBB¯ MEASUREMENTS

Figure 3.1: Geometry of the vertex detector for the early detector set-up. Quadrants assumed to be deployed are shaded. Superlayers 3 to 6 are installed. In superlayers 3–5, only quadrants 3 and 4 are equipped. on the invariant mass of two triggered clusters. The calorimeter cluster reconstruction and pretrigger simulation were made with CARE [67]. The obtained efficiencies are consistent with a detailed pretrigger simulation (see the note on physics options [4]). The clusters form a RoI to the second level trigger simulation L2simu [66]. Two track candidates are created for each cluster, one of each charge. The propagation through the magnet is based directly on this RoI without using any information from tracking devices. The algorithm for second level trigger tracking in VDS, L2sili,isa two-dimensional Kalman filter with a fast multiple-scattering correction. To keep the multiplicity down, cuts are invoked after each superplane. The total efficiency of the second level trigger on the reduced silicon geometry is given in Fig. 3.7 for an ET cut at 1.0 and 1.5 GeV and for B J/ψX as well as direct J/ψ. L2sili serves here also as a pattern-recognition tool. T→racks found by the second level trigger are used in the analysis. The matching of tracks with clusters in the ECAL is taken from the RoI information. (Reconstruction of clusters need not be redone, since the reconstruction program was used for the first level trigger simulation.) A four-parameter Kalman- filtering refit [68] of the tracks from the second level algorithm improves the vertex resolution and minimizes the tails. The refit makes a multiple-scattering correction using the energy of the corresponding ECAL cluster. The invariant-mass distribution of lepton pairs from J/ψ is shown in Fig. 3.4. Track pairs with an invariant mass > 2.5 GeV are subjected to a vertex fit using methods in the vertex package [70]. The interplay between efficiency and rejection of direct J/ψ depends on the longitudinal vertex resolution. The residuals of the vertex z-coordinate have been studied with different cuts on the number of hits required on a track. The efficiency as a function of the cut on the number of hits per projection is shown in Fig. 3.5. When 3.2. THE OPTIMAL GEOMETRY 73

Figure 3.2: Geometry of the electromagnetic calorimeter for the early detector set- up. Cells equipped with readout/pretrigger electronics are shaded. The contours of the vertex detector are drawn for comparison of the geometrical acceptances. 74 CHAPTER 3. OPTIMIZATION FOR σBB¯ MEASUREMENTS

y/cm y/cm

x/cm x/cm

Figure 3.3: Impact points in ECAL of electron and positron tracks from J/ψ events. The tracks are reconstructed in the L-shaped VDS as in Fig. 3.1. The magnetic ﬁeld is switched oﬀ in the left picture and switched on in the right picture.

3 hits per view are required, tails are still visible (Fig. 3.6a), which might become ≥dangerous to a b¯b cross section measurement. Raising the cut to 4 hits per view, the tails are considerably smaller and the vertex resolution is 470≥µm, as shown in Fig. 3.6b. Note that no systematic shift is observed. The z-residual normalized to the estimated error dz/σz is shown for the same cuts on the number of coordinates (Fig. 3.6c and 3.6d). Figure 3.7 summarizes the trigger and analysis cuts and efficiencies for B J/ψ X and the background of direct J/ψ . The numbers are given for a pretrigger→cut on the transverse energy component at ET > 1.0 GeV and invariant mass > 1.8GeV. The acceptances and efficiencies are very similar for the direct J/ψ and the inclusive 0 0 J/ψ from B decays. The two-body decay B J/ψKS is also presented. The acceptance is higher for this decay. ‘Track qualit→y’ is a cut on the number of hits in each view (x and y) of a track. The variation of the track-quality cut shows that Nhits/view 4 appears to be a good choice. The second level trigger efficiency given refers to the≥looser requirement of 2 hits per view. A cut on the χ2 on the track is already included in the second leve≥l trigger efficiency. There is no efficiency given for matching of tracks to clusters, since it is made inside the second level trigger. The mass window is at 2.9GeV 6, which is motivated by the pull distribution (Fig. 3.8). The reductions of direct J/ψ (numbers within parentheses) are estimated using the same figure. The retained efficiency for B J/ψX is 0.6% after the decay-length cut, while none of the 20 000 direct J/ψ even→ts survive the cuts. This leads to an estimate of 29 8 events for the this detector geometry scenario (17 6eventsforE > 1.5 GeV), ± ± T 3.2. THE OPTIMAL GEOMETRY 75

Figure 3.4: The invariant-mass distribution of electron clusters from J/ψ from B decays. The magnetic ﬁeld is switched oﬀ. Bremsstrahlung correction is included. 76 CHAPTER 3. OPTIMIZATION FOR σBB¯ MEASUREMENTS

1.00 1 GeV, B ψ 0 0.90 J/ KS 1 GeV, J/ψ

Efficiency 0.80 ψ 0 0.70 1.5 GeV, B J/ KS 0.60 1.5 GeV, J/ψ 0.50 0.40 0.30 0.20 0.10

> 3 > 4 > 5 #hits

Figure 3.5: The efficiency of the track quality cut as a function of the number of hits required per projection on a track. The efficiencies were calculated from triggered event samples, which already included the requirement of 2 hits per projection. 0 ≥ 0 Events with electrons from direct J/ψ and from B J/ψKS are plotted. The efficiencies of the inclusive B J/ψX are indistinguis→hable from those of the direct J/ψ. → 3.2. THE OPTIMAL GEOMETRY 77

a) b)

c) d)

Figure 3.6: Vertex resolution using L2simu and a full reﬁt using the method described in Ref. [68]. For the two upper plots the distance is given in cm for a cut on the number of hits per view (x and y) at 3and 4. For the two lower plots, the ≥ ≥ distance is given in units of σz for the same cuts on the number of coordinates. 78 CHAPTER 3. OPTIMIZATION FOR σBB¯ MEASUREMENTS

Figure 3.7: Trigger and reconstruction efficiencies using L2simu and a full refit using the method described in Ref. [68]. The quality cut is a cut on the number of hits per view (x and y) at 4. Dots are B J/ψX, squares are direct J/ψ and triangles 0 0 ≥ → are B J/ψKS. All efficiencies are presented relative to the original number of events. →The cuts were applied in the order of presentation. The error bars refer to the J/ψ from B decays. The errors of the direct J/ψ are one order of magnitude smaller. 3.2. THE OPTIMAL GEOMETRY 79

basedonacrosssectionof12nb. The direct J/ψ production surpasses that from B decays by three orders of magnitude, so an absolute estimate of this background including tails in the vertex resolution requires huge Monte Carlo event samples. In order to exploit the maximum information, the sample of 20 000 direct J/ψ events is digitized using all cells of the calorimeter and all four quadrants in the VDS superlayers SI03...SI06, which gives a much higher yield but should not change the pattern-recognition effects significantly at Nhits/view 4, though the event kinematics are not quite identical. The resulting residual distributio≥ n is shown in Fig. 3.8. Beyond three standard deviations, moder- ate tails are visible which can be fitted by superimposing a second Gaussian with a double width, σ2 = 2.2. There are still a few events outside the fitted distribution. The additional tail possibly extending beyond six standard deviations would require another order of magnitude of statistics to parametrize properly. Note that no asymmetry of the tails upstream or downstream of the production point is observed, which is essential for using the upstream part to probe the background. If the situation looks the same for the geometry in Fig. 3.2 and Fig. 3.1, this tail will multiply to 30 events above 6σz (averaged over upstream and downstream events and scaled∼). This corresponds to an efficiency of 0.1% for the vertex cut and a total efficiency of 4 10−6. ∼ · For an ET cut at > 1.5 GeV, a single Gaussian fit describes the distribution with the statistics available (Fig. 3.9). There are tails reaching beyond 6σ and amounting to 5 events after rescaling. ∼Including no other source of background than direct J/ψ, the signal over background is S (dz/σ > 6) =1.0 0.5 (3.1) z B ± for ET > 1.0GeV and S (dz/σ > 6) =3.4 3.2 (3.2) z B ± for ET > 1.5 GeV. The statistical uncertainties are high. It is observed that the pattern-recognition dilutions are quite well controlled, even with a reduced vertex- detector set-up and an algorithm which is not intended to be used for optimal parameter estimations. In summary, for a low b¯b cross section assumption of 12 nb, the reconstructed rates of J/ψ from B decays and cc¯ J/ψ background are roughly of the same size. Figure 3.10 illustrates the situation→. If the cut is placed at 7σz, there remains 15 9 direct J/ψ while the number of signal events is 29 8 (appearing unchanged due to±the statistical uncertainty), giving a signal over backg±round of S (dz/σ > 7) =1.9 1.3 (3.3) z B ± for ET > 1.0GeV. Efficiencies are very uncertain and depend very strongly on geometry, alignment, noise and readout efficiencies. A more universal useful number that comes out of 80 CHAPTER 3. OPTIMIZATION FOR σBB¯ MEASUREMENTS

Figure 3.8: Vertex resolution using L2simu and reﬁt. The distance is given in dz/σz for a cut on the number of hits per view (x and y) at 4. The distribution is parametrized by a double Gaussian ﬁt. ≥ 3.2. THE OPTIMAL GEOMETRY 81

Figure 3.9: Vertex resolution using L2simu and reﬁt. Only tracks with pT > 1.5 GeV are accepted. The distance is given in dz/σz for a cut on the number of hits per view (x and y) at 4. ≥ 82 CHAPTER 3. OPTIMIZATION FOR σBB¯ MEASUREMENTS

Figure 3.10: Vertex distribution of reconstructed J/ψ vertices using L2simu and reﬁt. The distance is given in units of σz for a cut on the total number of hits per view at 4. The distribution of B J/ψX (shaded) is rescaled to the order of magnitude ≥expected in 106 s. The double→Gaussian ﬁt (unshaded) illustrates the background of 38 000 direct J/ψ reconstructed during this period. The cut on the transverse energy∼ component is ET > 1.0 GeV. 3.2. THE OPTIMAL GEOMETRY 83

this study is the comparison with the magnetic field on or off. 4700 J/ψ and 7400 B J/ψX Monte Carlo events were produced for this purpose, with the same geo→metry configuration but with the magnetic field on. When there is a magnetic field, bremsstrahlung losses become a problem. Brems- strahlung losses before the magnet can be found by extrapolating a straight line from the electron track parameters at production and searching for clusters at the impact point of the extrapolation on the calorimeter. This procedure requires first level trigger electronics, which are not necessarily available at this early stage of running. In the presence of a magnetic field, the event profiles differ in the bending plane and the non-bending plane, so that the pT is better replaced by the Ktrig cut:

1 1 E>Ktrig + . · x2 + y2 x2 + y3 ! | | p p Using this cut with the Ktrig parameter at 1100 GeV cm seems sufficient to reduce the rates even without an invariant-mass cut, applied ·on the clusters [4]. In the second level trigger, bremsstrahlung losses are accounted for during the track extrapolation through the magnet by enlarging the search window. Each cluster is connected with two track candidates: one for an electron and one for a positron hypothesis. Owing to this increased amount of track candidates, and the larger search windows, the requirements on the track must be larger to reduce the rates. The requirement of 3 hits is found to be sufficient. Apart from the b≥remsstrahlung effect, signal is also lost due to a smaller overlap between ECAL and SVD (as can be discerned from Fig. 3.3). With a full-coverage ECAL, the difference in acceptance efficiency between magnetic field on and off would be smaller. In the offline reconstruction, bremsstrahlung that occurs before the magnetic field is corrected for. A cluster is defined as a bremsstrahlung cluster if it is located at the same y-position as the reconstructed electron or positron and if the x-position corresponds to a continuation of the original trajectory before the magnet (see Fig. 3.11): 1 yγ ye < 2 1 1 | − | · σ2 + σ2 yγ ye

C1 1 xγ xe < 2 1 1 . − ± Ee · σ2 + (σ2 +C /E2) xγ xe 2 e

The deviation of the lepton track depen ds only on the energy of the lepton, Ee and on a constant C1, which contains the average ﬁeld integral, the average z-distance between the cluster and the centre of the magnet and the average slope θye .The constants C1 and C2 are determined by Monte Carlo studies [52]. The values used are C1 = 585 and C2 = 10. Each cluster is assigned to both an electron and a positron hypothesis. In the electron hypothesis, the bremsstrahlung cluster is accepted if xγ

E e x e γ x By dz

Figure 3.11: Schematic picture of bremsstrahlung in front of the magnet.

MassJ/ψ /GeV

Figure 3.12: The invariant-mass distribution of electron clusters from J/ψ from B decays. The magnetic ﬁeld is switched on. Bremsstrahlung correction is included. The empty histogram contains all reconstructed cluster pairs. The shaded histogram was obtained by requiring a VDS match on both electrons. 3.2. THE OPTIMAL GEOMETRY 85

J/ Ψ B J/Ψ 1

0.5 N(Magnet On) / Off)

FLT SLT Total Efficienc y

Figure 3.13: Comparison of trigger and reconstruction efficiencies for J/ψ and B J/ψX events, with magnetic field off and on. The first level trigger (FLT) an→d total efficiency is presented relative to the original number of events and the second level trigger (SLT) efficiency relative to the number of events after FLT. The total efficiency is calculated before any cut on the decay length.

positron hypothesis if xγ >xe. The energy of the bremsstrahlung cluster is then added to the energy of the reconstructed electron or positron. The corrected mass distribution of lepton pairs from J/ψ is presented in Fig. 3.12. Some overcorrection is unavoidable. The comparison of magnetic field on and off is done for equal input rates and equal trigger output rates. The relative efficiencies are presented in Fig. 3.13. The first and second level trigger efficiencies are larger without any magnetic field. The tracks accepted by the second level trigger are generally better in the magnet-on case, because of the higher requirements at second level trigger level. This gain at analysis level is cancelled by the broader invariant-mass distribution (Figs. 3.4 and 3.12). For the comparison of the total signal rate, the cut on the invariant mass is placed at 2.5 GeV

L-shape Open-L Back-to-back

Figure 3.14: Diﬀerent possible conﬁgurations of the VDS. One layer is drawn schematically in the xy-projection.

VDS Configuration In the rest system of the J/ψ the two electrons go back to back. The L-shaped configuration of the VDS is therefore not the optimal one. The pots are movable (Chapter 2, Section 2.2) so that an open-L configuration (see Fig. 3.14) can be chosen relatively easily after the initial hardware studies. A back-to-back configuration requires a reinstallation of the modules. To gain any statistics with a VDS reconfiguration, the ECAL electronics have to be installed respective reinstalled in the same way to match the acceptance. The simulation is done with a fully equipped ECAL. The relative acceptances are depicted in Fig. 3.15. The result is the same for direct J/ψ and J/ψ from B (which confirms the earlier results on the similar acceptance for the two types of events). The acceptances for the open-L and back-to-back configurations are presented relative to the ‘default’ L-shaped configuration after the second level trigger (left) and after quality cuts required for analysis (right). The statistical accuracy is naturally lower for the sample with good quality tracks. As expected, it can however be discerned that the importance of an optimal VDS configuration is more pronounced when more hits are required on the tracks. The gain when going to well separated modules appears to be of the same magnitude with and without magnetic field. This is natural, since ECAL is simulated with its full acceptance. The presentation on the open-L configuration includes, apart from the statistical error, also an uncertainty connected to the artificial boundaries introduced in the Monte Carlo simulation of the horizontal sector.

Main-tracker configuration The production of the OT modules is spread over a long time. In such a situation it is likely to be provided with an incomplete tracking system during some running periods. The question is where the first modules should be placed to maximize the physics reach. It is assumed that when the OT planes arrive, also the muon system and the trigger will be operational. Since the magnetic field most probably will be 3.2. THE OPTIMAL GEOMETRY 87 A 4 4

3 3

2 2

1 1 N(VDS Configuration) / N

A B C A B C VDS Configuration

Figure 3.15: Efficiency of J/ψ events for the open-L (B) and back-to-back (C) VDS configuration normalized to the efficiency for the L-shape (A). Dots represent a simulation with a magnetic field and circles without magnetic field. a) SLT efficiency (number of hits per projection 2 for two tracks from the RoI). b) SLT and number of hits per projection 4 for t≥he tracks from J/ψ. ≥ switched on, the muon channel is the cleanest and is therefore studied. IT modules are not considered in the study. For an efficient muon trigger adjacent TC01 and TC02 modules are required. The superlayers are constructed in two halves, one on each side (+x and x)ofthe proton and electron beam. For the same number of half-superlayers, there− are two basic options. An interesting question is whether the higher acceptance is achieved when the half-superlayers are placed behind each other in z to have good pattern recognition and track reconstruction, or when complete superlayers are installed for higher trigger efficiency and the full azimuthal acceptance. An interesting situation appears when there can be in the order of five half- superlayers ready. If the choice is free between TC and PC layers, there are two main options for the installation: x coverage and symmetric coverage, as depicted in Fig. 3.16. − The difference in acceptance of J/ψ when the azimuthal coverage is reduced to the x side is less than half because the J/ψ decays tend to produce two leptons whic−h are 180◦ apart in azimuthal angle. The leptons normally do not go in the same hemisphere unless the transverse momentum of the J/ψ is very large. The x OT superlayers extend to the +x side on the lower side and also slightly on the upp− er side as seen in Figs. 3.16 and 3.17. About two thirds of the J/ψ-decays accepted by a x OT superlayer are of lower pT and accepted inside this small region, with the−leptons directed upwards respective downwards. The acceptance is illustrated in Fig. 3.18, where the leptons accepted in a x-sided OT geometry are − 88 CHAPTER 3. OPTIMIZATION FOR σBB¯ MEASUREMENTS

a) symmetric coverage option b) x coverage option −

Figure 3.16: Detector options as drawn by the HERA-B event display [69]. projected onto a vertex superlayer. Owing to the magnetic field, some negatively charged leptons which are initially on the +x side fall inside the acceptance of the OT (and vice versa for positively charged leptons). For a very few adjacent superlayers for pattern recognition, like in Fig. 3.16a, the normal track-finding algorithm is not efficient. In this case, upstream propagation can be used. The lepton seed comes from the ECAL or the muon system as a starting point for the track finding. Ranger [68] is applied for track propagation. In the initial comparison between the two OT configurations, the complete VDS is installed. Ideal pattern recognition, using Monte Carlo information, is applied for the VDS track reconstruction. Pattern-recognition effects in the VDS have less influence on a comparison between OT configurations. The matching between OTR and VDS track segments is performed using methods in Ref. [76]. For matching, the track parameters of the main-tracker segments are constrained to the wire position, assigned with an uncertainty defined by the lateral thickness of the target wire, the size of the beam spot at the target wire and, in the case of beauty decays, the mean displacement of the secondary vertex at which the lepton originates. The segments are then propagated to the first vertex-detector module which is hit by the track. A match is accepted if the intercepts (x, y)and slopes (θx,θy) of the segments agree within margins defined such that the ghost rate is low. The margins are x 2 mm, y 2.5 mm, θx 0.0015, θy 0.002. For each accepted match, the hits of ±both main t±racker and VD±S segments are± passed through a full Kalman filter refit using methods in Ref. [68].

Leptons with pT > 0.5GeV and p>5 GeV are selected and oppositely charged leptons are combined in pairs. Lepton pairs with invariant masses compatible with the J/ψ mass are subjected to a vertex ﬁt. The invariant-mass distribution is shown in Fig. 3.19. J/ψ candidates from beauty decays are selected by requiring a vertex separation distance. The vertex resolution σz is about 300 µm, for a complete VDS 3.2. THE OPTIMAL GEOMETRY 89

250 250 TC02 TC02 200 200 y / cm y / cm

150 150

100 100

50 50

0 0

-50 -50

-100 -100

-150 -150

-200 -200

-250 -250 -300 -200 -100 0 100 200 300 -300 -200 -100 0 100 200 300 x / cm x / cm µ+ µ-

Figure 3.17: Impact points of positively charged (left) and negatively charged (right) leptons from J/ψ decays in the trigger chamber TC02. Small dots represent all simulated leptons, full dots are those accepted by a x OT geometry and by the complete analysis chain. −

and selecting only tracks from OT (Fig. 3.20). The significantly better resolution compared with the about 500 µm found for the full main-tracker acceptance, is due to the large opening angle between the lepton tracks when both leptons are in the OT and none in the IT. The cut on the vertex separation is placed at 2 mm, which corresponds to 7σz. The efficiencies are summarized in Fig. 3.21. The trigger efficiency is larger for the OT configuration with the trigger chambers TC01 and TC02 covering the full acceptance like in Fig. 3.16a. On the other hand, main tracking and matching is less efficient for tracks crossing the superlayers of this configuration. The total yield, running with a 4 MHz single interaction rate for a duration of 106 s, is summarized in Fig. 3.22 for the two configurations in Fig. 3.16 and the reference configurations, where all superlayers in the pattern and trigger regions are installed. With a complete VDS, the configuration in Fig. 3.16a gives about twice the yield of the configuration in Fig. 3.16b. From Fig. 3.18 it can be concluded that with a half-sided OT geometry, one VDS quadrant can be saved. This observation is interesting for economic reasons, since the vertex detector suffers radiation damage. The best adoption of a reduced VDS to this kind of OT geometry is to exclude the lower-right quadrant and shift the other quadrants so that a mirrored VDS geometry is obtained. The total number of VDS superlayers can also be reduced and the best choice is found from Fig. 3.23, where the probabilities that muons from J/ψ decays traverse the different VDS superlayers 90 CHAPTER 3. OPTIMIZATION FOR σBB¯ MEASUREMENTS

6 6 SI03 SI03 y / cm y / cm 4 4

2 2

0 0

-2 -2

-4 -4

-6 -6 -6 -4 -2 0 2 4 6 -6 -4 -2 0 2 4 6 x / cm x / cm µ+ µ-

8 8 SI06 SI06

y / cm 6 y / cm 6

4 4

2 2

0 0

-2 -2

-4 -4

-6 -6

-8 -8 -8 -6 -4 -2 0 2 4 6 8 -8 -6 -4 -2 0 2 4 6 8 x / cm x / cm µ+ µ-

Figure 3.18: Impact points of positively charged (left) and negatively charged (right) leptons from J/ψ decays in the vertex superlayers SI03 and SI06. Small dots represent all simulated leptons; full dots are those accepted by a x OT geometry and by the complete analysis chain. − 3.3. SEMILEPTONIC DECAYS 91

2 2 χ =19.69 χ =23.26 a) b) ndf = 19 ndf = 18 µ=3.091 GeVµ=3.096 GeV σ=28 MeVσ=27 MeV

mµ + µ − / GeV mµ + µ − / GeV

Figure 3.19: Invariant-mass distributions of muon pairs from J/ψ decays for a) symmetric and b) x coverage OT configurations. − are plotted. The expected physics yield in a scenario when three quadrants of the VDS superlayers SI03–SI06 are installed is presented in the same histogram in Fig. 3.22. With a VDS of this configuration, a x OT geometry with matching acceptance gains with respect to the double-sided g−eometry of Fig. 3.16a. The yields are of the same size. The x type OT configuration of Fig. 3.16b is then preferred because of the possibilities−it offers to study alignment and pattern-recognition performances. With two or fewer quadrants per VDS superlayer, the +x OT planes become more or less useless for physics measurements where vertex information is needed.

3.3 Semileptonic decays

The best channel for the measurement of σb¯b appears to be B J/ψX, using the J/ψ trigger. The cross section for B double semileptonic decays→is of similar magnitude and a reconstruction of this type of events would increase the sample of B hadrons. The signature of B-hadron production in the double semileptonic channel BB ℓ+ℓ−X (where B stands for any hadron containing a b-quark) is not as clear as →in the J/ψ case. Good tracking is necessary to measure the impact points, which have to be clearly separated from the main vertex. The J/ψ background is easily reduced by requiring separate origins of the leptons. A dangerous background is the double semileptonic decay of D mesons. The lifetime of the charged D meson is 1.06 10−12 s, which is not much shorter than that of the B (1.56 10−12 s). In 7% of the t·riggered sample of charmed hadrons decaying semileptonical·ly, both hadrons are charged D- mesons. Assuming a b¯b cross section of 12 nb, this amounts to 20% of the B-hadron 92 CHAPTER 3. OPTIMIZATION FOR σBB¯ MEASUREMENTS

δz/cm

δz/σz

Figure 3.20: Longitudinal position δz of reconstructed J/ψ vertices relative to the primary interaction vertex. Direct J/ψ decays from charm production are represented by the unshaded histograms. J/ψ decays from beauty are represented by the shaded histograms. The horizontal axis of the upper plot measures δz in centimetres and the horizontal axis of the lower plot displays δz/σz,whereσz is the longitudinal vertex resolution estimated by the vertex fit. The RMS and fit parameters refer to the distribution of direct J/ψ. The number of entries for J/ψ decays from beauty is scaled according to the expected number of reconstructed events using a reduced OT geometry (five half-superlayers on the x side) and a reduced VDS geometry (four superlayers of each three quadrants). −The dashed distributions are blown up Gaussians of σ = 300 µm and σ =1. The number of events under these Gaussians corresponds to the expected number of reconstructed J/ψ. Tails are not included in the dashed distribution. 3.3. SEMILEPTONIC DECAYS 93

1.00 0.90

Efficiency 0.80 0.70 Trigger 0.60 Main Tracking 0.50 Matching 0.40 Total 0.30 0.20 0.10

- - OT OTOT5/2 OT5/2

Figure 3.21: Efficiencies of the trigger, main-tracking and matching steps relative to the number of events remaining after the preceeding step. The efficiencies are given for the symmetric and x coverage OT configurations and for the reference configurations, where all superlayers− in the pattern and trigger chambers are installed on the x side and on both sides. − 94 CHAPTER 3. OPTIMIZATION FOR σBB¯ MEASUREMENTS

6 1000

400

200 # Reconstructed Events / 10 s - - OT OT OT5/2 OT5/2

Figure 3.22: Physics yield, running with 4 MHz single interaction rate for a duration of 106 s, with full VDS (light grey) and VDS with three quadrants installed in four superlayers (dark grey). The yield is presented for the two reduced OT conﬁgurations and for the reference conﬁgurations. 3.3. SEMILEPTONIC DECAYS 95

0.20 0.25 a) b) 0.25 0.15 0.15 Acceptance 0.10 Acceptance 0.10

0.05 0.05

0 0 0 50 100 150 0 50 100 150 z / cm z / cm

Figure 3.23: Probabilities that muons from J/ψ decays traverse the individual superlayers SI01–SI07 of the vertex detector, plotted as functions of the z-position of the superlayers. The plots show the probabilities a) before and b) after passing the events through the first level trigger simulation and using a x OT geometry. − 96 CHAPTER 3. OPTIMIZATION FOR σBB¯ MEASUREMENTS sample. The inelastic background has been studied at the physics level in Ref. [53] with promising results. Background of wrong combinations and misidentified hadrons have not been studied for the b¯b cross section. A certain hadron suppression can be obtained by cuts on the cluster shape, as described in Ref. [4]. It is also possible that reconstruction in the RICH could reduce the hadron background. This chapter reports on the possibilities to handle the open-charm background. In the text, D generally stands for any charmed hadron, including baryons. B stands for all mesons and baryons with beauty flavour. The electron case is studied because the ECAL seems to be equipped earlier than the muon system and the main tracker. The four middle superlayers (3–6) of the VDS and the ECAL are assumed to be equipped to 100%. After the initial running it is planned to switch on the magnet. The magnetic field integral between VDS and ECAL is 2.2 Tm. The expected rates are presented in Table 3.1.

Table 3.1: Expected rates of BB e+e−X events before and after trigger. B stands for any b-ﬂavoured hadron. The →rates are calculated for a b¯b cross section of 12 nb. Also listed are the rates of the inelasic background and the background of DD ℓ+ℓ−X, where D stands for any charmed hadron. →

Event type Cross-section No. of events in Ktrig = branching 106 sand4MHz 1500 × ratio single interaction rate

Inelastic 13 mb 4 1012 < 1kHZ · DD e+e−X 300 nb 108 16 000 → BB e+e−X 0.1 nb 54 000 6 000 →

16 000 b¯b events and 15 000 000 cc¯ events have been generated, where both heavy hadrons decay semileptonically and both leptons are electrons. The pT distributions for the generated events are shown in Fig. 3.24. For the charm sample, a cut at generator level at around 1 GeV increases the production speed by several orders of magnitude. After trigger, the pT distribution looks like Fig. 3.26. The cuts at generator level were chosen at 1.1 GeV for the lepton with highest pT and 1.0 GeV for the other. The ﬁrst level trigger has been simulated using the HERA-B software, L1simu [64]. The trigger rates have been studied for single interactions, with the magnetic ﬁeld switched on and the full acceptance of ECAL. The trigger selects two or more clusters in the ECAL with high energy and transverse energy. No coincidences in the tracking planes are required. Clusters are selected with energies depending on the 3.3. SEMILEPTONIC DECAYS 97

pT/GeV

Figure 3.24: The pT distribution of leptons from double semileptonic decays generated with PYTHIA. The full line depicts the charmed hadron decays and the dotted line the B-hadron decays. Observe that the distributions are not scaled according to the relative contributions.

radial position, using the Ktrig cut:

1 1 E>Ktrig + . · x2 + y2 x2 + y3 ! | | p p The Ktrig constant is set to 1500 GeV cm. With this value, the rates will be less than 1 kHz. The trigger efficiency is 11·% for BB ℓ+ℓ−X and the D double semileptonic background is reduced by a factor of 2 10→−4. For BB e+e−X, secondaries from X (which in·the Monte Carlo simulation are always two c→harmed mesons), can also give rise to a cluster which passes the trigger criteria. The result is an energy distribution of the electron clusters from the first generation of the B decays as presented in Fig. 3.25. Only electrons from the first generation of the B decays are considered in the analysis, which leads to an additional loss of the order of 25% after trigger to exclude events where those electrons have low energy. The excluded events need not be considered as background if the events are well understood, but may enhance the sample of reconstructed B hadrons. Higher level triggers have not been studied here. The efficiencies are very high and they will not reduce the background of charmed mesons. The track reconstruction in the VDS is performed with the tracking methods for ideal pattern recognition in [68]. Ideal pattern recognition (using Monte Carlo information) is used in the vertex detector for tracks with momentum p>1GeV and at least 10 hits in the vertex detector. A total track-finding efficiency of 90% is 98 CHAPTER 3. OPTIMIZATION FOR σBB¯ MEASUREMENTS

E/EThreshold

Figure 3.25: The distribution of cluster energy over threshold energy of electrons from the ﬁrst generation of double semileptonic decays processed through a ﬁrst level trigger simulation based on cluster information alone. The full line depicts the charmed hadron decays and the dotted line the B-hadron decays. Observe that the distributions are not scaled according to the relative contributions. 3.3. SEMILEPTONIC DECAYS 99

pT/ GeV pT/ GeV

Figure 3.26: The pT distribution of leptons from double semileptonic decays. The full line depicts the charmed hadron decays and the dotted line the B-hadron decays. The first histogram contains the leptons with the higher pT of the two in the same event and the second the leptons with the lower pT. introduced explicitly. For single interaction events, pattern-recognition effects should not be too important, but should be kept in mind. The cut on the cluster shape should be placed such that the hadron background is sufficiently reduced. Since this background has not been studied, the cut is chosen such that the efficiency for electrons is 90%. Clusters in ECAL are matched ideally with tracks in VDS. The matching efficiency is still only about 60%. This is a geometrical effect. The acceptance of the four middle VDS superlayers does not cover the entire ECAL acceptance.

From the pT distributions in Fig. 3.26 of leptons from beauty and charm semileptonic decays, it is clear that increasing the pT cut will not signiﬁcantly reduce the D background further without losing a substantial part of the signal. In the case that the rates need to be reduced further, an asymmetric trigger with the higher pT cut around 2 GeV, while the lower pT cut is kept at around 1.5 GeV, is a good alternative.

Since the pT cut is not suﬃcient to suppress the D background, other ways to separate it from the signal must be used as a complement. The mass can not be measured directly, since only one or sometimes two tracks from the decay can be reconstructed and the particle identiﬁcation is poor with this reduced detector. With a second track, the decay vertex could be reconstructed and the decay length measured in this way. As explained by Fig. 3.27, the decay length is correlated with the impact parameter of the decay lepton. The separation improves further due to 100 CHAPTER 3. OPTIMIZATION FOR σBB¯ MEASUREMENTS

ψ δ vertex D+ lepton

θ Target D0 δ vertex lepton

Figure 3.27: Schematic picture of a double semileptonic D decay. For equal production and decay angles, the impact parameter δvertex of the decay lepton is larger for long- lived hadrons.

the in general lower pT of the D hadron. The impact parameter cut and the pT cut are correlated: δ = γβcτ sin θ sin ψ. vertex B| | For highly relativistic B mesons with momenta larger than about 10 GeV the increase in the average decay length is compensated for by the decrease in the average decay angle, sin ψ γ−1 [42], so that the average impact parameter δ is ∝ h vertexi δ cτ . h vertexi∼ Rather than cutting on each side separately, the cut is made on the product of − ℓ+ ℓ the absolute value of the two impact parameters: δvertex δvertex, which is written 2 · δvertex for short. Presuming that the position of the main vertex is known exactly, the separation between B hadrons and charmed hadrons is very good (Fig. 3.28). To simulate a realistic situation at an early stage of HERA-B running, the main vertex position was smeared with the thickness of the wire (50 µm 500 µm) and the size of the beam spot (500 µm). As seen in Fig. 3.29, it is no long×er possible to separate even the short-lived D hadrons. An alternative method is to look at the distance of closest approach between the leptons (Fig. 3.30). This parameter is equivalent to the impact-parameter product but independent of the main vertex reconstruction. As a result, this parameter gives a very clear separation between D and B events. The distribution of the track-to- track distance parameter is shown in Fig. 3.31a and Fig. 3.31b for D and B hadrons, respectively. With a cut on δtrack > 0.08 cm, the D background can be reduced to the 10% level. The track-to-track distance distributions can be ﬁtted with an exponential. The slope is characteristic for the mean decay length of the decaying hadrons. All D hadrons are grouped under the same ﬁt in Fig. 3.31a, which leads to a small tail at 3.3. SEMILEPTONIC DECAYS 101

2 δvertex/ cm

Figure 3.28: The impact parameters of leptons from double semileptonic decays. The horizontal axis displays the impact parameter of one lepton multiplied by the impact parameter of the other lepton in the same event. The Monte Carlo information on the position of the main vertex is used without smearing of the coordinates. The reconstruction was made on muons with a detector consisting of ﬁve half OT superlayers installed on the x side (referred to as scenario 3B in Ref. [1]) and a pT cut on the muons at 1.5−GeV. The events under the dotted line contain decays of B hadrons and events under the full line contain decays of charmed hadrons. The scales correspond to the expected number of reconstructed events running with 4 MHz single interaction rate for a duration of 106 s. 102 CHAPTER 3. OPTIMIZATION FOR σBB¯ MEASUREMENTS

2 δvertex/ cm

Figure 3.29: The impact parameters of leptons from double semileptonic decays. The horizontal axis displays the impact parameter of one lepton multiplied by the impact parameter of the other lepton in the same event. The events under the dotted line 0 + contain decays of B , B and Λb with antiparticles. Events under the full line contain 0 decays of D , DS and their antiparticles. Note that the D sample should be rescaled by a factor of 6 and the D sample by a factor of 3 to reﬂect the scenario described in the text. 3.3. SEMILEPTONIC DECAYS 103

0 lepton D δ Target track D0 lepton+

lepton

B δtrack Target B

lepton+

Figure 3.30: Schematic picture of a double semileptonic D decay and a double semileptonic B decay. The distance between the two decay leptons, δtrack, is larger for long- lived hadrons. high distances. In Fig. 3.31c and Fig. 3.31d, the total distribution is shown and fitted with a double exponential. The slope on the upper part corresponds well to the slope in Fig. 3.31a and the slope on the lower part, dominated by B events, corresponds to the slope in Fig. 3.31b. The success of the fit suggests further studies, with more statistics, on the possibilities to calculate the B contribution from such a fit. It would also be interesting to investigate whether this method can be used for lifetime measurements. One should bear in mind that pattern-recognition effects might distort the distributions and dilute the power of the method. An even more powerful method is to reconstruct a common vertex of the two leptons and require it to lie on the production vertex. This fit should fail for double semileptonic decays, where the two leptons have different origins, separated from the main vertex. The failure is more distinct for B hadrons, whose decay leptons are more separated from each other and from the main vertex than the leptons from D hadrons. The χ2 distribution of this fit is shown in Fig. 3.32. A cut at χ2 > 1000 removes the D background almost completely, whereas a large fraction of the signal is kept. The drawback with this method is that it heavily relies on that the detector and the reconstruction are well understood. The trigger and reconstruction efficiencies are summarized in Table 3.2. To calculate what the efficiencies mean in terms of obtained statistics and reduc- ¯ tion power, the size of the bb cross section, σb¯b, is needed. The theoretical calculations predict a cross section between 12 and 29 nb [9]. The two experimental measurements 104 CHAPTER 3. OPTIMIZATION FOR σBB¯ MEASUREMENTS

δtrack/ cm δtrack/ cm

Figure 3.31: Distance between tracks for electrons from double semileptonic decays. a) D decays with an exponential fit. b) B decays with an exponential fit. c) B and D decays with statistics scaled according to the expected number after 106 s. (The shaded entries show the contribution from B decays.) d) Same as c. (The distribution has been fitted with two exponentials in the D respective the B dominated regions.) 3.3. SEMILEPTONIC DECAYS 105

χ2

Figure 3.32: The χ2 of a vertex ﬁt of the two leptons from double semileptonic decays, constrained to the wire. The distributions of B and D decays are plotted in the same histogram for comparison. Note that the D sample should be rescaled by a factor of 6andtheDsamplebyafactorof3toreﬂectthescenariodescribedinthetext.

Table 3.2: Efficiencies obtained on a sample of Monte Carlo simulated events containing the decay BB e+e−X. Also listed are the reduction efficiencies for the background of DD e→+e−X. The total efficiency is given for the two alternative cuts on the distance→ between tracks and the χ2 of a vertex fit. (∗The efficiencies for the cluster shape cut, the pattern recognition, and the matching between clusters and tracks are introduced explicitly.) N(Signal : BB e+e−X) N(DD e+e−X) → → Generated MC Events 16 000 15 000 000 Trigger 11% 2 10−4 · Energy cut on clusters 74% 78% Cut on cluster shape∗ 81% 81% Track acceptances 58% 59% Pattern recognition∗ 90% 90% Matching efficiency∗ 90% 90% δ > 0.08 cm 11% 0.3% tracks ≈ Total Efficiency 0.3% 2 10−7 ≈ · χ2 > 1000 19% 0.2% ≈ Total Efficiency 0.6% 1 10−7 ≈ · 106 CHAPTER 3. OPTIMIZATION FOR σBB¯ MEASUREMENTS

Table 3.3: The number of double semileptonic decays expected during a running period of 106s. The number of reconstructed events and the signal over charmed background are presented for two diﬀerent analysis methods.

σb¯b 12 nb 24 nb 36 nb N(produced BB ℓ+ℓ−X) 54 000 108 000 162 000 → Method 1: Distance of closest approach, δtrack > 0.08 N(reconstructed BB ℓ+ℓ−X) 160 20 320 40 480 60 − N(BB→ℓ+ℓ X) → ± ± ± + − 8 6 16 11 24 17 N(DD→ℓ ℓ X) ± ± ± Method 2: Vertex reconstruction, χ2 > 1000 N(reconstructed BB ℓ+ℓ−X) 320 30 650 60 970 90 − N(BB→ℓ+ℓ X) → ± ± ± + − 30 30 70 70 100 100 N(DD→ℓ ℓ X) ± ± ± that exist give contrary results [44, 46]. Considering these predictions, the result of this study is given for three values of σb¯b. Table 3.3, presents the number of events recorded during a running period of 106 s. The errors reﬂect the size of the Monte Carlo sample used in this study. No systematic eﬀects or uncertainties in used parameters, cross sections and assumptions were included in the calculation of the errors.

In summary, for σb¯b = 12 nb and running with a single interaction rate of 4 MHz for 106 s (typically a month in absolute time), the track-to-track distance cut leads to 160 20 reconstructed double semileptonic events. The ratio of reconstructed signal even±ts to the open-charm background is 8 6. ± Using the vertex-ﬁt method, there would be 320 30 reconstructed double semileptonic events. The signal to charmed background w±ould be 30 30. ±

3.4 Υ reconstruction

Among the physical goals of early HERA-B runs, the study of hadronic production of dileptons seems to be of particular interest as it makes it possible to test our knowledge of both quark–antiquark (continuum) and gluon (leptonic decays of heavy quarkonia) distributions in hadrons. The mechanism of hadronic production of heavy-quarkonium states is described in Chapter 1, Section 1.3. The heavy mass of the b-quark makes the Υ measurements an interesting test of NRQCD. In particular, the discrepancies in P-wave ratios found in the charm quarkonia and the fraction of transversely polarized J/ψ are expected to be smaller in the b¯b system. The feasibility to measure J/ψ production is already treated in connection with the b¯b cross section above. In this chapter the feasibility to measure the rate of Υ production is reported. The two scenarios with five half OT planes installed on the x side or on both sides are studied here. − The total Υ cross section is estimated to be around 130 pb. This number is obtained by integrating the Fermilab fixed-target results [75] of differential cross 3.4. Υ RECONSTRUCTION 107

section per unit rapidity over a na¨ive Monte Carlo rapidity distribution. Assuming the interaction rate of 4 MHz, about 40 000 Υ resonances will be produced during a running time of 106 s. 810 of them will decay to muon pairs and candidate for measurements.

Table 3.4: Total statistics expected for an integrated running time of 106 s at 4 MHz interaction rate (single interactions) for muonic decays of Υ resonances. No. of events, N N(Υ µ+µ−) → Inelastic 4 1012 · Υ(nS) 40 000 810 Υ(1S) 23 200 580 Υ(2S) 13 800 180 Υ(3S) 2900 50

In total, about 6000 Υ(1S) µ+µ− have been generated with Monte Carlo simulation to obtain the reconstruction→ efficiencies. Software described in Section 3.2 is the basis for this study. The events are first required to pass the first level trigger simulation. The event rejection of the second level trigger is considered as included in the final analysis. Matched lepton tracks from Υ µ+µ− undergo the cuts below. → Trigger: p > 0.5GeV. • T Trigger: p>5GeV. • Geometry: dp/p2 < 0.01/GeV. • Reconstruction of Υ: vertex χ2 < 10. • Reconstruction of Υ: m(Υ) 400 MeV. • ± 2 The track parameter cuts, pT,p,dp/p are fully included in the trigger rejection. The Υ vertices have been reconstructed using the vertex package [70]. The efficiency is 98–99%. The overall results for the different scenarios are summarized in Fig. 3.33. (The numbers assume a complete vertex detector.) The mass resolution of reconstructed Υ(1S) is 1.1% (Fig. 3.34). For an incomplete vertex detector, the most favourable configuration was found to be four superlayers with three quadrants out of four, placed in such a way that it covers almost all the acceptance of the reduced OT (Section 3.2). With this reduced vertex detector, the x OT geometry of Fig. 3.16 is preferred. In the summary histogram of Fig. 3.35,− the rates with a reduced vertex detector are only given for the x OT geometry. Figure− 3.36 represents the acceptance vs. transverse momentum (the number of reconstructed Υ’s divided by the number of generated Υ’s). Although the acceptance 108 CHAPTER 3. OPTIMIZATION FOR σBB¯ MEASUREMENTS

1.00 0.90

Efficiency 0.80 0.70 Trigger 0.60 Main Tracking 0.50 Matching 0.40 Total 0.30 0.20 0.10

- - OT OTOT5/2 OT5/2

Figure 3.33: Reconstruction efficiencies for the decay Υ µ+µ−. A complete vertex detector is assumed. The full OT geometries are represe→nted for comparison. of p is rather small for both the x and complete OT scenarios, it varies little over T − the entire spectrum of pT, covering most of the highly populated dynamical range. The main sources of background underneath the Υ signal are dileptons from normal inelastic events, ghost tracks and misidentified hadrons, and events with charm-quark production which may result in genuine dileptons, The main physical background is the Drell-Yan process. This background should be of the same size as for the experiment at Fermilab [75]. Assuming a rapidity distribution similar to the Υ rapidity distribution and integrating over an invariant- mass range of 2σ of the mass resolution (i.e. 400 MeV), the Drell-Yan cross section is 0.9 pb, wh±ich corresponds to 350 such events produced. It is assumed that acceptance∼ and trigger and reconstruction∼ efficiencies are the same for signal and background. Hence, as a rough estimate, the signal-to-background ratio is dσ(Υ(1S) µ+µ−) → 1.4. dσ(Drell-Yan) ∼ The background of fake tracks has not been studied. According to this preliminary study, it seems it will be possible to include Υ meson analysis in the early-run physical topics. With a Υ cross section of 130 pb 3.4. Υ RECONSTRUCTION 109

m(µ+µ−)/GeV

Figure 3.34: Mass distribution of reconstructed Υ µ+µ−. → and the speciﬁed running conditions, 39 2 dimuonic decays, Υ µ+µ−,canbe expected to be reconstructed in total. O±f these, of the order of 28→ originate from the Υ(1S) state, nine from Υ(2S) and a couple (undetectable) from Υ(3S). With the predicted mass resolution the resonances can be separated from the continuum. The ratio of the Υ(1S) signal to the Drell-Yan background is of the order of 1.4. In the future, careful tuning of cuts has to be performed as well as ∼background studies. Also the electron channel should be investigated. The large invariant mass of the leptons from Υ makes it possible to look for this type of events with a quite rudimentary detector, maybe even just the calorimeter alone. 110 CHAPTER 3. OPTIMIZATION FOR σBB¯ MEASUREMENTS 6

400

200

# Reconstructed Events / 10 s - - OT OT OT5/2 OT5/2

Figure 3.35: The expected yield of reconstructed Υ µ+µ−, running with 4 MHz single interaction rate for a duration of 106s. With →full VDS (light grey) and VDS with three quadrants installed in four superlayers (dark grey). 3.4. Υ RECONSTRUCTION 111

Complete OT - E(p T) 5/2 OT

p T GeV/c

Figure 3.36: Acceptance of Υ mesons decaying into muon pairs as a function of pT. The acceptance is shown for a scenario with a complete OT and with ﬁve half- superlayers on the x side. − Chapter 4

The golden decay

The main goal of the HERA-B experiment is to measure CP violation in the golden 0 0 channel, B J/ψKS. The parameter sin 2β has been measured directly by OPAL[41] and→CDF[17]. CDF has obtained the value

+0.41 sin 2β =0.79−0.44 , which is consistent with large CP violation in the B system as predicted by theory. From the size of the errors, it is clear that more precise measurements are desired. Various planned and upgraded experiments striving for this purpose are presented in Chapter 2, Section 2.7. In this chapter, the capacities for HERA-B to contribute to the world average of sin 2β are investigated. The full analysis of the golden channel includes understanding of the golden decay, the background and the tagging of the flavour of the B meson. In this chapter the reconstruction of the golden decay is performed on Monte Carlo data. The method is supposed to be applicable to simulated as well as real response from the complete detector, with the exception of track reconstruction in the vertex detector, where ideal pattern recognition has been performed, using Monte Carlo information. In the main tracker, full pattern recognition has been used in accordance to Chapter 2, Section 2.6. In the VDS, tracks with a momentum larger than 1 GeV and at least eight hits in the VDS are reconstructed using tracking methods for ideal pattern recognition in Ref. [68]. The matching of tracks between the main tracker and the VDS is also done ideally, using the Monte Carlo information. Matched tracks are subjected to a refit using methods in [68]. An estimate of ∆ sin 2β is given from the obtained efficiencies.

4.1 Extracting a CP violation signature

To obtain a CP-violation measurement, the time-dependent asymmetry in Eq. (1.53) is plotted and the CP measurement, sin 2β, obtained from the ﬁt. 4.1. EXTRACTING A CP VIOLATION SIGNATURE 113

The asymmetry depends on sin 2β according to

a(t)=sin2β sin xdt, (4.1) where t is measured in units of the average B lifetime, γτB. The mixing parameter 0 xd =∆mBτB 0.72 [58] determines the time-integrated probability that a B (or 0 ≈ 0 0 B¯ ) decays as a B¯ (or B ). Consider the asymmetry measured at the times ti.For linear ﬁtting the error on the parameter sin 2β,isgivenas

2 1 σ = 2 sin 2β (sin xdti) i 2 σi P in the case of perfect tagging. σi is the standard deviation of the measurement at the time ti. For asymmetry measurements, when the asymmetry is small, it holds that 1 σi = , (4.2) √ni where ni is the total number of events in the sample. This gives

2 1 −ti σsin 2β = 2 ,ni = N(t =0)e . (4.3) i ni sin xdti The summation is replacedPby an integral giving the statistical error 1 1 1 1 ∆sin2β 1 = , (4.4) ≈ N(0) · ∞ 2 N(t ) · M(t0) e−t sin2 x t dt 0 t0 d p p R with 1 1+4x2 cos 2x t +2x sin 2x t 2 M(t )= d − d 0 d 0 . (4.5) 0 2(1 + 4x2) d M grows with the decay-time cut t0, reﬂecting how the asymmetry builds up slowly. An asymmetry can also be obtained from the time-integrated rates. Integrating separately for the B0 in Eq. (1.55) and the B¯0 in Eq. (1.56) gives

N B(t ) N B¯ (t ) A = 0 − 0 = M (t )sin2β, (4.6) int B B¯ int 0 N (t0)+N (t0) where sin x t + x cos x t M (t )= d 0 d d 0 , (4.7) int 0 1+x2 so that the error is 1 1 ∆sin2β (4.8) B B¯ · Mint(t0) N (t0)+N (t0) q 114 CHAPTER 4. THE GOLDEN DECAY in the case of perfect tagging. In order to determine the best choice of the decay cut t0, look at the part of the error which is dependent on the cut. 1 1 F (t0)= . (4.9) √e−t0 · M(t0)

This function stays rather ﬂat for t0 up to about 0.55 (as seen in Fig. 4.1), which is where the cut has been placed in the analysis. The interpretation of the curve is that the asymmetry at t<0.55 is so low that those extra events would hardly increase the accuracy of the measurement. The accuracy of a time-integrated asymmetry would even decrease without the cut. The decay-time cut can be increased to reduce background without losing much in the statistical signiﬁcance of the CP asymmetry.

a) b)

τ/τB τ/τB

2 Figure 4.1: a) Coefficient F (t0) and b) statistical factor K =1/M (t0) governing the dependence of ∆ACP on the decay-time cut t0, for a fixed total number of events. Top line: time-integrated asymmetry. Bottom line: fit to the time-dependent asymmetry. For the plot, the mixing parameter was set to xd =0.72.

2 The statistical factor from the ﬁt is represented as K =1/M (t0). Additional sources of error arise in determining the initial ﬂavour of the decaying B meson. The most powerful method is to partly reconstruct decays of the second B hadron in the event. The sign of the charge of a soft pion accompanying the B 4.1. EXTRACTING A CP VIOLATION SIGNATURE 115

Table 4.1: Tagging methods in HERA-B

TAG METHOD Lepton tag: The sign of a high-pT lepton, which can be associated with the second B meson in the interaction.

Kaon tag: The sign of a kaon, which can be associated with the second B meson in the interaction.

Charge tag: Counting the charges of secondary vertex tracks (weighted by the momentum, since hard tracks are more strongly correlated in charge with the fragmenting quark).

Soft pion: The sign of a soft pion either from the decay of an excited B∗∗ meson into the B under investigation, or from the local charge conservation in the quark fragmentation process. This tagging method has only been studied brieﬂy. It is not included in the presented combined tagging power.

meson under investigation could also serve as a tag. The different methods applicable to HERA-B are described in Section 4.6 and summarized in Table 4.1. Two effects dilute the tagging: Mixing of the tagging B. • Wrong tags due to particle misidentification, non-B tracks and ambiguous sig- • natures, etc. If no lifetime cuts are applied on the tagging B, the probability that it has changed its flavour when it decays is 2 xd χd = 2 . 2(1 + xd) The detectable CP asymmetry is reduced by a dilution factor D =1 2χ .The M − d dilution from mistagging, DT , depends in the same way on the probability for a wrong tag. The effects of dilutions and the probability to find a tag (ǫtag) are summarized in the tagging power, P = DM DT √ǫtag . The total error on the CP asymmetry is now

1 K ∆sin2β . (4.10) ≈ P sNt0 In the case that background can not be completely neglected, and R is the ratio of background and signal, the factor √1+R is to be multiplied with the statistical error. 116 CHAPTER 4. THE GOLDEN DECAY

Finally, systematic errors will add to the total uncertainty. Systematic errors include uncertainties in xd and the dilution factors. The dilution factors can be measured using a self-tagging decay. The self-tagging decay should preferably be a decay of a neutral B, to be sure to have the same flavour composition of the tagging B. A good reference channel is B0 J/ψK∗0 because of its relatively high branching ratio. → The largest systematic error comes from non-CP asymmetries. Non-CP asymmetries arise because of asymmetries in the detector acceptance, unequal production and tagging probabilities for B and B¯ and because of charge asymmetries in the backgrounds. Detector asymmetries include the hole for the electron-ring beam pipe (which has also motivated an asymmetric design of the OT planes, see Fig. 3.16), broken wires and damaged silicon detectors and noisy cells. The tagging probabilities differ for B and B¯ because the flavour composition of the tagging B is different and because the interaction length of K+ differs from the interaction length of K−. Reference channels without CP violation can be used to determine the non-CP asymmetries. To reach small statistical errors on the non-CP asymmetries, Monte Carlo models have to be provided. The Monte Carlo models are tuned by independent measurements on self-tagging decays.

4.2 The simulated event sample

0 0 11 200 B J/ψKS events have been generated with the HERA-B Monte Carlo simulation.→In 5400 of the events the J/ψ decays to µ+µ−, and in the other events 0 it decays to electrons and positrons. The KS from the signal B decays in all events to charged pions. Each golden event, which passes the trigger criteria, is combined with a number of inelastic interactions to form a HERA-B event. 13 000 inelastic interactions are generated. The results on the muon and electron samples are independent of each other, therefore some of the inelastic interactions combined with muon events have been reused for electron events. The number of inelastic interactions to combine is determined by Poisson statistics with a mean at 4.

4.3 Trigger simulation

The trigger efficiency is dominated by the geometrical acceptance. At pretrigger level, two leptons of equal flavour must appear either as penetrations into the muon chamber or as high-energy electromagnetic showers in the calorimeter. At the first level trigger, these depositions are associated with track candidates. The geometrical acceptance of the tracks has been checked. One digitized hit is required in each double layer in each trigger superlayer. When this requirement is met, the requirement of hits in ECAL or in the MUON system is automatically fulfilled. The TFU is not simulated. Instead the track parameters behind the magnet are given by Monte Carlo information from TC02 and from the trigger superlayer closest 4.3. TRIGGER SIMULATION 117

TC02 (z 0 ,x 0 ) MC01 (z m ,x m ) θ x Magnet

Figure 4.2: Simpliﬁed illustration of the TPU procedure using Monte Carlo information for the track parameters behind the magnet.

to the magnet (PC01). The situation is illustrated in Fig. 4.2. The momentum vector is found using the map of the magnetic ﬁeld and the invariant mass mJ/ψ is calculated arithmetically. Cuts are applied on the momentum (p>5 GeV) and the transverse momentum (pT > 0.5 GeV). The invariant-mass distribution of muon pairs is shown in Fig. 4.3a. A Gaussian smearing is applied on this distribution to simulate the use of look-up tables and obtain a realistic resolution (Fig. 4.3b).

The event will be accepted if 2.75 GeV

a) b) µ =3.131 GeV µ =3.128 GeV σ = 106 MeV σ = 168 MeV

GeV GeV

Figure 4.3: The invariant-mass distribution at trigger level of muons from J/ψ of golden decays: a) The distribution from the fast trigger simulation using Monte Carlo information; b) the same distribution, smeared with a Gaussian distribution to simulate the resolution obtained when look-up tables are being used.

Table 4.2: Trigger efficiencies for the golden decay in the cases where the J/ψ decays to muons and electrons. Also given are the efficiencies obtained from a detailed study by the first level trigger group [64].

Trigger (J/ψ µ+µ−) (J/ψ e+e−) → → No. of generated events 5400 5800 Geometry 67% 62% Momentum cuts 94% 74% Invariant-mass cut 98% 85% Total 62% 39% FLT [64] 55% 35% 4.4. ANALYSIS AND EFFICIENCIES 119

GeV GeV

Figure 4.4: The invariant masses of µ+µ− (left) e+e− (right) pairs of reconstructed J/ψ (shaded). The internal background is presented in white on top of the distribution. The J/ψ µ+µ− decays are ﬁtted with a Gaussian of µ =3.10 GeV and σ =19MeV. →

4.4 Analysis and eﬃciencies

The triggered J/ψ with tracks reconstructed is finally accepted if the decay vertex canbefittedwithagoodχ2. A cut is applied around the J/ψ mass. The invariant- mass distribution is shown in Fig. 4.4. For muons the window is mJ/ψ 60 MeV. For electrons, only the upper limit is set. The lower limit remains at the ±trigger cut at 2 GeV, to include also electrons which lost energy due to bremsstrahlung. The J/ψ reconstruction efficiency is 90% for muons and 92% for electrons. 0 For each selected J/ψ event the KS candidates are picked out. To be able to 0 reconstruct the momenta of the pions from the KS, there must be enough coordinates inside the magnet. Therefore, only kaons decaying up to the centre of the magnet are selected. This is equivalent to requiring hits in at least three OT superlayers or two IT superlayers inside the magnet (which is one superlayer less than with the design from 1995 [30]). To reject the copious background of hadrons produced at a main vertex, the χ2 distance of the pion tracks with a VDS segment, to each of the eight wires is required to be larger than 10. The distance in z between the first points of the two pions must not be larger than two superlayers. No particle identification is used to select pions. All combinations of selected particles from a common reconstructed 0 vertex and with an invariant mass compatible with the KS mass are accepted. 0 25% of all KS decay inside the simulated magnetic field. In these cases, as well as 0 when the KS decays just before the magnet, the vertex has to be reconstructed from track parameters obtained in the main tracker. The position and slopes of these tracks have worse resolutions than the position and slopes of tracks with a VDS segment. The scarce number of superlayers in the magnet might make it difficult to 120 CHAPTER 4. THE GOLDEN DECAY measure the curvature and obtain the track parameters at the point of the kaon decay. Moreover, the track reconstruction includes pattern-recognition effects, i.e. for kaon reconstruction inside and just before the magnet, there is no Monte Carlo information used. For these reasons, the kaon reconstruction without VDS information on both track segments is treated separately from the kaon reconstruction in front of the magnet. When both pion tracks of a kaon candidate have been reconstructed in the VDS, the vertex is reconstructed using the vertex package [70]. This reconstruction is very similar to the reconstruction of the J/ψ. Reconstructed kaons with χ2 < 30 and a mass within the window of m 0 0.010 GeV are accepted for further analysis The KS invariant-mass distribution of signal± and internal background is shown in Fig. 4.5a and Fig. 4.5c. Kaon candidates, for which one or both pions miss information from a VDS track segment, are fitted using algorithms from Ref.[71]. These routines perform vertex reconstruction in the inhomogeneous magnetic field of HERA-B. The ‘pseudoinvari- ant mass’ of track pairs is calculated at the first reconstructed points of the tracks. +0.2 To reduce the number of combinations for vertex fit, a window m 0 GeV is KS −0.1 0 defined. There are no KS events outside this window, which are also accepted by a vertex fit. Candidate pairs with common vertices (χ2 < 30) and invariant masses m + − = m 0 0.015 GeV are accepted. The true invariant-mass distribution of π π KS ± 0 the reconstructed KS candidates is shown in Fig. 4.5b and Fig. 4.5d after fit. 0 A cut is also applied on the position of the reconstructed KS decay vertex, to further reduce the combinatoric background. For kaons reconstructed in the VDS, the cut is placed on z 0 > 0 cm. Since the position of the target stations are 1.2 KS and 4.9 cm, this is already a cut on the decay length. For kaon candidates, witho− ut VDS−information on both pion tracks, the cut is placed such that it keeps 99% of the 0 true KS. In total, the cut on the decay length keeps 97% of the signal and reduces the internal background to 68%.

Cuts are also applied on the transverse (pT > 0.45 GeV) and total momentum 0 (p>4.5 GeV) of the reconstructed kaon. This keeps >99% of the golden KS but reduces the internal background to 86%. 0 The mass distribution of the reconstructed KS after fit and all cuts is shown in Fig. 4.5a and Fig. 4.5c for the VDS vertex reconstruction and in Fig. 4.5b and Fig. 4.5d for the vertex reconstruction including propagation in the magnetic field. The two upper plots show the blind distribution of all accepted combinations. In the 0 two lower plots, the distribution of KS from the golden decay and other combinations are shown separately. There is a peak in the background at the kaon mass, which comes from other kaons in the events. 0 0 The KS reconstruction efficiencies are summarized in table 4.3. The KS finding procedure inside the magnet deserves closer investigation. 0 0 0 For each KS candidate, the KS mass constraint is applied and the KS track 0 parameters are obtained. Each KS track candidate is then combined with the reconstructed J/ψ to form the secondary vertex of the B0 meson. Since the decay length of the J/ψ is negligible ( 10−10 m), the B0 decay vertex is reconstructed as ∼ 4.4. ANALYSIS AND EFFICIENCIES 121

a) b)

GeV GeV

c) µ =(0.4981 d) µ =(0.4980 0.0001) G±eV 0.0002)±GeV σ =(0.0036 σ =(0.0077 0.0002) G±eV 0.0003)±GeV

GeV GeV

0 Figure 4.5: The invariant masses of particles of reconstructed KS candidates for a) track pairs with VDS segments and b) at least one track with the ﬁrst point lying 0 inside the magnet. In the two lower plots the distribution of KS from the golden decay is displayed in the shaded histograms. Other combinations are displayed as white histograms. The distribution is shown seperately for c) track pairs with VDS segments and d) at least one track with the ﬁrst point lying inside the magnet. 122 CHAPTER 4. THE GOLDEN DECAY

0 Table 4.3: Geometry and reconstruction eﬃciencies for KS from the Golden Decay. 0 In the left column, the results are presented for KS with VDS track segments found 0 for the decay pions. In the right column the results are presented for KS,inthecase when the decay pions were not found in the VDS.

0 KS VDS Track Segments Main Tracker Segments Geometry 12% 43% Pattern Recognition 91% 91% +0.2 0 Mass window (definition) mK 0.010 GeV mK0 −0.1 GeV S ± S Mass window (efficiency) 96% 97% Vertex fit, χ2 < 30∗ 95% 66% Mass=mK0 0.015 GeV - 89% S ± Vertex position (definition) z>0.0cm 17 99% >99% Total 9% 22%

∗It is not possible to compare the vertex reconstruction eﬃciencies directly, because of the strong correlation between the mass cuts and the χ2 cut.

Table 4.4: Eﬃciencies for the reconstruction of the B0 decay vertex.

The B0 decay vertex (B0 J/ψK0 ) → S Channel (J/ψ µ+µ−) (J/ψ e+e−) → → Vertex fit, χ2 < 90 96% 95% Mass window (definition) mB0 0.030 GeV mB0 0.060 GeV Mass window (efficiency) ±92% ±59% Total 88% 56% a three-particle vertex, with a mass constraint on the two leptons. B0 candidates are accepted if the decay vertex is reconstructed (χ2 < 15) and the invariant mass is in the mB0 range: mµ+µ−K0 = mB0 30 MeV, which is about 2σ S ± (Fig. 4.6). In the electron channel, J/ψ e+e−, this window is of the double size. The B reconstruction efficiencies are summarized→ in Table 4.4. The candidates are fitted with a mass constraint also on the B0 mass and the B0 track parameters are obtained. The B0 candidates are required to point to a target wire. This can be done in two ways:

1. All main vertices are reconstructed on the target wires. The result for 200 events is shown in Fig. 4.7. If the B0 is compatible with one of them, this vertex is the primary vertex of the B0. For golden B this works in 81% of the cases in the muon channel. The main-vertex reconstruction can be improved, including corrections to account for multiple scattering in material traversed 4.4. ANALYSIS AND EFFICIENCIES 123

GeV GeV

Figure 4.6: The invariant masses of particles of reconstructed B0 mesons. The B0 mass resolutions are represented for J/ψ µ+µ− (left) and J/ψ e+e− (right). → →

between the ﬁrst measured point of the tracks and the target station.

2. If the B0 does not point to any of the main vertices, the distance to a target wire is computed and a primary vertex with the B0 only is reconstructed.

0 + − 0 + − 0 In total 92% of B decaying to µ µ KS and 87% of the e e KS decays point to a target wire. With this last requirement fulfilled, the golden decay is reconstructed. The cuts and obtained efficiencies are summarized in Table 4.5. The resolutions in z of the reconstructed decay vertex and production vertex of the B0 are presented in Fig. 4.8. The true J/ψ events selected by the first level trigger will include all background J/ψ produced directly at the target wires, as well as fake J/ψ from double semileptonic charm decays. The most efficient reduction of this background comes from a requirement of secondary-vertex separation. A cut on the distance of the J/ψ from the target is applied already at the second level trigger. To increase statistical accuracy the secondary-vertex criterion is considered only at the end of this analysis. Apart from being crucial for the rejection of background, the measurement of the decay length of the B0 meson is necessary to fit the time-dependent asymmetry. The cut on the decay length should be adjusted according to the rate of the background. In this analysis it is chosen as τ<0.55 τB, for reasons explained in Section 4.1. The efficiency is 57 3% in the muon channel. In the electron channel, the efficiency is higher 71 5%. T±his is explained by bremsstrahlung effects. Because of bremsstrahlung inside±the magnetic field, the momenta of the electrons are underestimated. To obey the mass constraints on B and J/ψ,theB vertex fit tries to correct for this by increasing the momenta estimates but also the estimates of the slopes, which leads to a larger z-coordinate of the reconstructed B decay vertex, as 124 CHAPTER 4. THE GOLDEN DECAY

y/cm

x/cm

Figure 4.7: The x- and y-positions of main vertices reconstructed in 200 events containing the decay B0 J/ψK0 . → S

a) b)

( z z )/cm (z z )/cm reconstruction − MC reconstruction − MC Figure 4.8: The Monte Carlo resolution of the z-coordinate of reconstructed vertices 0 0 + − from B J/ψKS,whereJ/ψ µ µ : a) the decay vertex of the B meson; b) the main vert→ex of the B meson. → 4.5. BACKGROUND 125

τ/τB

Figure 4.9: The proper decay time of reconstructed B0 before (empty) and after the vertex cut (shaded). seen in Fig. 4.10. Bremsstrahlung corrections and other possibilities to recover from this tail in the resolution of the decay vertex should be investigated. To estimate the total efficiency for the golden decay, the particle identification efficiencies and efficiencies for pattern recognition in the VDS are introduced explicitly. The overall efficiencies are summarized in Table 4.5. The total efficiency is 5.7 0.3% for the muon channel and 2.4 0.2% for the electron channel. ± ± One should bear in mind that pattern-recognition effects in the VDS might dilute the resolutions and reduce the sample of reconstructed golden decays.

4.5 Background

The rates of various backgrounds have been studied in the proposal [29] and the rate of the background of direct J/ψ produced at the target has been investigated in Refs. [6, 7]. This type of background is the least reduced by trigger and reconstruction cuts. It is nevertheless not the most dangerous background, since the cross section is ‘only’ a few thousand times larger (σJ/ψ = 300–400 nb/nucleon as compared to e.g. the double semileptonic charm-decay cross section of 30 µb) and the decay cut is very effective in this case. Dangerous background is hadrons which are misidentified as muons, due to decay 0 in flight or punch-through in the muon chamber, and then combined with any KS to form a fake golden event. The total rate per year after all cuts is less than 10−6 [29]. The ratio of background over signal was found to be R<0.35 for muons and R<2 126 CHAPTER 4. THE GOLDEN DECAY cm )/ MC Z − d e t uc r nst o c e r Z (

Decay-length /cm

Figure 4.10: The Monte Carlo resolution of the reconstructed B decay vertex versus the decay length of the B. The type of events is B0 J/ψK0 ,whereJ/ψ e+e−. → S → 4.6. B FLAVOUR DETERMINATION 127

Table 4.5: Efficiencies for the golden decay reconstruction in the HERA-B experiment. The trigger efficiencies are taken from Ref. [64]. The geometrical acceptance for leptons from J/ψ is included in the trigger efficiency. The total main-tracker pattern-recognition efficiency includes tracking of the four particles from the golden decay (ℓ+ℓ−π+π−). Particle-identification efficiencies and efficiencies for pattern recognition in the VDS are introduced explicitly.

Summary on eﬃciencies for B0 J/ψK0 → S Channel J/ψ µ+µ− J/ψ e+e− → → First level trigger 55% 35% 0 Geometry for pions from KS 55% 55% Main-tracker pattern recognition 87% 87% J/ψ reconstruction 91% 92% 0 KS reconstruction 62% 62% B0 reconstruction 88% 56% Compatibility with main vertex 92% 87% Decay-length cut 57% 71% VDS pattern recognition 90% 90% Particle ID 94% 85% Total 5.7% 2.4%

for the electron channel in the most pessimistic case. According to the discussion in the proposal, the eﬀectiveness of the vertex cut is underestimated and therefore the rejection factor is an underestimate. The vertex cut is expected to clean the muon channel, while for the electron channel the background might be in the 10% range. To control the background, the decay-length cut must be adjusted. The internal background in the sample used in this analysis was 1.2 0.6% of the signal in the muon channel and 1.5 0.9% in the electron channel. T±he (internal) background can be reduced by optimizing± the cut on the distance of the tracks from the main vertex. This cut will hardly reduce the signal since a decay-length cut is applied in any case.

4.6 B ﬂavour determination

Information on the original flavour of the B meson decaying to the CP eigenstate 0 J/ψKS is needed in order to determine the CP asymmetry. The flavour can be determined from the other B hadron in the event, which is of opposite flavour. This B hadron is called the tagging B. Exclusive reconstruction of the tagging B has poor efficiency. The flavour of the tagging B can also be determined from the charge of the decay products, as illustrated in Fig. 4.11. The dependence of the charge on the B flavour is explained in Chapter 1, Section 1.2 and Fig. 1.3. The B hadrons decay semileptonically in 24% of all cases, which translates to ∼ 128 CHAPTER 4. THE GOLDEN DECAY

Same side tagging: e+ π+ 0 + B e- B** π+ - b + K0 π S π+ b Opposite side tagging:

B- K- D0 e-

Figure 4.11: A signature of a golden decay. The same-side tagging concerns the pions created in connection with the B which decays golden. The opposite-side tagging methods include a lepton from the semileptonic decay of the tagging B, a charged kaon from the decay of a secondary D meson, and the counting of charges from secondary vertices. a maximum tagging power of 0.49 for this method. The lepton tag is diluted by leptons from charm decays (b c ℓ), which have the wrong charge; • → → muons from kaon and pion decays; • photon conversion into an electron and positron pair; • particle misidentification. • The probability of a wrong tag, f , enters in the tagging power as P = D √ǫ,where D · D =1 2fD and ǫ is the efficiency of the tag. To r−educe this background, cuts have to be applied on the kinematics of the lepton and the distance to the B primary vertex and other primary vertices. The tag has been studied by D. Samtleben in Ref. [72], which will be referred to as S98. A final efficiency of 17% was obtained, and combined with the dilution the tagging power is 0.20. In a study by T. Lohse [73] the tagging power is 0.19. This study will be referred to as L97. A charged kaon is produced in 88% of the B decays. Randomly charged kaons from decays of frequently mixing Bs mesons or from secondary Ds decays dilute this tag. Similar cuts are applied on the kaon as on the lepton. The tagging power is found to be 0.15 in S98 and 0.21 in L97. There are two basic approaches for the conventional charge tag. In both approaches, charged tracks are selected which originate from a secondary vertex, that is, are of a certain distance from the B main vertex and other main vertices. To 4.6. B FLAVOUR DETERMINATION 129

reduce the influence from background, tracks with high momentum or transverse momentum will be given a larger weight. The total charge is a weighted sum of all selected charges: w q Q = i i i . w P i i In L97, the weight is the momentum ofPthe track. The efficiency is almost 100%. The dilution is high because even a small net charge will give a tag. This small net charge can come from a few small momentum tracks, which can originate from the main vertex. When the tagging B is neutral, there will also be no net charge and the charge tag is not applicable. The total tagging power is only 0.10. In S98, the weight 2 is the squared transverse momentum and a cut is applied at pTiqi 0.8toremove events with a neutral B and reduce the influence of background. The≥ efficiency of the tag is 38% and the total tagging power 0.22. P The flavour of the signal B can also be determined from the charge of particles which are produced together with the B and are strongly correlated in flavour composition. The production of excited states, which subsequently decays to Bπ is likely to account for some of the B production. The B∗ mass is too low (5.32 GeV) to decay to Bπ. The masses of the higher excited states B∗∗ can be calculated from HQET (Chapter 1, Section 1.1) and is found to be 5.8 GeV. A reconstructed pion from the main vertex of the golden decay, which f∼orms an invariant mass of 5.8 GeV with the B, is a candidate for a tag. The power of this tag depends strong∼ly on the rate of B∗∗ production, which is unknown. A charged pion with correlated flavour composition can also be produced in the fragmentation process as shown in Fig. 4.11. This pion is very difficult to identify in the hadronic environment and the tag is not likely to be very efficient. The information from the various tagging methods should be combined to give the highest possible statistical significance. One way of doing this is to divide the events in 13 classes of tag configurations. The classes represent all combinations of the three tags depending on whether they give a prediction on the flavour and if predictions from different tags agree or disagree. In the case that two or three tags disagree, the choice is determined such that the combined dilution of the class is positive. This is a natural choice since the dilution, D =1 2fD, is larger than zero for a correct, non-random tagging method. The 13 classes− are statistically independent and their statistical powers can be added in quadrature. In S98 the combined tagging power is 0.29 0.02 and in L97 it is 0.28. It is worth noting that although the individual powers±for the three tags on average are better in S98 than in L97, the final tagging powers are equal within the errors. The described method of combining the tags is not the optimal solution and is less optimal when the tags are of similar reliability, 2 as in S98. For example, the power of the charge tag depends on the size of pTiqi. A procedure to decide in each individual event which tag to believe would increase the tagging power. One way to solve the problem is the use of neural netPworks. Promising results are presented in a study by M. Langer in Ref.[74]. She obtains a total tagging power of 0.31 0.02 and there are still opportunities for improvements, in particular in the charge ±tag. 130 CHAPTER 4. THE GOLDEN DECAY

4.7 The precision of sin 2β Experimental and theoretical status The CDF measurement of sin 2β constrains contributions from new physics. Assum- ing CKM unitarity and Standard Model dominance in tree decays, the β angle can be constrained from the sides of the triangle [55]:

0 β π/6or5π/6 β 2π. (4.11) ≤ ≤ ≤ ≤ The constraint includes hadronic uncertainties. In particular it is assumed that V V 0.10. The 95% CL lower bound from CDF is | ub cb|≤ sin 2(β + θ ) 0, (4.12) d ≥ which constrains the new-physics contribution, θd [55]:

sin 2θ 0.87 at 95% CL on sin 2β. (4.13) d ≥− Using the one-sigma deviation of the mean from CDF, the bound is

sin 2θ 0.6 (4.14) d ≥− Within the Standard Model, the constraint on sin 2β from the CDF measurement is weak compared with the indirect bounds from measurements of V /V , ∆m | ub cb| B and ǫK. V /V measures one of the sides of the unitary triangle: | ub cb| V ∗ V ub ud = ρ¯2 +¯η2 . V ∗ V cb cd p

In the (ρ, η) plane, the constrai nts of the ratio are represented by two circles centred at origo. The ratio can be determined directly from inclusive semileptonic decays using the end-point analysis presented in Chapter 1, Section 1.2 and Ref. [26]. Vcb can also be determined separately from inclusive semileptonic decays and from the exclusive ∗ decay, B D ℓν, by the method described in Chapter 1, Section 1.1. Vub is measured by the Ca→bbibo-suppressed b u transition. 0 →¯0 ∗ The measurement of B B oscillations determines VtdVtb . This constrains the length of the other side of the− unitary triangle: | | V V ∗ td tb = (1 ρ¯)2 +¯η2 . (4.15) V ∗ V − cb cd p

This describes a circle in the ρ,¯ η¯ pla ne, with the centre at (ρ¯ =1, η¯ =0). Thetheo- retical uncertainties can be decreased by measuring the ratio to B B¯ oscillations. s− s At present only a lower limit on ∆mBs has been obtained. CP violation in K0 K¯ 0 mixing constrains the triangle as a hyperbola in the (ρ,¯ η¯) plane. − 4.7. THE PRECISION OF SIN 2β 131

_ 1 η 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 ρ_

Figure 4.12: The 95% CL for (ρ,¯ η¯). The boundaries from Vub/Vcb , ∆mB and ǫK , including experimental and theoretical uncertainties are sho|wn. The| theoretical parameters are scanned within the boundaries of the experimental results. The picture is from Ref. [35].

The present constraints from experimental measurements are displayed in Fig. 4.12 in the (ρ,¯ η¯) plane and in Fig. 4.13 in the (sin 2α, sin 2β) plane. Also shown are the theoretical boundaries, with the parameters scanned within the boundaries deﬁned by experiment. The overall results constrain the sin 2β parameter to

0.4 < sin 2β<0.8 (4.16)

Expected HERA-B contribution The statistical error on sin 2β is (Section 4.1)

1 K ∆sin2β = √1+R, P sNt0 · where P is the tagging power, K the statistical factor, N the total number of reconstructed signal events and R the ratio of background and signal. The statistical factor has been calculated in the analysis to be

K =1.6 0.1 ± for a cut at t0 =0.55, where t0 is measured in units of the average B lifetime, γτB. Without a cut on the target-vertex separation, the statistical factor is K0 3.1. With current methods, the combined tagging power for HERA-B is found≈to be P 0.3 (Section 4.6). R depends on the b¯b cross section, but is poorly known. It is ≈ 132 CHAPTER 4. THE GOLDEN DECAY

) 1 β sin(2 0.8

0.6

0.4

0.2

-0.2

-0.4

-0.6

-0.8

-1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 sin(2α)

Figure 4.13: The 95% CL for (sin 2α, sin 2β). Each contour is a 95% CL of theoretical calculations with a ﬁxed set of parameters. The parameters are scanned within the boundaries given by experimental results. The picture is from Ref. [35]. 4.7. THE PRECISION OF SIN 2β 133

set to 10% for the electron channel for the lowest cross section and neglected for the higher cross sections. The systematic error is estimated to be less than 0.05 [29]. Table 4.6 presents the number of events recorded during a running period of 107 s, which corresponds to one year. The number of events is given before and after the selection on the basis of the decay length.

Table 4.6: Statistics on the golden decay in one year, for three diﬀerent values of the b¯b cross section. The number of reconstructed decays is presented separately for the muon and electron channels and refers to the number of events before the decay- length cut. Selected events are those passing this cut. Background is only accounted for in the electron channel and is assumed to be negligible in the muon channel. The statistical error on sin 2β is presented, as well as the total error assuming a systematic error of 0.05.

σb¯b 12 nb 24 nb 36 nb N(produced B0 J/ψK0 ) 11 000 22 000 32 000 → S N(reconstructed events, J/ψ µ+µ−) 520 22 1038 44 1557 66 N(reconstructed events, J/ψ → e+e−) 187±11 374±22 561±33 → ± ± ± N(selected events, J/ψ µ+µ−) 307 17 613 34 919 67 N(selected events, J/ψ → e+e−) 129± 9 258±18 387±27 → ± ± ± N(background) + − R = N(selected B0→J/ψK0 ) (J/ψ e e ) 0.10 S → ∆sin2β (statistical) 0.20 0.02 0.14 0.01 0.117 0.003 ∆sin2β (total) ±0.21 ±0.15 ± 0.13 ∼ ∼ ∼

The errors on N reflect the size of the Monte Carlo sample used in this study. No other uncertainties were included in the calculation of the errors. The result means that to obtain an error on sin 2β of 0.1, which is sufficient for a 4σ measurement over the entire allowed CP parameter space, HERA-B has to run for one to four years depending on the size of the b¯b cross section. A 3σ measurement is likely to be achieved after one year of running. The presented numbers have to be viewed with regard to the obvious need of optimization in some aspects of the event-reconstruction process, for example in the 0 KS finding and the vertex reconstruction inside the magnetic field. In studies with a homogeneous magnetic field of 8 kG from z = 360 540 cm (equivalent to an integral of 2.2 Tm), the kaon-reconstruction efficiency −was 91% [6, 7]. A reasonable goal is to achieve the same with the inhomogeneous field. The main vertex of the B is not always reconstructed. This may be attributed to the fact that multiple scattering between the main vertex and the first point of the track is not yet taken into account in the covariance matrix of the track parameters. Earlier studies show that > 99% of the main vertices can be found in the muon channel and 96% in the electron channel [6, 7]. ∼ The decay length has not been well determined in the electron channel, due to 134 CHAPTER 4. THE GOLDEN DECAY bremsstrahlung effects. Including particle ID, the electron tracks can be refitted with bremsstrahlung correction and the decay-length cut applied properly. Chapter 5

Summary

HERA-B comes into operation during a period of transition for high-energy physics in Europe. The Large Electron-Positron collider (LEP) experiments are analysing their final data and the experiments around the Large Hadron Collider (LHC) are still being prepared. HERA-B is essentially alone in Europe in conducting precision tests of the Standard Model and operation under interaction rates and occupancies of the next-generation hadronic experiments. This thesis included a comparison of the situation with the B-factories at Stanford Linear ACcelerator (SLAC) and the High Energy Accelerator Research Organization in Japan (KEK), as well as with the experiments at LHC and at the Tevatron. HERA-B will be able to perform physics measurements during the construction phase, before the detector is completed. In this thesis, extensive studies on optimal geometries of a partial detector were presented. In the initial running a partial vertex detector and calorimeter are installed. For hardware and alignment reasons, the preferred initial layout of the available vertex-detector modules is a geometry which is suboptimal for a J/ψ trigger and physics measurements. It was shown that 50% more statistics can be achieved with a relatively simple modification of the layout. Three to four times more statistics can be achieved with an optimal geometry, which would require a reinstallation of the modules. Measurements of b¯b, J/ψ and Υ productions at HERA-B kinematics will give important insights into QCD models. The b¯b cross section is in addition a crucial parameter in the performance of B physics. Under the condition that the geometrical acceptance of the calorimeter matches that of the vertex detector, a b¯b cross section measurement can be carried out even with the suboptimal geometrical layout of the vertex detector. A minimal running period of about a month (106 s) is needed to collect sufficient statistics. It was observed that even with a reduced vertex-detector set-up and an algorithm which is not intended to be used for optimal parameter estimates, the pattern- recognition dilutions are quite well controlled, and the J/ψ from B decays can be separated from J/ψ originating from the main vertex. With a rudimentary detector, consisting only of a trigger on clusters in the 136 CHAPTER 5. SUMMARY calorimeter and tracking in the vertex detector, it is favourable to switch off the magnetic field. Bremsstrahlung inside a magnetic field will lead to photon depositions at a position in the calorimeter which differs from the position of the electron. This will lead to a smearing of the invariant-mass distribution. There will also be more combinatorics due to the charge ambiguity. As a result, the expected amount of statistics will be reduced by about 50% in the case of a magnetic field. A study on doubly semileptonic decays was presented. The study was made with the calorimeter and four complete vertex-detector superlayers and the magnetic field switched on. It was shown that the doubly semileptonic decays of b-hadrons can be separated from the doubly semileptonic decays of c-hadrons. The Outer Tracker (OT) superlayers are divided in two halves, to accommodate the holes for the beam pipes in a technically convenient way. An interesting situation during the production and installation of the OT modules appears when there are in the order of five halves of superlayers ready. These can then be positioned to constitute two whole superlayers covering the total geometrical lateral acceptance. The x side of a superlayer will be constructed and installed first for practical reasons. T−he x side superlayers cover a little more than half of the horizontal plane. If there is an− extra half-superlayer it will probably be a x side superlayer, therefore an extra half-superlayer will increase the acceptance and− tracking resolution for a little more than half of the tracks. Alternatively, the first superlayers can all be constructed as x planes and be positioned after each other along the beam. It was shown that−an OT geometry with the entire azimuthal acceptance gives about twice the statistics of a x side geometry. − If the vertex detector is only partially installed, the x side OT geometry provides a similar amount of statistics as the full-acceptance geo−metry. In such a situation, the x side geometry is preferred, due to the advantages it offers for pattern recognition a−nd alignment studies. A vertex-detector geometry was presented with an acceptance optimally matching the x OT acceptance. − A study on the reconstruction of the dimuonic decay of Υ quarkonium was presented. The x side geometry of the OT was assumed. Vertex information was used, but is less critica− l in the reconstruction of Υ, since no cut can be applied on the position of the decay vertex. Owing to the large invariant mass of the Υ quarkonium, the decay to two leptons provides a clean signal on top of the large hadronic background from the main vertex. 0 0 The golden decay, B J/ψKS, was simulated with available Monte Carlo techniques for HERA-B. Ea→ch golden decay was combined with a number of inelastic interactions. The number to combine was determined by Poisson statistics with a mean at four. The procedure results in realistic events resembling the situation at the time when HERA-B comes into full operation. The simulated event sample was reconstructed with available reconstruction tools. Monte Carlo information was only used in the track reconstruction in the vertex detector for the assignment of hits to particle trajectories. It was found that there is need for improvements in the vertex finding inside the magnetic field, in the main-vertex reconstruction and in the treatment of bremsstrahlung corrections of electron tracks. The total trigger 137 and reconstruction efficiency was found to be (5.7 0.3)% for the muon channel (J/ψ µ+µ−)and(2.4 0.2)% for the electron chan±nel (J/ψ e+e−). Including possible→ improvements, t±he total efficiency in the muon channel→will be about 9%. The efficiency depends on the choice of the decay-length cut. This choice is crucial for the rejection of background but not for the accuracy of the measurement. Depending mainly on the b¯b cross section, the precision on sin 2β was estimated to be 0.12 < ∆sin2β<0.20 in one year. This is sufficient for a measurement which will signify a value on sin 2β different from zero to a certainty of at least three standard deviations. HERA-B has a high potential for B physics including also Bs mesons. HERA-B will be able to measure not only the β angle but also the α and γ angles as well as the sides of the unitarity triangle. There are also various possibilities to find CP violation beyond the Standard Model and come a step closer to the riddle of matter–antimatter asymmetries in the universe. Acknowledgements

I used to say that I did not have any interests. There were many things I liked to do, certainly, but they were not special enough to call them interests. Then I had this urge for knowledge about reality; a self-nutrifying hunger for insight into the laws and essences of the world, nature and universe, which are in fact only three words for the same unexpressable everything. This obsession was far too fundamental in me to ever occur to me as being an interest. I did not call it physics until I had to decide what to do after school. Even then I did not know in which branch of physics my needs could be best satisfied. I was searching my way to where I belong. In this searching I am filled with warm gratitude to my parents who gave me my psychological freedom, which illuminates my life, and my secure background as a stable platform necessary for this freedom to blossom and be able to play freely. Particle physics is a big world with many interplayers and much fighting for one’s own importance. At least it appears so to a newcomer who does not know the rules of the game. It is certain that I would not have had the strength to go on and find my position in this maze without the support of good friends. I am thinking of Jan-Erik and Asa˚ , in particular Jan-Erik’s all wise words about universities and scientists. When something upset me he had already seen worse examples and managed to convince me that I could take it (and more). Both he and As˚ a thought much better of me than I deserved and this helped me enormously to break through into this world. The breakthrough of which I am speaking is of course the coming to CERN. I want to mention Lennart Samuelsson and Mattias Severin at Linköping University who helped me to be accepted that summer of 1993. Here, for the first time, I met people who were thinking like I about the unexpressable everything. Here I saw for the first time the colourful, flourishing transparencies of Cecilia Jarlskog. She has been an invaluable source of knowledge. I am very happy for all she has given me. It was encouraging to learn that I was welcome to continue contributing to particle physics. Of great importance were my supervisor there, Marcio Nessi, and Ana Henriques Correia and the portuguese group in ATLAS where I worked. Important were also (and still are) the group in Copenhagen who were sorry that a Swede could not get a PhD position in Copenhagen at that time for bureaucratic reasons (and as a matter of fact managed to change the rules shortly afterwards). I would like to thank my supervisor Torsten A˚kesson who helped me to transform my work at 139

CERN into a diploma thesis and who put faith in me and even built a bridge over the dark uncertainty between that stay at CERN and the PhD position in Lund. I thank him for always believing in me and making me a soldier of physics and for making me believe that I am able to make good contributions to science and helping me to construct a thesis with his support, ideas and good advice. After my first years in the ATLAS collaboration, I switched to HERA-B and moved my activities to DESY Zeuthen. The hospitality of the DESY Zeuthen institute and the HERA-B group led by Hermann Kolanoski during these three years I regard as quite remarkable. For my direct work, the friendliness and helpfulness of everybody in DESY Zeuthen has been most valuable and made my stay there a very pleasant one, of which I will always have fond memories of. I am thinking not only of the HERA-B software group and my ambassadors Michael Walter and Hermann Kolanoski, but also other physicists in the institute as well as the people who provide the computing power, in particular Thorsten Kleinwort and his support on the PC-farm. And what would the institute have been without the theory group? Thank you Jochen for always being there a staircase up, prepared to greet me with a smile whenever I needed one. The DESY Zeuthen institute maintains a close collaboration with the Humboldt University in Berlin. I have felt equally welcome also in that group thanks to the generosity of Thomas Lohse and Rainer Mankel. My very special thanks go to Rainer Mankel who has been very important to me in my work and in my presentation of it in meetings and in internal notes. In the spirit of these days, I would like to nominate him as ‘the colleague of the century’, if such a distinction exists. Students in the particle physics department in Lund have a marvellous way of maintaining a sort of solidarity in spite of distances in time and space. For me, in particular, the friendships of Ulrik Egede, Elisabeth Falk Harris and Oxana Smirnova have been valuable during the whole time. For valuable help in specific parts of the thesis I thank Thomas Lohse for provid- ing the pictures to the chapter about the Monte Carlo generator; Fedor Ratnikov, Joachim Flammer, Sören Schmidt, Stefania Xella and Stefan Scarein for information concerning the trigger; and Alexander Somov for his collaboration on the Υ studies. Torbjorn¨ Sjost¨ rand has been of great help on the physics of heavy-flavour production and its implementation in the Monte Carlo generators. Torsten A˚kesson, Göran Jarlskog and Oxana Smirnova have been friendly to read and comment my thesis. Richard Cook was proofreading the english text. And by the way, the poem in the preface was reviewed by Iris Abt. This work was supported financially by the Swedish Natural Science Research Council, Svenska Institutet and Fysiografiska Sa¨llskapet. I got some interests as a souvenir of this journey towards my PhD. One point I want to make concerns people and the impact of culture on individuals. The cultural differences between countries in Europe are quite vague but the sheer number of them makes it very interesting to travel and work in various places. The other point is due to the effect that Jan-Erik expressed once in a very nice way. It is about that glorious halo that a young fresh student can see dangling above the world of science. This halo has broken, as it does when you get too close to a saint. But it is because 140 CHAPTER 5. SUMMARY of this broken halo that also physics has turned into a burning interest of mine. I would like to finish by thanking nature itself with some cryptic words in my own language:

Ja kante ta en kvark Ja kante ta en kraft Ja hante f˚att ork ma¨t heller

Ja kante samℓein Ja kante ra¨kne ut Ja hante f˚att ti ma¨t heller

Föℓääs˚a stort o pyttesm˚att ma¨ ˚a ℓä finns ej pℓats darop¨ pe for¨ aℓℓtda¨

Ja kante ta en o¨ Ja kante ta en sjo¨ Ja kante ta skogen heller

Ja kante ta en hind Ja kante ta en lind Ja kante ta livet heller

V˚aran jord as¨ toroka¨ℓeken mä ˚a ℓä finns ej rum i hjärtat for¨ aℓℓtda.¨

Ja kante kℓejve in Ja kante skrejve ner Ja kant’ a¨te oppet heller

Ja kante famne om Ja kante m˚aℓeav Ja ser p˚a, ˚a ℓää vackert s˚a ℓävärker. Appendix A

Kalman ﬁlter

In several places at the track reconstruction in HERA-B, the Kalman-filter technique is used for progressive parameter estimates. Kalman filtering is a fast progressive fit adopting the least squares method. The Kalman filter predicts the position of the next hit using the known track parameters and their covariance matrix at the current step. The filtering is the update of track parameters and the covariance matrix from the new measured hit. The quality of each step is calculated from the χ2 contribution.

After initialization of the track parameters, the Kalman ﬁlter follows the track step by step from one hit to the next. In this way, pattern recognition and track reconstruction are performed in parallel.

Detailed information about Kalman ﬁltering can be found in Ref. [77]. The basic principles are presented here. The nomenclature of the algebraic description is as follows: 142 APPENDIXA. KALMAN FILTER

x¯k The state vector (for example the track parameters), at the step k, including k measurements.

Ck The covariance matrix of state vector x¯k.

Fk Matrix or function describing the propagation of track parameters from k 1tok. − Ak Matrix or function describing the updating of track parameters from k +1tok (smoother).

mk The coordinate measured at the step k. mk can be a vector of parameters or just a number.

Vk The error of the measurement mk.

Hk Matrix or function describing the projection of xk on the coordinate expected to be measured at the step k.

Qk Process noise, for example multiple scattering.

rk Residual. The diﬀerence between the estimated and measured coordinate.

Rk The covariance matrix of the residual rk.

Kk Gain matrix. The matrix which contains the updating information. It relates the error of the measurement to the error of the prediction (the error at the previous state).

The projection Hk is a matrix in a linear system like for example MSGC and silicon devices. In Honeycomb Drift Chamber devices, where the wire information is supplemented by a drift time, the projection is a slightly nonlinear function. The transport Fk is a matrix in a linear system and a function in a nonlinear system like in the presence of a magnetic ﬁeld. In the following, Hk and Fk will be treated as matrices. The procedure is illustrated in Fig. A.1. The incorporation of another hit in the track reconstruction follows essentially the ﬁve steps below. 1. A prediction of the track parameters at the next step k is calculated from the present state using the track-model Fk: ′ ′ T x¯k = Fkx¯k−1 Ck = FkCk−1Fk + Qk . (A.1)

Qk contains random perturbation of the trajectory, like multiple scattering and energy losses, dE/dx.

2. Measurements mk within a region determined by x¯k and Ck are searched for. For every measurement, the residual rk is estimated: r′ = m H x¯′ R′ = V + H C′ HT . (A.2) k k − k k k k k k k 143

layer k k-1 k-2 k-3

a mk-3 mk-2 particle m mk-1 trajectory k b mk-2

Filtering direction

Figure A.1: Illustration of a Kalman Filter. The cones represent the ﬁltered values and the predictions of the next point. The measured points mi are denoted together with their errors. The transported parameter is the weighted mean of the measured and the predicted points. After each step, the precision is improved, as shown by the narrower cones.

In HERA-B, most tracking devices measure only one coordinate, so that mk and Vk are just numbers. 3. Filtering. The system state vector is updated.

′ T ′ T −1 Kk = CkH (Vk + HkCkHk ) , (A.3)

x¯ =¯x′ + K (m H x¯′ ) C =(1 K H )C′ . (A.4) k k k k − k k k − k k k

4. The χ2 contribution of the new ﬁltered hit is calculated from the ﬁltered residual: r =(1 H K )r′ R =(1 H K )V (A.5) k − k k k k − k k k and 2 T −1 χk = rk Rk rk . (A.6)

5. There is also a smoother process, which means that the information from the last ﬁltered hits are propagated backwards to make information from all points available also at previous hits.

T −1 Ak−1 = Ck−1Fk (Ck) , (A.7)

x¯n = x + A (¯x x¯′ ) Cn = C + A (C C′ )AT , (A.8) k−1 k−1 k−1 k − k k−1 k−1 k k − k k 144 APPENDIXA. KALMAN FILTER

r = m H x¯n , (A.9) k−1 k−1 − k k−1 Rn = R H A (C C′ )AT HT . k−1 k−1 − k−1 k−1 k − k k−1 k−1 This last step is iterated backwards for all points of the track. The smoother is only useful if the full state vector is needed at every point of the trajectory. If there is more than one hit, which is consistent with the prediction at the ﬁrst step, the hit with the smallest χ2 contribution is selected. An alternative solution is to split the track and follow several candidates until the fake ones can be rejected at later steps. In this local procedure, the full information of the trajectory is only available after the calculation of the parameters at the last measured point. For track reconstruction in a hadronic environment with the order of hundred tracks per event, there are essential advantages over global methods, where the track parameters are determined at all points in parallel.

In the prediction step, noise signals and hits from other tracks are discarded • from the fit. The influence of random perturbation is accounted for in a very efficient way, • by introducing an additional covariance term, Q, in the prediction step. The calculation time is smaller. In the filter step, there is an inversion of a • matrix with the dimension of the measurement, which in many cases is just a number. In a global fit the update requires an inversion of a matrix with the dimension of the state vector. The computation of the χ2 contribution for each hit makes the selection between • several candidates possible without having to reconstruct the whole track. This is important at high track densities. Different tracking devices with different resolutions, materials and different • ways of obtaining the coordinates can be combined in a relatively uncomplicated way. Bibliography

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[2] T.Lohse,R.Mankel,Detector optimization for the 1998 physics run, HERA-B 97-148, talk presented on the PRC meeting, 24 July, 1997.

[3] T. Lohse, Update on 1998 physics with HERA-B HERA-B 97-244, talk presented at the PRC–Referee meeting, 28 November, 1997.

[4] R. Mankel et al., HERA-B physics options in the 1998 run, HERA-B 98-132 (1998). J. Ivarsson, Prospects of measuring the b¯b cross section in the J/ψ channel with the HERA-B 98 detector conﬁguration, HERA-B 98-143 (1998).

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