DOCSLIB.ORG

Non-Resonant Diagrams in Radiative Four-Fermion Processes

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Non-Resonant Diagrams in Radiative Four-Fermion Processes FR9700401 KEK-CP-015 KEK Preprint 94-46 LAPP-Exp.-94.09 June 1994 H Non-resonant Diagrams in Radiative Four-fermion Processes J. FUJIMOTO, T. ISHIKAWA, S. KAWABATA, Y. KURIHARA, Y. SHIMIZU and D. PERRET-GALLIX Submitted to the Proceedings of Physics at LEP200 and Beyond, Teupitz/Brandenburg, Germany, April 10 -15,1994. L.A.P.P. B.P. 110 F-74941 ANNECY-LE-VIEUX CEDEX • TELEPHONE 50.09.16.00+ • TELECOPIE 50 2794 95 National Laboratory for High Energy Physics, 1994 KEK Reports are available from: Technical Information & Library National Laboratory for High Energy Physics l-lOho,Tsukuba-shi Ibaraki-ken, 305 JAPAN Phone: 0298-64-1171 Telex: 3652-534 (Domestic) (0)3652-534 (International) Fax: 0298-64-4604 Cable: KEK OHO E-mail: LIBRARY®JPNKEKVX (Bitnet Address) [email protected] (Internet Address) Non-resonant diagrams in radiative four-fermion processes J. Fujimoto, T. Ishikawa, S. Kawabata, Y. Kurihara. Y. Shiniizu » and D. Perret-Gallixb * Miuanii-Tateya Collaboration. KEK, Japan bLAPP-IN2P3/CNRS, France + The complete tree level cross section for e c~ —» e~utud-y is computed and discussed in comparison with + + the cross sections for e e~ —• e~utud and e e~ —• udud. Event generators based on the GRACE package for the non-radiative and radiative case are presented. Special interest is brought to the effect of the non-resonant diagrams overlooked so far in other studies. Their contribution to the total cross section is presented for the LEP II energy range and for future linear colliders (-/a =500 GeV). Effects, at the W pair threshold, of order 3% {e~Ptui) and 27% (udud) are reported. Similar behaviour for the radiative case is shown. At -Ja = 500 GeV, the relative contribution of the non-resonant diagrams for the radiative channel reaches 42.5%. 1. Introduction processes, and they will contribute to the overall mass and width measurement uncertainties. Two years ago. a complete calculation of It has been recognized, since some time [3], two four-fermion final states in e+e~ collisions. + + that the radiative corrections in W pair produc- e e~ —» e~Deud and e e~ —» udud, was re- tion have to be included for a precise comparison ported at the Sotchi meeting [1]. It was shown with measurements at the e+e~ colliders. Initial that the non-resonant diagrams play an impor- state radiations (ISR) reduce the available center tant role below the W pair threshold (up to 27% of mass energy. Close to the W pair threshold, at \/s = 150 GeV) and exhibit a non-negligible ISR will, therefore, enhance the relative contri- effect at higher energy (7% at y/s = 190 GeV). bution of non-resonant diagrams. Final state ra- In these results, in addition to a set of exper- diative corrections will contribute to additional imental loose constraints, a cut on the 0 angle uncertainties on the mass reconstruction, unless of the outgoing electron was applied to cope with the photon is detected and properly accounted gauge violations appearing in the subset of 7 — W for in the mass reconstruction algorithm. How- diagrams. Below threshold, the non-resonant di- ever, photons coming from the intermediate W, agrams competing only with the off-shelluess of which can be mis takingly recognized as final state the resonant ones, their relative contribution be- bremsstrahlung. will introduce additional uncer- comes quite large. The non-resonant diagrams tainties. are dominated by t-channel 7 — W graphs in sim- ilarity with the well-known two-photon (7 - 7) Although a number of studies has been car- processes. Hence the cross section increases with ried out in these last years, including [4][5], we the energy and the contribution of non-resonant present, for the first time, the complete tree level processes keeps growing in contrast to that of res- computation of one of the radiative four-fermion onant diagrams which falls with the energy. This processes. This work can be used as a benchmark effect was confirmed at this workshop by the anal- for testing the validity of simplified and therefore ysis of selected final states based on a dedicated faster generators. four-fermion generator [2]. The non-resonant pro- cesses are essentially single W or no W produc- tion. Some examples of these type of diagrams 2. The GRACE system for the radiative case can be seen on Fig.lb,2. As The GRACE system [6] has been used to far as the W mass reconstruction is concerned, perform the very lengthy computations involved these diagrams should be counted as background in the study of most radiative processes. The GRACE package is a complete set of tools for d V, e w (a) Figure 2. (Fig.l cont.) Some examples of diagrams from the radiative process e+e~ —» e V. e~Ptudy: Other non-resonant diagrams. W\ d u| the basic integration variables to regularize the u divergencies appearing in the integration of the T/ e e e > e matrix element. The best kinematics will give the best accuracy for a given computation time. e v. e v. 3. Four-fermion production w\— d d 7 The results presented hereafter have been ob- tained using the following set of parameters: / e e Mz = 91.1 GeV (b) Tz = 2.534 GeV a = 1/137 Figure 1. Some examples of diagrams from the l 2 + sin 9w = 1 - (M, V/M|) radiative process e e~ —• e~veudy. a) Resonant diagrams. b)Nou-resouant 7 — W diagrams. MW = 80 GeV mu = md = 0.1 GeV computing tree level processes. All the phases involved in a given computation are covered: The width of the W is taken from the Particle from the process definition (specification of the Data Table; IV = 2.25 GeV. The gauge boson initial and final particles) to the event genera- (W.Z) widths are assumed to be constant in the tor. It is composed essentially of three compo- calculation. Furthermore some realistic experi- nents: the diagram generator, the construction of mental cuts have been introduced: the matrix element based on helicity amplitude function from the CHANEL [7] library and the 6€ > 8, 20, 30, 40° 8 multi-dimensional phase space integration pack- 172° > 07, 0,,, > ° age BASES [8] associated with the event genera- £7 > 1 GeV, £e,,,, > 1 GeV tor SPRING [8]. Fermion masses are properly introduced in the helicity amplitudes. The particle width is intro- where 6e.6y and 6qq are angles measured from duced into the gauge boson propagators when the incident e~ beam and -Be.j,, are the energies the denominator can vanishes for positive squared of filial e~.q and q. respectively. The electron momentum transfer. A gauge iuvariance checking polar angle cut is introduced to avoid an undesir- program is automatically built by the system. able gauge violation for extremely forward direc- Only the kinematics for complex processes has tions [9] caused inevitably by the finite width of to be written by the user. The issue, here, is to W boson when the subset of 7 - W diagrams is figure out what is the best transform to apply to considered. 1.2 1 i; •_• •_!_' i The gauge iuvariance of the amplitude is a) checked numerically for a random selection of the 1.0 boson gauge parameters at several points in the phase space. The errors are within the preci- 0.B sion of numerical calculation (typically less than 12 O(10~ ) in double precision) when the W width 0.6 is turned off. Further gauge cancellations are 111' * 1111111 I I I I I t I M checked to confirm that the obtained cross sec- b) e+e"-»u3ud tions are stable against finite width. The pro- 1.0 nit, cedure is as follows: first extract the product of gauge boson propagators without width as an 0.8 overall factor of the whole amplitude. Then re- place them by those with finite width. As a result, 0.6 one is left with rigorously gauge invariant anipli- 1 1 1 tude[10]. For the resonant diagrams, this method 160 180 200 220 240 gives the same results as ordinally method. While VS (G«V) for the 7 - W diagrams, this gives 10% smaller results. Figure 4. Energy dependence of the relative con- tribution of resonant diagrams in a) e+e~ —• 0.6 + I • - L— T e~Peud and b) e e~ —» udud with 0C > 8° to 0.5 the full computation. 0.4 0.3 0.2 RMS • 0.1 and udud. Fig.3 shows the cross sections ver- 0.0 i..|..t..rr,r 4-f-rrf |fTH | 1 i i T; 1.5 B) «V-»UQUd ~ sus the center of mass energy around the W pair threshold. The solid line represents the case where all diagrams are included, the dashed line the contribution of the resonant diagrams only. In the udud channel, one can observe the onset of the Z resonant diagrams as a small shoulder starting around 2Mz- The behaviour below the 160 180 200 220 240 W pair threshold can be better seen in fig.4 where VS (G«V) the ratio of the three main resonant diagrams over the complete calculation is plotted for the same + Figure 3. Cross sections for a) e e —» e veud range of center of mass energy. In the e~ueud and b) e+e~ —» udud versus CM. energy with channel, the effect is of the order of ±3% around Be > 8°. The solid curves are for all diagrams v/5 = 160 GeV. while in udud it readies -28%. and dashed ones for three resonant graphs. The At the energy of future LC, 300 GeV.
Load more

Recommended publications
  • Arxiv:Hep-Ph/9910338V1 14 Oct 1999
    hep-ph/9910338 DTP/99/94 PSI PR-99-24 October 1999 Resummation of double logarithms in electroweak high energy processes 1 2 3 4 V.S. Fadin, ∗ L.N. Lipatov, † A.D. Martin, ‡ and M. Melles § 1) Budker Institute of Nuclear Physics and Novosibirsk State University, 630090 Novosibirsk, Russia 2) St. Petersburg Nuclear Physics Institute, 188350 and St. Petersburg State University, St. Petersburg, Russia 3) Department of Physics, University of Durham, Durham, DH1 3LE, UK 4) Paul Scherrer Institute (PSI), CH-5232 Villigen, Switzerland. Abstract + At future linear e e− collider experiments in the TeV range, Sudakov dou- ble logarithms originating from massive boson exchange can lead to significant corrections to the cross sections of the observable processes. These effects are arXiv:hep-ph/9910338v1 14 Oct 1999 important for the high precision objectives of the Next Linear Collider. We use the infrared evolution equation, based on a gauge invariant dispersive method, to obtain double logarithmic asymptotics of scattering amplitudes and discuss how it can be applied, in the case of broken gauge symmetry, to the Standard Model of electroweak processes. We discuss the double logarithmic effects to both non-radiative processes and to processes accompanied by soft gauge boson emission. In all cases the Sudakov double logarithms are found to exponentiate. We also discuss double logarithmic effects of a non-Sudakov type which appear in Regge-like processes. ∗[email protected] †[email protected] ‡[email protected] §[email protected] 1 Introduction + The Next Linear Collider (NLC) will explore e e− processes in the TeV energy regime, and probe the Standard Model of elementary particles to great accuracy.
    [Show full text]
  • RADIATIVE RETURN at NLO and the MEASUREMENT of the HADRONIC CROSS-SECTION ∗ German´ Rodrigo
    TTP01-26 RADIATIVE RETURN AT NLO AND THE MEASUREMENT OF THE HADRONIC CROSS-SECTION ∗ German´ Rodrigo Institut f¨ur Theoretische Teilchenphysik, Universit¨at Karlsruhe, D-76128 Karlsruhe, Germany. TH-Division, CERN, CH-1211 Gen`eve 23, Switzerland. e-mail: [email protected] + The measurement of the hadronic cross-section in e e− annihilation at high luminosity factories using the radiative return method is motivated and discussed. A Monte Carlo generator which simulates the radiative + process e e− γ + hadrons at the next-to-leading order accuracy is pre- sented. The analysis→ is then extended to the description of events with hard photons radiated at very small angle. PACS numbers: 13.40.Em, 13.40.Ks, 13.65.+i 1. Motivation Electroweak precision measurements in present particle physics provide a basic issue for the consistency tests of the Standard Model (SM) or its ex- tensions. New phenomena physics can affect low energy processes through quantum fluctuations (loop corrections). Deviations from the SM predic- tions can therefore supply indirect information about new undiscovered par- ticles or interactions. The recent measurement of the muon anomalous magnetic moment a µ ≡ (g 2)µ/2 at BNL [1] reported a new world average showing a discrepancy at− the 2.6 standard deviation level with respect to the theoretical SM eval- uation of the same quantity which has been taken as an indication of new physics. For the correct interpretation of experimental data the appropriate inclusion of higher order effects as well as a very precise knowledge of the ∗ Presented at the XXV International Conference on Theoretical Physics \Particle Physics and Astrophysics in the Standard Model and Beyond", Ustro´n, Poland, 9-16 September 2001.
    [Show full text]
  • Radiative Four-Fermion Processes at LEP2
    EPJ manuscript No. (will be inserted by the editor) Radiative four–fermion processes at LEP2 G. Montagna1, M. Moretti2, O. Nicrosini3, M. Osmo1, F. Piccinini3 1 Dipartimento di Fisica Nucleare e Teorica - Universit`adi Pavia and INFN - Sezione di Pavia, via A. Bassi 6, Pavia, Italy 2 Dipartimento di Fisica - Universit`adi Ferrara and INFN - Sezione di Ferrara, Ferrara, Italy 3 INFN - Sezione di Pavia, via A. Bassi 6, Pavia, Italy and Dipartimento di Fisica Nucleare e Teorica - Universit`adi Pavia Received: date / Revised version: date Abstract. The production of four fermions plus a visible photon in electron-positron collisions is analyzed, with particular emphasis on the LEP2 energy range. The study is based on the calculation of exact matrix elements, including the effect of fermion masses. In the light of the present measurements performed at LEP, triple and quartic anomalous gauge couplings are taken into account. Due to the presence of a visible photon in the final state, particular attention is paid to the treatment of higher-order QED corrections. Explicit results for integrated cross sections and differential distributions are shown and commented. The features of the Monte Carlo program WRAP, used to perform the calculation and available for experimental analysis, are described. PACS. 12.15.Ji – 13.40.Ks – 13.85.Hd 1 Introduction Quartic vertices involving only massive gauge bosons give rise to six-fermion final states and are outside the sensi- tivity of LEP, being accessible only at the energies of a One of the main goals of electroweak physics at LEP2 is − future e+e Linear Collider (LC).
    [Show full text]
  • Arxiv:Hep-Ph/9407308V3 22 Jul 1994 B Shimizu Y
    1 Non-resonant diagrams in radiative four-fermion processes J. Fujimoto, T. Ishikawa, S. Kawabata, Y. Kurihara, Y. Shimizu a and D. Perret-Gallixb a Minami-Tateya Collaboration, KEK, Japan bLAPP-IN2P3/CNRS, France + − − The complete tree level cross section for e e e ν¯eudγ¯ is computed and discussed in comparison with + − − + − → the cross sections for e e e ν¯eud¯ and e e udu¯ d¯. Event generators based on the GRACE package for → → the non-radiative and radiative case are presented. Special interest is brought to the effect of the non-resonant diagrams overlooked so far in other studies. Their contribution to the total cross section is presented for the LEP II energy range and for future linear colliders (√s =500 GeV). Effects, at the W pair threshold, of order 3% − (e ν¯eud¯) and 27% (¯udud¯) are reported. Similar behaviour for the radiative case is shown. At √s = 500 GeV, the relative contribution of the non-resonant diagrams for the radiative channel reaches 42.5%. 1. Introduction far as the W mass reconstruction is concerned, these diagrams should be counted as background Two years ago, a complete calculation of processes, and they will contribute to the overall two four-fermion final states in e+e− collisions, + − − + − mass and width measurement uncertainties. e e e ν¯eud¯ and e e udu¯ d¯, was re- → → It has been recognized, since some time [3], ported at the Sotchi meeting [1]. It was shown that the radiative corrections in W pair produc- that the non-resonant diagrams play an impor- tion have to be included for a precise comparison tant role below the W pair threshold (up to 27% with measurements at the e+e− colliders.
    [Show full text]
  • Monte Carlo Simulation of Radiative Processes in Electron-Positron Scattering
    MONTE CARLO SIMULATION OF RADIATIVE PROCESSES IN ELECTRON-POSITRON SCATTERING R.H.P. KLEISS MONTE CARLO SIMULATION OF RADIATIVE PROCESSES IN ELECTRON-POSITRON SCATTERING Proefschrift ter verkrijging van de graad van Doctor in de Wiskunde en Natuurwetenschappen aan de Rijksuniversiteit te Leiden, op gezag van de Rector Magnificus Dr. A.A.H. Kassenaar, Hoogleraar in de faculteit der Geneeskunde, volgens besluit van het College van Dekanen te verdedigen op dinsdag 22 juni 1982, te klokke 15.15 uur. door Ronaldus Hendricus Petrus Kleiss geboren te Schiedam in 1955 Druk: NKB Offset bv - Leiden Promotor: Prof. Dr. F.A. Berends Referenten: Prof. Dr. K.J.F. Gaemers Dr. R. Gastmans I'- ll This investigation is part of the research program of the Stichting voor Fundamenteel Onderzoek der Materie (F.O.M.) which is financially supported by the Nederlandse Organisatie voor Zuiver Wetenschappelijk Onderzoek (Z.W.O.). ii ï CONTENTS ti f: CHAPTER I : OUTLINE CHAPTER II : INTRODUCTION 1. e e physics f V 2. Radiative corrections •;.f 9 i'i- 3. Event generators 11 References 12 CHAPTER III: REMARKS ON MONTE CARLO TECHNIQUES 1. Introduction 11+ 2. Multidimensional probability distributions lit 3• Simulation techniques 15 k. Some technical remarks 20 References 22 CHAPTER IV : PAIR PRODUCTION OF MUONS AND QUARKS 1. Introduction 23 2. Lowest order cross section 2k 3. Virtual corrections 27 h. Soft bremsstrahlung 31 5- Hard bremsstrahlung 35 References 37 CHAPTER V : APPROXIMANTS AND EVENT GENERATION I 1. Introduction 38 2. Soft Part 39 3. Initial state radiation h. Final state radiation References hi CHAPTER VI EVENT WEIGHTS 1.
    [Show full text]
  • Dark Matter Indirect Detection and Bremsstrahlung Processes
    Dark Matter Indirect Detection and Bremsstrahlung Processes Thomas David Jacques Submitted in total fulfilment of the requirements of the degree of Doctor of Philosophy August 2011 School of Physics The University of Melbourne Abstract It is now well established that some form of Dark Matter (DM) makes a sizeable contribution to the total matter-energy abundance of the Universe, yet DM still evades detection and its particle properties remain unknown. Indirect detection provides an important probe of some of these fundamental properties. DM self- annihilation throughout the Universe is expected to lead to an observable signal of standard model particles at Earth, and any observed flux of standard model particles from a particular region acts as an upper limit on the annihilation signal from that region. In Chapter 1, we give an introduction to our current knowledgeofDM.Webegin with the historic and recent evidence for the existence of DM based on its gravi- tational effects, before describing our current knowledge of DM formation history and abundance. We then describe and compare a number of competing DM den- sity profiles for our galaxy, highlighting the large uncertainties towards the Galactic center. There are currently a large number of DM candidates, sometimes called the ‘Candidate Zoo’. We briefly introduce several of the most popular candidates, de- scribing their history and motivation. We then move on to describe current searches for DM, focusing on indirect detection, which aims to detect DM via an observable flux of its SM annihilation products. We detail the major constraints on the DM self-annihilation cross section, and examine some potential signals from DM annihila- tion.
    [Show full text]
  • Mass Biases in Reconstructing Exclusive Radiative Hadronic Decays of W Bosons at the LHC
    Mass biases in reconstructing exclusive radiative hadronic decays of W bosons at the LHC. W. J. Murray1 and E. Jones2 1University of Warwick & STFC RAL 2University of Warwick Abstract The search for exclusive hadronic vector boson decays is an ongoing part of the LHC programme where, to date, no such decays have been observed. In addition to the intrinsic interest in the branching ratios, there is potential for a measurement of the W boson mass quite distinct from the usual methods. The radiative decay modes offer good potential channels for this search; however, we highlight three issues with it not previously discussed: particle misidentification, partial reconstruction and the impact of interference with QCD. These issues cause shifts in the peak position of tens or hundreds of MeV/c2. 1 Introduction arXiv:2009.01073v2 [hep-ex] 27 Apr 2021 Exclusive decays of W and Z bosons to hadronic final states have never been observed. Low-multiplicity final states could potentially be experimentally accessible and, in particular, radiative decays of vector bosons are promising channels with many theoretical predictions of the branching ratios avail- able [1, 2, 3, 4, 5]. However, there is not universal agreement between these predictions. For example, the W ±!π±γ branching ratio is estimated to be of the order of 10−9 in Ref. [1] and Ref. [4], whereas Ref. [5] proposes values as high as 10−7. 1 There are experimental limits on many two-body Z decays. These include radiative decays to final states such as π0γ [6], ηγ and η0γ [7], !γ [8], φγ [9], J= γ and Υγ [10], as well as non-radiative modes such as π0π0 [6].
    [Show full text]
  • Second-Order Leptonic Radiative Corrections for Lepton-Proton Scattering
    MITP/18-108 November 14, 2018 Second-Order Leptonic Radiative Corrections for Lepton-Proton Scattering R.-D. Bucoveanu (a), H. Spiesberger (b);(c) (a) PRISMA Cluster of Excellence, Institut f¨urKernphysik, Johannes Gutenberg-Universit¨at, D-55099 Mainz, Germany (b) PRISMA Cluster of Excellence, Institut f¨urPhysik, Johannes Gutenberg-Universit¨at, D-55099 Mainz, Germany (c) Centre for Theoretical and Mathematical Physics, and Department of Physics, University of Cape Town, Rondebosch 7700, South Africa E-mail: [email protected], [email protected] Abstract The interpretation of high-precision lepton-nucleon scattering experiments requires the knowledge of higher-order radiative corrections. We present a calculation of the cross section for unpolarized lepton-proton scattering including leptonic radiative corrections up to second order, including one- and two-loop corrections, radiation of one and two photons and one- loop corrections for one-photon radiation. Numerical results are given for the planned P2 experiment at the MESA facility in Mainz, and some results are also discussed for Qweak and the suggested MUSE experiment. arXiv:1811.04970v1 [hep-ph] 12 Nov 2018 1 1 Introduction Lepton scattering has been, and continues to be, an extremely important experimental technique to study properties of matter. Elastic and inelastic electron nucleon scattering has allowed us to obtain information about form factors and structure functions or, at higher energies, parton distribution functions. Particularly interesting modern research topics include the investigation of the spin structure of the proton or the recently observed discrepancy in the determination of the proton charge radius between different experimental techniques. Precision measurements with polarized electrons are also used to study weak interactions.
    [Show full text]
  • Standard Model Fermion Hierarchies with Multiple Higgs Doublets
    Technische Universität München & Max Planck Institut für Physik Standard Model Fermion Hierarchies with Multiple Higgs Doublets Dissertation by Ana Solaguren-Beascoa Negre Physik Department T30d Technische Universität München Physik Department T30d Max Planck Institut für Physik Standard Model Fermion Hierarchies with Multiple Higgs Doublets Ana Solaguren-Beascoa Negre Vollständiger Abdruck der von der Fakultät für Physik der Technischen Universität München zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften genehmigten Dissertation. Vorsitzender: Univ.–Prof. Dr. Lothar Oberauer Prüfer der Dissertation: 1. Univ.–Prof. Dr. Alejandro Ibarra 2. Univ.–Prof. Dr. Andrzej Buras Die Dissertation wurde am 25.04.2016 bei der Technischen Universität München eingereicht und durch die Fakultät für Physik am 24.05.2016 angenommen. Abstract The origin of the hierarchies in the Standard Model fermion masses and mixing angles is one of the most puzzling questions in particle physics. In addition, experiments have shown that neutrinos are massive particles, in contrast with the Standard Model predictions. All of these issues indicate the existence of new physics. In this thesis we study extensions of the Standard Model with new Higgs doublets to solve these questions. The lighter fermion masses are generated with small quantum effects, reproducing the hierarchies between the different fermion mass generations. Moreover we can generate neutrino masses in the context of the see-saw mechanism, by extending the model with at least one right-handed neutrino. The mixing angles are calculated using zero-th order in perturbation theory. The Cabibbo– Kobayashi–Maskawa matrix can be generated with a hierarchical structure, whereas the Pontecorvo–Maki–Nakagawa–Sakata matrix follows an anarchical structure, in agreement with experiments.
    [Show full text]
  • Relativity in Physics for the 21St Century
    The Universe, Vol. 5, No. 1 January-March 2017 Regular Article Relativity in Physics for the 21st Century W-Y. Pauchy Hwang∗1 1Asia Pacific Organization for Cosmology and Particle Astrophysics, Center for Theoretical Sciences, Department of Physics, and Institute of Astrophysics, National Taiwan University, Taipei, Taiwan 106 At the beginning of the 21st Century, we may declare that we are living in the quantum 4-dimensional Minkowski space-time with, via the gauge principle, the force-fields gauge-group structure, SUc(3) × SUL(2) × U(1) or SUL(2) × U(1) × SUf (3), built-in from the very beginning. From there, it emerges the Standard Model that describes the smallest units of matter such as electrons, neutrinos, and quarks. I would like to point out as well as to discuss a few major century errors dictated by the God, throughout the 20th Century. We, as the human being, are sometimes so helpless in the struggles for the true knowledge. 1 A Question to Dirac and thus we don't need the infinite sea of elec- trons. P.A.M. Dirac discovers the Dirac equation, rather than inventing this equation [1]. In our Apparently, Dirac knew these also, since he World (or, our Universe), the basic units of mat- knows the language so well. Later on, he pub- ter, such as electrons, neutrinos, and quarks, lished \Quantum Mechanics" which the mean- are the smallest objects ever exist in nature. ing of quantization was elucidated in great de- These smallest units of matter obey Pauli's ex- tail. There is no \second quantization" and, clusion principle, as fermions, satisfying the anti- also, there is no \electron sea" whatsoever.
    [Show full text]
  • Bremsstrahlung
    TESTING THE LOW ENERGY THEOREM FOR SPINLESS “PROTON-NEUTRON” BREMSSTRAHLUNG A thesis presented to the faculty of the College of Arts and Sciences of Ohio University In partial fulfillment of the requirements for the degree Master of Science Yurii Pidopryhora June 2003 This thesis entitled TESTING THE LOW ENERGY THEOREM FOR SPINLESS “PROTON-NEUTRON” BREMSSTRAHLUNG BY YURII PIDOPRYHORA has been approved for the Department of Physics and Astronomy and the College of Arts and Sciences by Daniel R. Phillips Assistant Professor of Physics and Astronomy Leslie A. Flemming Dean, College of Arts and Sciences PIDOPRYHORA, YURII M.S. June 2003. Physics and Astronomy Testing the Low Energy Theorem for Spinless “Proton-Neutron” Bremsstrahlung (193pp.) Director of Thesis: Daniel R. Phillips In this thesis the accuracy of using the Low energy theorem (soft-photon approxi- mation) to estimate the amplitude for spinless “proton-neutron” bremsstrahlung is investigated. For this purpose spinless elastic scattering and bremsstrahlung theories are constructed. An exact expression for the bremsstrahlung amplitude is derived and an original proof of the Low energy theorem is given in this case. Computa- tions are performed which compare the exact value of the bremsstrahlung amplitude to the Low energy theorem’s approximation thereof in different scattering configu- rations. We find that in most of the cases considered the Low energy theorem is a good estimate for the “exact” spinless “proton-neutron” bremsstrahlung amplitude. This result may be used to justify Low energy theorem estimates of cross-sections for neutrinostrahlung processes, relevant in astrophysics. Detailed explanations are given so that this text may be used as a reference by students and teachers of nuclear physics and quantum mechanics.
    [Show full text]
  • Polarized QED Splittings of Massive Fermions and Dipole Subtraction for Non-Collinear-Safe Observables
    Nuclear Physics B 800 (2008) 146–189 www.elsevier.com/locate/nuclphysb Polarized QED splittings of massive fermions and dipole subtraction for non-collinear-safe observables Stefan Dittmaier ∗, Alois Kabelschacht, Tobias Kasprzik Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), D-80805 München, Germany Received 13 February 2008; accepted 17 March 2008 Available online 20 March 2008 Abstract Building on earlier work, the dipole subtraction formalism for photonic corrections is extended to various photon–fermion splittings where the resulting collinear singularities lead to corrections that are enhanced by logarithms of small fermion masses. The difference to the earlier treatment of photon radiation is that now no cancellation of final-state singularities is assumed, i.e. we allow for non-collinear-safe final-state radiation. Moreover, we consider collinear fermion production from incoming photons, forward-scattering of incoming fermions, and collinearly produced fermion–antifermion pairs. For all cases we also provide the corresponding formulas for the phase-space slicing approach, and particle polarization is supported for all relevant situations. A comparison of numerical results obtained with the proposed subtraction procedure − − − + and the slicing method is explicitly performed for the sample process e γ → e μ μ . © 2008 Elsevier B.V. All rights reserved. 1. Introduction Present and future collider experiments require precise predictions for particle reactions, i.e. for most of the relevant processes radiative corrections have to be calculated. This task becomes arbitrarily complicated if either the order in perturbation theory (loop level) or the number of external particles is increased, or both. In recent years the needed techniques and concepts have received an enormous boost from various directions; for a brief overview we refer to some recent review articles [1,2].
    [Show full text]