Advanced Topics in Particle Physics
Probing the High Energy Frontier at the LHC
Ulrich Husemann, Klaus Reygers, Ulrich Uwer Heidelberg University Winter Semester 2009/2010
Summary: Factorization
The full picture:
" ...
2 f(xi,Qi ) σˆ Jet ... Jet
σ = dx dx f (x , µ2 ) f (x , µ2 ) σˆ (x x s, µ2 , µ2 ) ⊗ Hadronization QCD j k j j F k k F · j k F R jk Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 4 2 Summary: Scales
Two new energy scales introduced as “artifacts” of QCD renormalization & factorization procedures after T. Plehn, arXiv:0910.4182 Plehn, T. after
Renormalization Scale μR Factorization Scale μF
Source: UV divergence Source: collinear IR divergence
Reference scale for running Separation of long-distance 2 2 coupling αS(μR ) physics into PDFs fi(xi, μF )
Resummation of QCD vacuum ! Resummation of parton splitting [hep-ph] polarization loops → DGLAP equations → RGE for αS
Numerical result of perturbative calculation changes as function μR und μF , but physics is scale independent
Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 4 3
Overview
Today’s program: Fragmentation and hadronization Monte Carlo generators Jets at hadron colliders Literature: Ellis et al.: Jets in Hadron-Hadron Collisions Sjöstrand, Mrenna, Skands: Pythia 6.4 Physics and Manual, JHEP 05 (2006) 026 Blazey et al.: Run II Jet Physics, hep-ex/0005012 Salam: Jets, Lecture at the 2008 CTEQ-MCnet Summer School
Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 4 4 Chapter 4
Basics of Hadron Collider Physics
Parton Luminosity
Rewrite factorization ansatz Example: gg Parton Luminosity τ dL (note: plots shows jk ) Partonic cross section: strong sˆ dτ CTEQ6L1: gg dependence on available 106 center of mass energy 105 104 " = xjxks → decrease with 1/" 103 102 Product of PDFs: depends only 101 0 0.9 TeV 10 2 TeV on energy fractions, define 10-1 4 TeV 6 TeV -2 scaling parameter 10 7 TeV -3 Parton Luminosity [nb] 10 10 TeV 14 TeV sˆ 10-4 τ = xj xk ≡ s 10-5 10-6 10-2 10-1 100 101 Introduce (dimensionless) [TeV] “parton luminosity” Ljk via Quigg: arXiv:0908.3660v2 [hep-ph] 1 dσ dLjk dLjk dx 2 τ 2 = σˆ jk with = f (x, µ ) f , µ dτ dτ · dτ x j F k x F jk τ Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 4 6 From Partons to Jets
Strong interactions: pT range of Dijet Production at LEP: hadrons w.r.t. initial parton + e e− Z qq¯ limited → → Run:event 4093: 1000 Date 930527 T ime 20716 Ct rk(N= 39 Sump= 73.3) Ecal (N= 25 SumE= 32.6) Hcal (N=22 SumE= 22.6) Ebeam 45.658 Evis 99.9 Emiss -8.6 Vtx ( -0.07, 0.06, -0.80) Muon(N= 0) Sec Vtx(N= 3) Fdet(N= 0 SumE= 0.0) Expect jets = bundles of particles Bz=4.350 Thrust=0.9873 Aplan=0.0017 Oblat=0.0248 Spher=0.0073 at high energies First observation of jets in e+e– collisions with ECMS > 6 GeV (SPEAR, SLAC, 1975) Later also observed in hadron- hadron collisions (e.g. CERN ISR)
Y Goal: infer parton properties X Z
from jet properties 200. cm. 5 10 20 50 GeV Centre of screen is ( 0.0000, 0.0000, 0.0000) → calculate and/or model fragmentation & hadronization Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 4 7
From Partons to Jets
Hadronization & Decay
Parton Shower Hard Scattering Incoming Proton Incoming Proton
Underlying Event
[T. Gleisberg et al., JHEP02 (2004) 056] Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 4 8 From Partons to Jets
Steps from partons produced in hard Fragmentation subprocess to color neutral hadrons: Fragmentation: partons can split into other partons (“parton shower”) → QCD: resummation of leading logarithmic contributions Hadronization: parton shower forms hadrons → non-perturbative, only Hadronization & Decay models Decay of unstable hadrons → pert. QCD, electroweak theory In practice: all of the above handled by Monte Carlo (MC) simulations
Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 4 9
Sudakov Form Factor
Parton shower related to DGLAP equation:
Probabilities of parton splitting (recall splitting functions Pji for splitting of parton j from parton i) zp Pqq p (1 z)p − Solution of DGLAP equation: “Sudakov form factor” t 1 dt αS ∆i (t) = exp dy Pji (y) − t 2π j t0 0 Interpretation: integrated probability for a parton not to split Poisson probability as an analogy n ν ν e− ν (n; ν)= (0; ν)=e− P n! → P Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 4 10 Sudakov Form Factor
Eb Evolution parameter t in Δi(t): simplest choice parton virtuality t Ea Ec Final state showers (after hard scattering) are timelike: propagators with p2 > 0 Eb Ea 2 t pa 2EbEc(1 cos θ) > 0 ≡ ≈ − Ec Initial state showers (before hard t, E scattering) are spacelike: p2 < 0 2 timelike
t p 2E E (1 cos θ) < 0 spacelike ≡ b ≈− a c − t0: radiated partons get too soft, shower unresolvable → cut-off for x, p parton shower evolution (# 1 GeV)
Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 4 11
Sudakov Form Factor
Sudakov picture of parton shower well suited for MC simulations Basic algorithm (Markov chain: each step requires only knowledge from previous step)
Start from virtuality t1 and momentum fraction x1
Generate target virtuality t2 with random number Rt ∈ [0,1] ∆(t2) = Rt (probability to evolve from t1 to t2 without radiation) ∆(t1)
Generate target momentum fraction x2 with Rx ∈ [0,1]
x2/x1 αS 0 dz 2π P(z) = Rx 1 αS 0 dz 2π P(z)
Generate random azimuthal angle with Rϕ ∈ [0,2$]
Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 4 12 Parton Shower MC
Physical picture: parton shower = resummation of all leading logarithmic emissions (“leading log” showers) Main MC packages with leading log parton showers Pythia: http://home.thep.lu.se/~torbjorn/Pythia.html Herwig: http://hepwww.rl.ac.uk/theory/seymour/herwig/ Different choices for evolution variable Pythia 6.2 and earlier: virtuality t = p2 → need to insert correction to suppress soft gluon emission by hand (“angular ordering”)
2 2 Pythia 6.3 and newer: relative pT = p z (1–z) → angular ordering ensured automatically Herwig: explicit angular ordering by E2 (1–cos θ) Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 4 13
Hadronization Models
Non-perturbative transition from partons to hadrons → rely on phenomenological models Models based on MC simulations very successful: Generation of complete final states: can be used for by experimentalists in detector simulation Caveat: tunable ad-hoc parameters Most popular MC models: Pythia: Lund string model (no connection to string theory!) Herwig: Cluster model
Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 4 14 Independent Fragmentation
Simplest approach: independent fragmentation of each parton (Field, Feynman, Nucl. Phys. B136 (1978) 1) 4 R.D. Field, R.P. Feynman/A parameterization of the properties ofquark]ets Start with original quark "HIERARCHY" OF FINAL MESONS
Generate quark-antiquark :5 3 2 I I = RANK pairs from the vacuum (af) (rc) (cb) (Be) (~'G) l V SOME "PRIMARY" →!form “primary meson” with MESONS DECAY energy fraction z V 3 2 I = RANK (ac) (~b) (Bo) Continue with leftover quark "PRIMARY" MESONS with energy fraction 1–z Stop at lower energy cutoff Non-perturbative “fragmentation function” D(z): ORIGINAL QUARK probability to find hadron OF FLAVOR "o" with energy fraction z inFig. jet 1. Illustration of the "hierarchy" structure of the final mesons produced when a quark of type "a" fragments into hadrons. New quark pairs bl~, cc-, etc., are produced and "primary" Probing the High Energy Frontier at the LHC,mesons Heidelberg are formed. U, The Winter "primary" Semester meson ba 09/10,that contains Lecture the original 4 quark15 is said to have "rank" one and primary meson c'b rank two, etc. Finally, some of the primary mesons decay and we assign all the decay products to have the rank of the parent. The order in "hierarchy" is not the same as order in momentum or rapidity.
The "chain decay" ansatz * assumes that, if the rank-1 primary meson carries away a momentum ~1 (from a quark jet of type "a" and momentum I¢o) the remain- ing cascade starts with a quark of type "b" with momentum Ig I = Wo - ~1 and the remaining hadrons are distributed in exactly the same way as the hadrons which come from a jet originated by a quark of type "b" with momentum lg I . It is further Stringassumed Model that for very high momenta, all distr~utions scale so that they depend only on ratios of the hadron momenta to the quark momenta. Given these assumptions, complete knowledge of the structure of a quark jet is determined by one unknown function f(r/) and three parameters describing flavor, primary meson spin, and Lund string model transverse momentum to be discussed later. The function f07) is defined by (Andersson et!al., Phys. Rept. 97f(r/) d,/=(1983) the probability 31) that the first hierarchy (rank-l) primary meson 4 α (1/r 2) leaves the fraction of momentum 77 to the remaining cascade, (2.1) QCD potential V (r)= S + kr −3 r * We believe this recursive principle was first suggested by Krywicki and Petersson [6] and by → large r: tension of “colorFinkelstein string” and Peccei [7] in an analysis of proton-proton collisions. String formation between initial quark-antiquark pair String breaks up if potential energy large enough: new quark-antiquark pair(s) Gluons = “kinks” in string
Energy low enough: hadron formation [after: Ellis et al., QCD and Collider Physics] Very widely used: default in Pythia
Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 4 16 Cluster Model
Cluster model (Webber, Nucl. Phys. B238 (1984) 492) Color flow during hadronization confined: mainly low-mass connections → formation of color-neutral clusters of partons Gluons (=color-anticolor) split to quark-antiquark pairs Clusters decay according to phase space (i.e. isotropically) → no free tuning parameters [after: Ellis et al., Widely used: default in Herwig QCD and Collider Physics]
Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 4 17
Intermezzo
Monte Carlo Generators Overview MC simulations Monte Carlo simulations = in particle physics numerical methods based on Event Generator: random numbers simulate physics process (quantum mechanics: probabilities!) MC methods very powerful in particle physics Detector Simulation: Event generation: hard partonic simulate interaction with subprocess + fragmentation/ detector material hadronization (many programs, most popular: Pythia, Herwig) Digitization: Detector simulation: translate interactions with detector into realistic signals interactions of all outgoing particles in matter Reconstruction/Analysis: as for real data
Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 4 19
MC Generator Classes
Pure matrix element (ME) generators MC integration of cross section & PDFs, no hadronization (recall: cross section = |matrix element|2 ⊗ phase space) Useful for theoretical studies, no exclusive events generated Example: MCFM (http://mcfm.fnal.gov) → many LHC processes up to NLO Event generators: combination of ME and parton showers Typical: generator for leading order ME combined with leading log (LL) parton shower MC (more on NLO generators later) Exclusive events → useful for experimentalists Most prominent examples: Pythia, Herwig
Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 4 20 Event Generator Types MC tools for top physics in a nutshell
ME+PS Type I: leading order matrix element + leading log parton shower HerwigPythia HerwigPythia LO ME for hard processes (2→1 or 2→2) SingleTop, TopRex Phantom p1 p1 p3 AcerMC GRAPPA p 3 CompHEP ME+PS+merging p2 p2 p4 Alpgen PS: resummation of leading logarithms MadGraph Examples: Pythia, Herwig Sherpa LHC: large data samples NLO+PS → more sophisticated MC approaches MC@NLO POWHEG [F. Maltoni] TOP2008 Elba, Italy ! ! ! ! ! ! ! ! ! ! ! ! ! Fabio Maltoni! Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 4 21
Event Generator Types
Type II: LO ME + PS + merging p1 p3
MEs for 2→n processes (e.g. W/Z + jets) p4
p5 PS with LO generator (Pythia or Herwig) ... Examples: ALPGEN, MadEvent, Sherpa p2 pn+2 Challenge: remove overlap between jets from ME and jets from parton shower (MLM matching, CKKW) Z+2 Partons Z+ 1 Parton + Splitting g q q g + g g Overlap? Z Z q¯ q¯
Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 4 22 Event Generator Types
Type III: Next-to-leading order (NLO) ME + PS Hard process simulated to NLO accuracy (real & virtual corrections) → improved description of cross sections & kinematic distributions Mechanism to remove phase-space overlap between jets from NLO ME and leading log PS: subtraction of parton emissions from PS that are already generated in hard process at NLO Fairly recent development but heavily used at ATLAS & CMS Examples: MC@NLO (since 2002), POWHEG (since 2007)
Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 4 23
GEANT
GEANT = GEometry And Geant4 ATLAS Geometry Tracking (cut-away view) Detailed description of detector geometry (sensitive & insensitive volumes) Tracking of all particles through detector material → detector response Visualization tools
Developed at CERN since [http://geant4.kek.jp/~tanaka/GEANT4/ATLAS_G4_GIFFIG/] 1974 (FORTRAN) Today: Geant4 (C++) Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 4 24 Chapter 5
Jets at Hadron Colliders
Jet Algorithms
Goal: infer properties of quarks & gluons from jets Theoretical considerations Unknown momentum fractions of colliding partons → unknown boost of final state Quarks/gluons are colored, jets are color-neutral → no exact assignment of jets to partons Experimental considerations: Interactions of additional partons in beam hadrons (“underlying event”) → additional activity in detector LHC at design luminosity: approx. 25 simultaneous interactions in a single bunch crossing (“pileup”)
Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 4 26 A Jet is (not) a Jet
Different “levels” of jets Parton-level jet: used in perturbative QCD calculations →!“theory jets” Particle-level jet: reconstruct jet from bundle of hadrons Calorimeter jet: form jet out of clusters of energy depositions (purely experimental)
Goals for jet algorithms: Independent of jet level, invariant under final state boosts
[CDF] Comparison with theory: IR safe Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 4 27
Jets (p. 8) A Jet is (not) a Jet Introduction Jets as projections Background Knowledge Robust jet definition → stable on all jet levels
! ! p " K
LO partons NLO partons parton shower hadron level
Jet Def n Jet Def n Jet Def n Jet Def n
jet 1 jet 2 jet 1 jet 2 jet 1 jet 2 jet 1 jet 2
[Salam:Projection Jets, Lecture to jets at should 2008 be CTEQ-MCnet resilient to Summer QCD eff ectsSchool]
Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 4 28 Classes of Jet Algorithms
Iterative cone algorithms: jet Jet Cones in (y,ϕ) Space defined as energy flow ࢥ R within a cone of radius R in R (y,ϕ) or (η,ϕ) space: Jet 2 Jet 1 R = (y y )2 +(φ φ )2 − 0 − 0 y Sequential recombination Sequential Recombination Step 1: 4 algorithms: 1 5 2 6 Define distance measure dij 3 Step 2: 4 Calculate dij for all pairs of 1 particles, combine particles 2 56 3 with minimum dij below cut 4 Step 3: 12 Stop if minimum dij above cut 56
3 Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 4 29
First Comparison “By Eye”
Different jet algorithms → different results
Cone Algorithm (R=1) Recombination Algorithm (R=1)
[Cacciari, Salam, Soyez, JHEP 04 (2008) 063]
Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 4 30 ET and b) a seed is removed from the seed list section, has a boundary that is sensitive to the when it is within a jet found using a seed that number of particles present and their relative an- is higher on the list. For such an algorithm con- Infraredgle (i.e., the boundary Safety is sensitive to the mass of max sider the configuration illustrated in Fig. 3. The the jet). The bound ET = √s/2appliesonly difference between the two situations is that the for collinear particles and massless jets. In the central (hardest) parton splits intoJets two almost and divergencescase of massive jets the boundary for ET is larger collinear partons. The separation between the than √s/2. Boundary stability is essential in or- two most distant partons is more than RQCD:but less IR divergencesder to perform due soft to gluon soft/collinear summations. emission of partons than 2R. Thus all of the partons can fall within asingleconeofradiusR around the centralExperiment: par- 5. allOrder jet Independence: energies Thefinite algorithm should find ton(s). However, if the partons are treated as the same jets at parton, particle, and detector seeds and analyzed with the candidate algorithm level. This feature is clearly desirable from the suggested above, different jets will beCompare identified experimentstandpoint and of both theory: theory and experiment.jet algorithms to be in the two situations. On the left, whereapplied the sin- both 6.forStraightforward parton level Implementation: and experimentalThe algorithm jets gle central parton has the largest E→T ,asingle IR safety importantshould be straightforward requirement to implement in per- jet containing all three partons will be found. In turbative calculations. the situation on the right, the splitting of the central parton leaves the right-most partonExample: with certain cone algorithms and soft gluon emission the largest ET .Hencethisseedislookedatfirst and a jet may be found containing only→ the two right- cones merge due to soft gluon: not IR safe most and two central partons. The left-most par- ton is a jet by itself. In this case the jet number changes depending on the presence or absence of acollinearsplitting.Thissignalsanincomplete cancellation of the divergences in the real and vir- tual contributions to this configuration and ren- ders the algorithm collinear unsafe. While the al- [Blazey et al., hep-ex/0005012] gorithm described here is admittedlyProbing an extremethe High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 4 31 case, it is not so different from some schemes used in Run I. Clearly this problem should be avoided by making the selection or ordering of seeds and Figure 1. An illustration of infrared sensitivity in cone jet clustering. In this example, jet clustering be- jet cones independent of the ET of individual par- ticles. gins around seed particles, shown here as arrows with length proportional to energy. We illustrate how the 3. Invariance under boosts: The algorithm should presence of soft radiation between two jets may cause a find the same solutions independent of boosts in merging of the jets that would not occur in the absence the longitudinal direction. This is particularly of the soft radiation. important for pp collisions where the center-of- mass of the individual parton-parton collisions is Cone Algorithms typically boosted with respect to the pp center- of-mass. This point was emphasized in conversa- 2.2. Experimental Attributes of the Ideal tions with the Jet Definition Group LesBasic Houches algorithm: [ Algorithm search for all stable cones 7].1 Once jets enter a detector, the effects of particle Assign partonshowering, if distance detector response, from cone noise, andcenter energy (y fromC,ϕC) is % R: 4. Boundary Stability: It is desirable that the kine- additional hard scatterings from the same beam cross- matic variables used to describe the jets exhibit 2 2 ∆ingiC will= subtly(y aiffecty theC ) performance+(φi ofφ evenC ) the mostR kinematic boundaries that are insensitive to the ideal algorithm.− It is the goal of− the experimental≤ details of the final state. For example, theTypical scalar choicegroups for to correct cone for size: such eRffects = 0.4, in each R= jet 0.7, analysis. R = 1.0 ET variable, explained in more detail in the next Ideally the algorithm employed should not cause the 1The Les Houches group discussed jet algorithms for both the corrections to be excessively large. From an “experi- Recalculate cone center: p = (Ei , pi ) (y , φ ) Tevatron and LHC, and they sharpened their algorithm re- mental standpoint” we addC the following criteria→ C for aC quirements by also requiring boundary stability (the kinematic desirable jet algorithm: i C boundary for the one jet inclusive jet cross section should beat ∈ the same place, ET = √s/2, independent of the numberIterate of fi- until cone is stable: (yC’,ϕC’) = (yC,ϕC) nal state particles), suitability for soft gluon summationsofthe 1. Detector independence: The performance of the theory, and simplicity and elegance. algorithm should be as independent as possible Seeding: 4 Ideal case: seedless search → try all possible seeds In practice: seedless search too slow, start with seed (e.g. all calorimeter towers with ET > 1 GeV) → IR unsafe
Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 4 32 Cone Algorithms
Seeded cone algorithms IR unsafe but heavily used at the Tevatron (e.g. CDF JETCLU) → refinements Refinements of simple cone algorithm Ratcheting: once a calorimeter cell is part of a cone it is never removed (even if it is outside the cone radius) Split/merge: jets with overlapping cones are merged if they share at least 75% of the energy, others are kept separate Seed cones: search for stable cones with radius R/2, final jets with radius R Midpoint algorithm: always add additional seeds half-way between two seeds → IR safety improved Recently: seedless IR safe cone algorithm “SISCone”
Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 4 33
Recombination Algorithms 2E E JADE algorithm: d = i j (1 cos θ ) ij Q2 − ij Distance measure: invariant mass of pair Used in early e+e– experiments (e.g. PETRA) Clusters all low-energy particles first → not ideal for parton reconstruction Cambridge/Aachen algorithm: ∆Rij d = d =1 with ∆R = (y y )2 +(φ φ )2 ij R iB ij i − j i − j Find dmin of all dij and diB (distance to beam pipe)
If dmin = diB: jet found → remove from list, else merge particles i and j by adding their 4-momenta Repeat until no particle is left
Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 4 34 Recombination Algorithms
2p 2p ∆Rij 2p General kT algorithm: d = min k , k diB = k ij T ,i T ,j R T ,i Weight distance with power 2p of transverse momentum kT p = 0: Cambridge/Aachen algorithm
p = 1: kT algorithm → cluster neighboring particles with most similar kT first → may “vacuum in” underlying event and pileup activity
p = –1: anti-kT algorithm (new ATLAS default) → cluster all soft particles around hard particle first → jets = perfectly round cones
All kT algorithms: IR safe Naïve implementation: computationally expensive → faster implementation in FastJet package
Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 4 35
but the intrinsic theoretical uncertainty is larger. Correspondingly the jets identified by the algorithms vary if we compare at the perturbative, shower, hadron and detector levels. Thus it is essential to understand these limitations of jet algorithms and, as much as possible, eliminate or correct for them to approach our percent level goal. It is the aim of the following review to highlight the issues that arose during Runs I and II at the Tevatron, discuss their current understanding, and outline possible preventative measuresComparison for the LHC [6]. on CDF Event
[Ellis et al., Jets in Hadron-Hadron Collisions] Figure 4: ImpactProbing the of High diff erentEnergy jet Frontier clustering at the LHC, algorithms Heidelberg on U, anWinterinteresting Semester 09/10, CDF Lecture event 4 taken36 in Run II. The segmentation in η and φ shown the lego plot corresponds to the calorimeter segmentation. Energy depositions in the electromagnetic portion of the calorimeter are colored red and those in the hadronic section are colored blue. The numbers in the figure are transverse momenta of the jets pointed to by the arrows, and different colors represent jets clustered by different algorithms.
3Jets:PartonLevelvsExperiment
3.1 Iterative Cone Algorithm 3.1.1 Definitions To illustrate the behavior of jet algorithms consider first the original Snowmass implementation of the iterative cone algorithm [9]. The first step in the algorithm, i.e., the identification of the sublists of objects corresponding to the jets, is defined in terms of a simple sum over all (short distance or long distance) objects within a cone centered at rapidity (the original version used the pseudorapidity 1 θ η = 2 log(cot 2 )) and azimuthal angle (yC , φC). Using the objects in the cone we can define a pT -weighted centroid via
2 2 k C iff (yk yC) +(φk φC ) Rcone, ⊂ ! − − ≤ k⊂C yk pT,k k⊂C φk pT,k yC · , φC · . ≡ " l⊂C pT,l ≡ " l⊂C pT,l " " 7 11 Summary of Systematic Uncertainties
We have presented the systematic uncertainties associated with the jet energy response. The systematic uncertainties are largely independent of thecorrectionappliedandmostly arise from the modeling of jets by the MC simulation and by the knowledge of the response to single particles. Figure 45 shows the individual systematic uncertainties as afunctionofjetpT in the central region, of the calorimeter, 0.2 < η < 0.6, of the calorimeter. They are | | Jet Energy independentScale and thus added in quadrature to derive the total uncertainty.
0.1 Determination of parton Quadratic sum of all contributions 0.08 Absolute jet energy scale energy from raw jet energy Out-of-Cone + Splash-out 0.06 Relative - 0.2<|!|<0.6 → calibration of jet energy Underlying Event scale (“JES”) Uncertainties on JES 0.04 CDF JES Uncertainty Individual cells: mask noisy 0.02 cells, ensure equal response 0 50 100 150 200 250 300 350 400 450 500 corr Calorimeter energy scale: pT (GeV/c)
Figure 45: Systematic uncertainties as a function of the corrected jet p in 0.2< η <0.6. correct for different response [Bhatti et al, NIM A566 (2006)T 375]| | to different particle types & For pT > 60 GeV/c theExperimental largest contribution arises from tool: the absolute jet energyscale T. AALTONEN et al. energiesPHYSICAL (“compensation”) REVIEW D 78, 052006 (2008) which is limited by the uncertainty of the calorimeter response to charged hadrons. A Dijet balance in QCD jets 1.2 78 |y|<0.1 0.1<|y|<0.7Additional energy in jet area 1.1 Jet 1 from underlying event, pileup 1 pT ,1 pT ,2 0.9 f = − Particles not grouped into jet (pT ,1 + pT ,2)/2 1.2 0.7<|y|<1.1 1.1<|y|<1.6
h (“out of cone”) Jet 2
→ 1.1 p C 1 Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 4 37 0.9 200 400 600 1.2 pJET (GeV/c) 1.6<|y|<2.1 T 1.1 Midpoint: R =0.7, f =0.75 cone merge 1 Parton to Hadron-level Correction
0.9 Uncertainty 0200400600 pJET (GeV/c) T
FIG. 14 (color online). The parton-to-hadron-level correction for five rapidity regions. The correction is derived from PYTHIA (solid line) and the difference between the HERWIG and PYTHIA prediction for the correction is conservatively taken as the systematic uncertainty (shaded bands). Jet Physics at the Tevatron at low p and is negligible at high p as shown in nsyst T T theory theory syst Fig. 14. i i;0 sj i;j (5) ¼ þ j 1 Â The uncertainty on the parton-to-hadron-level correction Tevatron: QCDX¼ jets part of mainstream physics program is estimated from the difference in the predictions for this data data stat is used where i and i À are the measured cross correction from HERWIG and PYTHIA. HERWIG does not section and its statistical uncertainty in the ith data point, include MPIs in its underlying event model, and instead theory theory stat and and À are the corresponding theoretical Examples:i i CDF inclusive jets, DØ dijet correlationsPHYSICAL REVIEW LETTERS week ending relies on initial state radiation (ISR) and beam remnants to PRL 94, 221801 (2005) 10 JUNE 2005 populate the underlying event. The difference between [Abazov et al.: PRL 94 (2005) 221801] al.: et [Abazov 13 5 HERWIG and PYTHIA is conservatively taken for this sys- 10 -1 10 to the maximum virtuality that can be adjusted in PYTHIA.
CDF data (1.13 fb ) dijet DØ The shaded bands in Fig. 3 indicate the range of variation tematic uncertainty, and this uncertainty is represented by 10 10 Systematic uncertainty ∆φ p max > 180 GeV (×8000) when the maximum allowed virtuality is smoothly in- 4 T the shaded bands in Fig. 14. max / d 10 130 < p < 180 GeV ( 400) creased from the current default by a factor of 4 [11]. 7 NLO pQCD T × 10 max dijet 100 < pT < 130 GeV (×20) These variations result in significant changes in the low Midpoint: R=0.7, f =0.75 σ max region clearly demonstrating the sensitivity of this VIII. RESULTS 4 merge 3 75 < pT < 100 GeV dijet
d 10 10 measurement. Consequently, global efforts to tune
The measured inclusive differential jet cross sections at dijet Monte Carlo event generators should benefit from includ- σ nb 10 2 the hadron level are shown in Fig. 15, and Tables VIII, IX, 1/ 10 ing our data. (GeV/c) -2 6 X, XI, and XII show the lists of the measured cross sections T 10 |y|<0.1 (x10 ) To summarize, we have measured the dijet azimuthal σ for each jet p and rapidity bin together with the statistical 2 decorrelation in different ranges of leading jet pT and T d -5 3
dYdp 10 and total systematic uncertainties, and parton-to-hadron- 10 0.1<|y|<0.7 (x10 ) observe an increased decorrelation towards smaller pT. NLO PQCD describes the data except for very large level correction factors. The ratios of the measured cross 10-8 0.7<|y|<1.1 where the calculation is not predictive. 1 dijet sections to the NLO pQCD predictions from FASTNLO We thank W. Giele, Z. Nagy, M. H. Seymour, and T. -11 -3 (corrected to the hadron level) based on the CTEQ6.1M 10 1.1<|y|<1.6 (x10 ) Sjo¨strand for many helpful discussions. We thank the staffs -1 PDF are shown in Fig. 16 together with the theoretical -6 at Fermilab and collaborating institutions, and acknowl- 10-14 1.6<|y|<2.1 (x10 ) 10 uncertainties due to PDF. The measured inclusive jet cross HERWIG 6.505 edge support from the Department of Energy and National 0 100 200 300 400 500 600 700 ` sections tend to be lower but still in agreement with the -2 PYTHIA 6.225 Science Foundation (USA), Commissariat a l’Energie JET 10 Atomique and CNRS/Institut National de Physique NLO pQCD predictions within the experimental and theo- pT (GeV/c) PYTHIA increased ISR Nucle´aire et de Physique des Particules (France), retical uncertainties. -3 (CTEQ6L) Ministry of Education and Science, Agency for Atomic To quantify the comparisons, a procedure based on the FIG.[Aaltonen 15 (color online). et Inclusiveal.: PRD jet cross 78 sections (2008) measured 052006] at 10 Energy and RF President Grants Program (Russia), 2 defined as the hadron level using the midpoint algorithm in five rapidity π/2 2π/3 5π/6 π CAPES, CNPq, FAPERJ, FAPESP, and FUNDUNESP regions compared to NLO pQCD predictions based on the ∆φ dijet (rad) (Brazil), Departments of Atomic Energy and Science and nbin data theory 2 nsyst CTEQ6.1M PDF. The cross sections for the five rapidity regions i i Technology (India), Colciencias (Colombia), CONACyT 2 ½ À s2; (4) 3 data stat 2 theory stat 2 j Probingare scaled bythe a factorHigh ofEnergy10 from Frontier each other at for the presentation LHC, HeidelbergFIG. U, 3 Winter (color online). Semester The 09/10,distributions Lecture in different 4 (Mexico), KRF (Korea), CONICET and UBACyT ¼ À þ dijet 38 i 1 i À i j 1 purposes. max X¼ ½ð Þ þð Þ X¼ pT ranges. Results from HERWIG and PYTHIA are overlaid on (Argentina), The Foundation for Fundamental Research max the data. Data and predictions with pT > 100 GeV are scaled on Matter (The Netherlands), PPARC (United Kingdom), by successive factors of 20 for purposes of presentation. Ministry of Education (Czech Republic), Natural Sciences and Engineering Research Council and WestGrid Project 052006-18 (Canada), BMBF and DFG (Germany), A. P. Sloan dijet in Figs. 1 and 2 were excluded because fixed-order Foundation, Civilian Research and Development perturbation theory fails to describe the data in the region Foundation, Research Corporation, Texas Advanced where soft processes dominate. Overall, NLO Research Program, and the Alexander von Humboldt dijet PQCD provides a good description of the data although Foundation. differences in shape can be discerned for dijet * 5=6. In this region, the observable probes the transition between two- and three-jet configurations. The cone algorithm is sensitive to the fine details of the event topology in this *Visitor from University of Zurich, Zurich, Switzerland. transition region. These details may not be adequately †Visitor from Institute of Nuclear Physics, Krakow, Poland. described by low-order PQCD, and higher-order calcula- [1] M. Dobbs et al., hep-ph/0403100. tions may be required. [2] We are using the iterative, seed-based cone algorithm including midpoints, as described on p. 47, Sect. 3.5 in Monte Carlo event generators, such as HERWIG and G. C. Blazey et al., in Proceedings of the Workshop: QCD PYTHIA, use 2 2 LO PQCD matrix elements with phe- ! and Weak Boson Physics in Run II, edited by U. Baur, nomenological parton-shower models to simulate higher- R. K. Ellis, and D. Zeppenfeld (Fermilab, Batavia, IL, order QCD effects. Results from HERWIG (version 6.505) 2000). and PYTHIA (version 6.225), both using default parameters [3] W. B. Kilgore and W. T. Giele, in Proceedings of the 35th and the CTEQ6L [9] PDFs, are compared to the data in Rencontres De Moriond, Les Arcs, France, 2000, edited by Fig. 3. HERWIG describes the data well over the entire J. Tran Thanh Van (EDP Sciences, Les Ulis, France, range including . PYTHIA with default 2001). dijet dijet parameters describes the data poorly—the distribution is [4] Z. Nagy, Phys. Rev. Lett. 88, 122003 (2002); Z. Nagy, Phys. Rev. D 68, 094002 (2003). too narrowly peaked at and lies significantly dijet [5] D0 Collaboration, V. Abazov et al., Nucl. Instrum. below the data over most of the dijet range. The maxi- Methods Phys. Res., Sect. A (to be published); T. 2 mum pT in the initial-state parton shower is directly related LeCompte and H. T. Diehl, Annu. Rev. Nucl. Part. Sci.
221801-6 Jet Physics at the LHC proton–(anti)proton cross sections QCD multijet production: 10 8 10 8 ѫtot Dominant high-pT process at Tevatron LHC hadron colliders 10 6 10 6 events/sec for L = 10 ѫ LHC: first tests of QCD b 10 4 10 4 predictions (including PDFs) 100 GeV Jets
jet at unprecedented energies 2 ѫ (E > ʚs/20) 2 10 jet T 10
ѫW
Not enough resources for ѫZ
ѫ QE 0 0 10 jet 10 3 ѫ (E > 100 GeV) detailed simulation (10 QCD jet T 33 events with 100 GeV/second!) –2 –2 10 10 cm → data-driven estimates
ѫt –2
jet s –4 ѫ (E > ʚs/4) –4 10 jet T 10 Many other processes with –1 ѫ (M = 150 GeV) multijet final states (top, Higgs H –6 –6 10 ѫ (M = 500 GeV) 10 Higgs, …) → important Higgs H background for LHC physics 0.1 1 10 ECMS (TeV) Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 4 39
Underlying Event
Physics motivation: LHC parton-parton cross section ⊗ PDFs larger than total cross section → multiple parton interactions in the same pp collision Definition: underlying event (UE) = everything but hard scattering (including initial/final state radiation & beam remnant)
Underlying Event
[R. Field]
[T. Gleisberg et al., JHEP02 (2004) 056] Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 4 40 Underlying Event
Idea: analyze events with &1 hard jet
Dijets: back to back in ϕ “Transverse” region very sensitive to the Study transverse region “underlying event”! (UE dominated) Tune MC generators to (Tevatron) data (e.g. Pythia “Tune A”) → valid @ LHC?
[R. Field]
[R. Field] Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 4 41