Determining the Strong Coupling Constant

Total Page:16

File Type:pdf, Size:1020Kb

Determining the Strong Coupling Constant Determination of the strong coupling constant αs at the LHC Klaus Rabbertz, KIT Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 1 Outline Introduction 2012: No LHC results yet PDG2012 Jet-like measurements Cross sections Ratios Normalised distributions top-quark pair production W/Z bosons Issues & perspectives Summary & outlook Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 2 Standard Model of Particle Physics Solid matter ... Cush, Wikipedia. … and three fundamental interactions. (no gravity) Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 3 Standard Model of Particle Physics Solid matter ... Electromagnetic interaction (magnets, electricity, ...) Cush, Wikipedia. … and three fundamental interactions. (no gravity) Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 4 Standard Model of Particle Physics Solid matter ... Electromagnetic interaction (magnets, electricity, ...) Weak interaction (β decays, sun, ...) Cush, Wikipedia. … and three fundamental interactions. (no gravity) Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 5 Standard Model of Particle Physics Strong interaction (nuclear forces, ...) Solid matter ... Electromagnetic interaction (magnets, electricity, ...) Weak interaction (β decays, sun, ...) Cush, Wikipedia. … and three fundamental interactions. (no gravity) Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 6 αs(MZ) world average versus time 1st estimate from G. Altarelli Start of FLAG Flavour Lattice Averaging Group +lattice NNLO PDG 2016 +LEP +HERA pre-LEP S. Bethke, arXiv:1907.01435. Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 7 αs(MZ) world average versus time 1st estimate from G. Altarelli +lattice NNLO PDG 2016 +LEP +HERA Large theoretical uncertainty from (PDF + αs) on Higgs x sections pre-LEP In particular tTH & gg-Fusion: 7-13% S. Bethke, arXiv:1907.01435. CERN YR, LHC Higgs xs WG. Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 8 QCD and asymptotic freedom Nobel prize 2004 Theory: Renormalisation group equation (RGE) Solution of 1-loop equation Running coupling constant D. Gross 'Strong' coupling weak for Q2 → ∞ , i.e. small distances Asymptotic freedom D. Politzer Perturbative methods What happens at large distances? usable Q2 → 0 ? Cannot be answered here! For Q2 → Λ2 perturbation theory not F. Wilczek applicable anymore! Physik Journal 3 (2004) Nr. 12 nobelprize.org Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 9 Unification of couplings? Unification of couplings e.g. in Minimal Supersymmetric Standard Model (MSSM)? We (LHC) are here Need to test RUNNING even – in particular? – when no SUSY found! J. Heisig, DESY Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 10 Jets at the LHC Abundant production of jets: 2 Jets at hadron colliders provide the largest dynamic range ever for αs(Q ) Plus insights into high-pT QCD, the proton structure, non-perturbative and electroweak effects at high Q Proton Structure Proton Structure (PDF) (PDF) Matrix Element Hadrons Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 11 Jets at the LHC Abundant production of jets: Extract αs(MZ), the least precisely known fundamental constant! Proton Structure Proton Structure (PDF) (PDF) Matrix Element Hadrons Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 12 W, Z, top at the LHC High-precision lepton measurements: W, Z, top measurements provide high-precision cross sections Also learn about electroweak parameters, the top mass, and the proton structure Proton Structure Proton Structure (PDF) (PDF) Matrix Element Muons Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 13 Jets at the LHC Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 14 2 Jet cross sections ~ αs Determination of α (M ) in single-parameter fit s Z Test consistency of running of αs(Q) Multi-parameter fit of α (M ) & PDFs s Z Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 15 All inclusive Large transverse momenta Proton Proton Every jet counts ATLAS: EPJC 73 (2013) 2509; JHEP 02 (2015) 153; JHEP 09 (2017) 020; JHEP 05 (2018) 195. Relevant ATLAS & CMS measurements: CMS: PRD 87 (2013) 112002; PRD 90 (2014) 072006; EPJC 75 (2015) 288; EPJC 76 (2016) 265; EPJC 76 (2016) 451; JHEP 03 (2017) 156. Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 16 Inclusive jets: cross section Overall agreement with predictions of QCD at NLO over many orders of magnitude in cross section and even beyond 2 TeV in jet pT and for rapidities |y| up to 3 ~ 5 at √s = 2.76, 7, 8, and 13 TeV. Here: anti-kt, R=0.4, 13 TeV Data vs. NLO pQCD x non-pert. x EW corrections Exp. uncertainties for |y| < 0.5 NLO: Ellis, Kunszt, Soper, PRL 69 (1992) 1496; Giele, Glover, Kosower, NPB 403 (1993) 633; Z. Nagy, PRD 68 (2003) 094002. Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 17 Inclusive jets: theory corrections anti-kt, R=0.4, 13 TeV, |y| < 0.5 Nonperturbative correction factors: Electroweak correction factors: - estimated from tuned MC event generators - calculated perturbatively - uncertainty of 5 – 15% at pT = 100 GeV - uncertainty small - strongly dependent on jet size R - strongly dependent on jet rapidity y - very important at high p - less important at high pT T EW: Dittmaier, Huss, Speckner, JHEP 11 (2012) 095. Frederix et al., JHEP 04 (2017) 076. Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 18 Inclusive jets: theory corrections anti-kt, R=0.4, 13 TeV, |y| < 0.5 Nonperturbative correction factors: Electroweak correction factors: - estimated from tuned MC event generators - calculated perturbatively - uncertainty of 5 – 15% at pT = 100 GeV - uncertainty small - strongly dependent on jet size R - strongly dependent on jet rapidity y - very important at high p - less important at high pT T EW: ALICE, arXiv:1909.09718. Dittmaier, Huss, Speckner, JHEP 11 (2012) 095. See also CMS, SMP-19-003. Frederix et al., JHEP 04 (2017) 076. Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 19 Inclusive jets: αs Sensitivity to α (M ) at NLO Χ2 fit of α (M ) for all jet p and |y| bins s Z s Z T - CMS: anti-k R = 0.7 at √s = 8 TeV - In fit: all exp. + PDF + NP uncertainties t - PDFs: CT10 NLO PDF sets for various α (M ) s Z - QCD scale choice: μR = μF = pT,jet Jets @ NNLO not fully used yet in fits @ LHC → in progress Results for ep: → Britzger et al., EPJC79 (2019) 845. Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 20 Inclusive jets: αs & PDFs Simultaneous fit of αs & PDFs possible combining HERA DIS & CMS jet data using xFitter Tool Reduced uncertainties of gluon PDF CMS results for α (M ) at NLO s Z Orange shading: external PDF sets Bluish shading: PDF fit incl. HERA data √s lum α (M ) exp NP scale s Z [TeV] [fb-1] PDF +53 7 5.0 0.1185 35 -24 +29 +53 8 19.7 0.1164 -33 -28 +23 +24 7 5.0 0.1192 -19 -39 +19 +22 8 19.7 0.1185 -26 -18 13 (7 TeV) / 18 (8 TeV) Question: How to deal with uncertainty of parameter fit Missing higher orders (aka scale uncertainty) xFitter (HERAFitter): Alekhin et al., EPJC 75 (2015) 304. in PDF fits? First progress → e.g. NNPDF, EPJC79 (2019) 931. Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 21 Dijets Large masses Proton Proton ATLAS: JHEP 05 (2014) 059; JHEP 05 (2018) 195. Relevant ATLAS & CMS measurements: CMS: PRD 87 (2013) 112002; EPJC 77 (2017) 746. Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 22 Triple-differential dijets Most measurements done with respect to dijet mass * and either max. rapidity |y|max (CMS) or rapidity separation y (ATLAS). One CMS result on α (M ): s Z Illustration of dijet event topologies Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 23 Triple-differential dijets Simultaneous fit of αs & PDFs combining HERA DIS & CMS djet data using xFitter Tool Data over NLO pQCD x non-pert. x EW corrections Reduced uncertainties of gluon PDF √s lum α (M ) exp NP scale s Z [TeV] [fb-1] PDF +53 7 5.0 0.1185 35 -24 +29 +53 8 19.7 0.1164 -33 -28 +23 +24 7 5.0 0.1192 -19 -39 +19 +22 8 19.7 0.1185 -26 -18 16-parameter fit +15 +31 8 19.7 0.1199 -16 -19 Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 24 Multi-jets and αs Higher multiplicity ATLAS: EPJC 75 (2014) 288. Relevant ATLAS & CMS measurements: CMS: EPJC 73 (2013) 2604; EPJC 75 (2015) 186; PAS-SMP-16-008 (2017). Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 25 Jet cross section ratios Determination of α (M ) in single-parameter fit s Z Test running of αs(Q) (reduced PDF dependence) Some reduction in sensitivity But cancellation of many systematic effects More scale choices Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 26 Sensitivity vs. systematic effects Inclusive 3-jet cross section Inclusive 3-jet to inclusive 2-jet cross section ratio Inclusive 2-jet cross section Reduced sensitivity Much reduced systematic uncertainty Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 27 3- to 2-jet ratios M. Wobisch R 3/2 2011 αs = 0.124 αs = 0.106 Fits only above 420 GeV 2 NNPDF CMS: R3/2 - Ratio of inclusive 3- to inclusive 2-jet events - anti-kT R=0.7 √s lum α (M ) exp NP scale → α s Z - Min. jet pT: 150 GeV s [TeV] [fb-1] PDF - Max. rap.: |y| < 2.5 7 5.0 0.1148 23 50 - Data 2011 7 TeV, 8 19.7 0.1150 22 +50 and 2012 8 TeV prel. Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 28 Running of αs(Q) Perform fits in fixed intervals NLO of the chosen scale Q Jet cross sections and ratios Needs an update for latest ATLAS, CMS, & H1 points ... New range explored at LHC Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 29 Running of αs(Q) Perform fits in fixed intervals NLO of the chosen scale Q → 8 TeV → ATLAS ttbar NNLO Normalised distributions Needs an update for latest ATLAS, CMS, & H1 points ..
Recommended publications
  • Quantum Field Theory*
    Quantum Field Theory y Frank Wilczek Institute for Advanced Study, School of Natural Science, Olden Lane, Princeton, NJ 08540 I discuss the general principles underlying quantum eld theory, and attempt to identify its most profound consequences. The deep est of these consequences result from the in nite number of degrees of freedom invoked to implement lo cality.Imention a few of its most striking successes, b oth achieved and prosp ective. Possible limitation s of quantum eld theory are viewed in the light of its history. I. SURVEY Quantum eld theory is the framework in which the regnant theories of the electroweak and strong interactions, which together form the Standard Mo del, are formulated. Quantum electro dynamics (QED), b esides providing a com- plete foundation for atomic physics and chemistry, has supp orted calculations of physical quantities with unparalleled precision. The exp erimentally measured value of the magnetic dip ole moment of the muon, 11 (g 2) = 233 184 600 (1680) 10 ; (1) exp: for example, should b e compared with the theoretical prediction 11 (g 2) = 233 183 478 (308) 10 : (2) theor: In quantum chromo dynamics (QCD) we cannot, for the forseeable future, aspire to to comparable accuracy.Yet QCD provides di erent, and at least equally impressive, evidence for the validity of the basic principles of quantum eld theory. Indeed, b ecause in QCD the interactions are stronger, QCD manifests a wider variety of phenomena characteristic of quantum eld theory. These include esp ecially running of the e ective coupling with distance or energy scale and the phenomenon of con nement.
    [Show full text]
  • 3.4 V-A Coupling of Leptons and Quarks 3.5 CKM Matrix to Describe the Quark Mixing
    Advanced Particle Physics: VI. Probing the weak interaction 3.4 V-A coupling of leptons and quarks Reminder u γ µ (1− γ 5 )u = u γ µu L = (u L + u R )γ µu L = u Lγ µu L l ν l ν l l ν l ν In V-A theory the weak interaction couples left-handed lepton/quark currents (right-handed anti-lepton/quark currents) with an universal coupling strength: 2 GF gw = 2 2 8MW Weak transition appear only inside weak-isospin doublets: Not equal to the mass eigenstate Lepton currents: Quark currents: ⎛ν ⎞ ⎛ u ⎞ 1. ⎜ e ⎟ j µ = u γ µ (1− γ 5 )u 1. ⎜ ⎟ j µ = u γ µ (1− γ 5 )u ⎜ − ⎟ eν e ν ⎜ ⎟ du d u ⎝e ⎠ ⎝d′⎠ ⎛ν ⎞ ⎛ c ⎞ 5 2. ⎜ µ ⎟ j µ = u γ µ (1− γ 5 )u 2. ⎜ ⎟ j µ = u γ µ (1− γ )u ⎜ − ⎟ µν µ ν ⎜ ⎟ sc s c ⎝ µ ⎠ ⎝s′⎠ ⎛ν ⎞ ⎛ t ⎞ µ µ 5 3. ⎜ τ ⎟ j µ = u γ µ (1− γ 5 )u 3. ⎜ ⎟ j = u γ (1− γ )u ⎜ − ⎟ τν τ ν ⎜ ⎟ bt b t ⎝τ ⎠ ⎝b′⎠ 3.5 CKM matrix to describe the quark mixing One finds that the weak eigenstates of the down type quarks entering the weak isospin doublets are not equal to the their mass/flavor eigenstates: ⎛d′⎞ ⎛V V V ⎞ ⎛d ⎞ d V u ⎜ ⎟ ⎜ ud us ub ⎟ ⎜ ⎟ ud ⎜ s′⎟ = ⎜Vcd Vcs Vcb ⎟ ⋅ ⎜ s ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ W ⎝b′⎠ ⎝Vtd Vts Vtb ⎠ ⎝b⎠ Cabibbo-Kobayashi-Maskawa mixing matrix The quark mixing is the origin of the flavor number violation of the weak interaction.
    [Show full text]
  • Coupling Constant Unification in Extensions of Standard Model
    Coupling Constant Unification in Extensions of Standard Model Ling-Fong Li, and Feng Wu Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213 May 28, 2018 Abstract Unification of electromagnetic, weak, and strong coupling con- stants is studied in the extension of standard model with additional fermions and scalars. It is remarkable that this unification in the su- persymmetric extension of standard model yields a value of Weinberg angle which agrees very well with experiments. We discuss the other possibilities which can also give same result. One of the attractive features of the Grand Unified Theory is the con- arXiv:hep-ph/0304238v2 3 Jun 2003 vergence of the electromagnetic, weak and strong coupling constants at high energies and the prediction of the Weinberg angle[1],[3]. This lends a strong support to the supersymmetric extension of the Standard Model. This is because the Standard Model without the supersymmetry, the extrapolation of 3 coupling constants from the values measured at low energies to unifi- cation scale do not intercept at a single point while in the supersymmetric extension, the presence of additional particles, produces the convergence of coupling constants elegantly[4], or equivalently the prediction of the Wein- berg angle agrees with the experimental measurement very well[5]. This has become one of the cornerstone for believing the supersymmetric Standard 1 Model and the experimental search for the supersymmetry will be one of the main focus in the next round of new accelerators. In this paper we will explore the general possibilities of getting coupling constants unification by adding extra particles to the Standard Model[2] to see how unique is the Supersymmetric Standard Model in this respect[?].
    [Show full text]
  • Strong Coupling and Quantum Molecular Plasmonics
    Strong coupling and molecular plasmonics Javier Aizpurua http://cfm.ehu.es/nanophotonics Center for Materials Physics, CSIC-UPV/EHU and Donostia International Physics Center - DIPC Donostia-San Sebastián, Basque Country AMOLF Nanophotonics School June 17-21, 2019, Science Park, Amsterdam, The Netherlands Organic molecules & light Excited molecule (=exciton on molecule) Photon Photon Adding mirrors to this interaction The photon can come back! Optical cavities to enhance light-matter interaction Optical mirrors Dielectric resonator Veff Q ∼ 1/κ Photonic crystals Plasmonic cavity Veff Q∼1/κ Coupling of plasmons and molecular excitations Plasmon-Exciton Coupling Plasmon-Vibration Coupling Absorption, Scattering, IR Absorption, Fluorescence Veff Raman Scattering Extreme plasmonic cavities Top-down Bottom-up STM ultra high-vacuum Wet Chemistry Low temperature Self-assembled monolayers (Hefei, China) (Cambridge, UK) “More interacting system” One cannot distinguish whether we have a photon or an excited molecule. The eigenstates are “hybrid” states, part molecule and part photon: “polaritons” Strong coupling! Experiments: organic molecules Organic molecules: Microcavity: D. G. Lidzey et al., Nature 395, 53 (1998) • Large dipole moments • High densities collective enhancement • Rabi splitting can be >1 eV (~30% of transition energy) • Room temperature! Surface plasmons: J. Bellessa et al., Single molecule with gap plasmon: Phys. Rev. Lett. 93, 036404 (2004) Chikkaraddy et al., Nature 535, 127 (2016) from lecture by V. Shalaev Plasmonic cavities
    [Show full text]
  • Critical Coupling for Dynamical Chiral-Symmetry Breaking with an Infrared Finite Gluon Propagator *
    BR9838528 Instituto de Fisica Teorica IFT Universidade Estadual Paulista November/96 IFT-P.050/96 Critical coupling for dynamical chiral-symmetry breaking with an infrared finite gluon propagator * A. A. Natale and P. S. Rodrigues da Silva Instituto de Fisica Teorica Universidade Estadual Paulista Rua Pamplona 145 01405-900 - Sao Paulo, S.P. Brazil *To appear in Phys. Lett. B t 2 9-04 Critical Coupling for Dynamical Chiral-Symmetry Breaking with an Infrared Finite Gluon Propagator A. A. Natale l and P. S. Rodrigues da Silva 2 •r Instituto de Fisica Teorica, Universidade Estadual Paulista Rua Pamplona, 145, 01405-900, Sao Paulo, SP Brazil Abstract We compute the critical coupling constant for the dynamical chiral- symmetry breaking in a model of quantum chromodynamics, solving numer- ically the quark self-energy using infrared finite gluon propagators found as solutions of the Schwinger-Dyson equation for the gluon, and one gluon prop- agator determined in numerical lattice simulations. The gluon mass scale screens the force responsible for the chiral breaking, and the transition occurs only for a larger critical coupling constant than the one obtained with the perturbative propagator. The critical coupling shows a great sensibility to the gluon mass scale variation, as well as to the functional form of the gluon propagator. 'e-mail: [email protected] 2e-mail: [email protected] 1 Introduction The idea that quarks obtain effective masses as a result of a dynamical breakdown of chiral symmetry (DBCS) has received a great deal of attention in the last years [1, 2]. One of the most common methods used to study the quark mass generation is to look for solutions of the Schwinger-Dyson equation for the fermionic propagator.
    [Show full text]
  • The Electron-Phonon Coupling Constant 
    The electron-phonon coupling constant Philip B. Allen Department of Physics and Astronomy, State University of New York, Stony Brook, NY 11794-3800 March 17, 2000 Tables of values of the electron-phonon coupling constants and are given for selected tr elements and comp ounds. A brief summary of the theory is also given. I. THEORETICAL INTRODUCTION Grimvall [1] has written a review of electron-phonon e ects in metals. Prominent among these e ects is sup ercon- ductivity. The BCS theory gives a relation T exp1=N 0V for the sup erconducting transition temp erature c D T in terms of the Debye temp erature .Values of T are tabulated in various places, the most complete prior to c D c the high T era b eing ref. [2]. The electron-electron interaction V consists of the attractive electron-phonon-induced c interaction minus the repulsive Coulombinteraction. The notation is used = N 0V 1 eph and the Coulomb repulsion N 0V is called , so that N 0V = , where is a \renormalized" Coulomb c repulsion, reduced in value from to =[1 + ln! =! ]. This suppression of the Coulomb repulsion is a result P D of the fact that the electron-phonon attraction is retarded in time by an amountt 1=! whereas the repulsive D screened Coulombinteraction is retarded byamuch smaller time, t 1=! where ! is the electronic plasma P P frequency. Therefore, is b ounded ab oveby1= ln! =! which for conventional metals should b e 0:2. P D Values of are known to range from 0:10 to 2:0.
    [Show full text]
  • How the Electron-Phonon Coupling Mechanism Work in Metal Superconductor
    How the electron-phonon coupling mechanism work in metal superconductor Qiankai Yao1,2 1College of Science, Henan University of Technology, Zhengzhou450001, China 2School of physics and Engineering, Zhengzhou University, Zhengzhou450001, China Abstract Superconductivity in some metals at low temperature is known to arise from an electron-phonon coupling mechanism. Such the mechanism enables an effective attraction to bind two mobile electrons together, and even form a kind of pairing system(called Cooper pair) to be physically responsible for superconductivity. But, is it possible by an analogy with the electrodynamics to describe the electron-phonon coupling as a resistivity-dependent attraction? Actually so, it will help us to explore a more operational quantum model for the formation of Cooper pair. In particularly, by the calculation of quantum state of Cooper pair, the explored model can provide a more explicit explanation for the fundamental properties of metal superconductor, and answer: 1) How the transition temperature of metal superconductor is determined? 2) Which metals can realize the superconducting transition at low temperature? PACS numbers: 74.20.Fg; 74.20.-z; 74.25.-q; 74.20.De ne is the mobile electron density, η the damping coefficient 1. Introduction that is determined by the collision time τ . In the BCS theory[1], superconductivity is attributed to a In metal environment, mobile electrons are usually phonon-mediated attraction between mobile electrons near modeled to be a kind of classical particles like gas molecules, Fermi surface(called Fermi electrons). The attraction is each of which performs a Brown-like motion and satisfies the sometimes referred to as a residual Coulomb interaction[2] that Langevin equation can glue Cooper pair together to cause superconductivity.
    [Show full text]
  • 1.3 Running Coupling and Renormalization 27
    1.3 Running coupling and renormalization 27 1.3 Running coupling and renormalization In our discussion so far we have bypassed the problem of renormalization entirely. The need for renormalization is related to the behavior of a theory at infinitely large energies or infinitesimally small distances. In practice it becomes visible in the perturbative expansion of Green functions. Take for example the tadpole diagram in '4 theory, d4k i ; (1.76) (2π)4 k2 m2 Z − which diverges for k . As we will see below, renormalizability means that the ! 1 coupling constant of the theory (or the coupling constants, if there are several of them) has zero or positive mass dimension: d 0. This can be intuitively understood as g ≥ follows: if M is the mass scale introduced by the coupling g, then each additional vertex in the perturbation series contributes a factor (M=Λ)dg , where Λ is the intrinsic energy scale of the theory and appears for dimensional reasons. If d 0, these diagrams will g ≥ be suppressed in the UV (Λ ). If it is negative, they will become more and more ! 1 relevant and we will find divergences with higher and higher orders.8 Renormalizability. The renormalizability of a quantum field theory can be deter- mined from dimensional arguments. Consider φp theory in d dimensions: 1 g S = ddx ' + m2 ' + 'p : (1.77) − 2 p! Z The action must be dimensionless, hence the Lagrangian has mass dimension d. From the kinetic term we read off the mass dimension of the field, namely (d 2)=2. The − mass dimension of 'p is thus p (d 2)=2, so that the dimension of the coupling constant − must be d = d + p pd=2.
    [Show full text]
  • The QED Coupling Constant for an Electron to Emit Or Absorb a Photon Is Shown to Be the Square Root of the Fine Structure Constant Α Shlomo Barak
    The QED Coupling Constant for an Electron to Emit or Absorb a Photon is Shown to be the Square Root of the Fine Structure Constant α Shlomo Barak To cite this version: Shlomo Barak. The QED Coupling Constant for an Electron to Emit or Absorb a Photon is Shown to be the Square Root of the Fine Structure Constant α. 2020. hal-02626064 HAL Id: hal-02626064 https://hal.archives-ouvertes.fr/hal-02626064 Preprint submitted on 26 May 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. V4 15/04/2020 The QED Coupling Constant for an Electron to Emit or Absorb a Photon is Shown to be the Square Root of the Fine Structure Constant α Shlomo Barak Taga Innovations 16 Beit Hillel St. Tel Aviv 67017 Israel Corresponding author: [email protected] Abstract The QED probability amplitude (coupling constant) for an electron to interact with its own field or to emit or absorb a photon has been experimentally determined to be -0.08542455. This result is very close to the square root of the Fine Structure Constant α. By showing theoretically that the coupling constant is indeed the square root of α we resolve what is, according to Feynman, one of the greatest damn mysteries of physics.
    [Show full text]
  • (Supersymmetric) Grand Unification
    J. Reuter SUSY GUTs Uppsala, 15.05.2008 (Supersymmetric) Grand Unification Jürgen Reuter Albert-Ludwigs-Universität Freiburg Uppsala, 15. May 2008 J. Reuter SUSY GUTs Uppsala, 15.05.2008 Literature – General SUSY: M. Drees, R. Godbole, P. Roy, Sparticles, World Scientific, 2004 – S. Martin, SUSY Primer, arXiv:hep-ph/9709356 – H. Georgi, Lie Algebras in Particle Physics, Harvard University Press, 1992 – R. Slansky, Group Theory for Unified Model Building, Phys. Rep. 79 (1981), 1. – R. Mohapatra, Unification and Supersymmetry, Springer, 1986 – P. Langacker, Grand Unified Theories, Phys. Rep. 72 (1981), 185. – P. Nath, P. Fileviez Perez, Proton Stability..., arXiv:hep-ph/0601023. – U. Amaldi, W. de Boer, H. Fürstenau, Comparison of grand unified theories with electroweak and strong coupling constants measured at LEP, Phys. Lett. B260, (1991), 447. J. Reuter SUSY GUTs Uppsala, 15.05.2008 The Standard Model (SM) – Theorist’s View Renormalizable Quantum Field Theory (only with Higgs!) based on SU(3)c × SU(2)w × U(1)Y non-simple gauge group ν u h+ L = Q = uc dc `c [νc ] L ` L d R R R R h0 L L Interactions: I Gauge IA (covariant derivatives in kinetic terms): X a a ∂µ −→ Dµ = ∂µ + i gkVµ T k I Yukawa IA: u d e ˆ n ˜ Y QLHuuR + Y QLHddR + Y LLHdeR +Y LLHuνR I Scalar self-IA: (H†H)(H†H)2 J. Reuter SUSY GUTs Uppsala, 15.05.2008 The group-theoretical bottom line Things to remember: Representations of SU(N) i j 2 I fundamental reps. φi ∼ N, ψ ∼ N, adjoint reps.
    [Show full text]
  • Lattice-QCD Determinations of Quark Masses and the Strong Coupling Αs
    Lattice-QCD Determinations of Quark Masses and the Strong Coupling αs Fermilab Lattice, MILC, and TUMQCD Collaborations September 1, 2020 EF Topical Groups: (check all that apply /) (EF01) EW Physics: Higgs Boson Properties and Couplings (EF02) EW Physics: Higgs Boson as a Portal to New Physics (EF03) EW Physics: Heavy Flavor and Top-quark Physics (EF04) EW Physics: Electroweak Precision Physics and Constraining New Physics (EF05) QCD and Strong Interactions: Precision QCD (EF06) QCD and Strong Interactions: Hadronic Structure and Forward QCD (EF07) QCD and Strong Interactions: Heavy Ions (EF08) BSM: Model-specific Explorations (EF09) BSM: More General Explorations (EF10) BSM: Dark Matter at Colliders Other Topical Groups: (RF01) Weak Decays of b and c Quarks (TF02) Effective Field Theory Techniques (TF05) Lattice Gauge Theory (CompF2) Theoretical Calculations and Simulation Contact Information: Andreas S. Kronfeld (Theoretical Physics Department, Fermilab) [email]: [email protected] on behalf of the Fermilab Lattice, MILC, and TUMQCD Collaborations Fermilab Lattice, MILC, and TUMQCD Collaborations: A. Bazavov, C. Bernard, N. Brambilla, C. DeTar, A.X. El-Khadra, E. Gamiz,´ Steven Gottlieb, U.M. Heller, W.I. Jay, J. Komijani, A.S. Kronfeld, J. Laiho, P.B. Mackenzie, E.T. Neil, P. Petreczky, J.N. Simone, R.L. Sugar, D. Toussaint, A. Vairo, A. Vaquero Aviles-Casco,´ J.H. Weber, R.S. Van de Water Lattice-QCD Determinations of Quark Masses and the Strong Coupling αs Quantum chromdynamics (QCD) as a stand-alone theory has 1 + nf + 1 free parameters that must be set from experimental measurements, complemented with theoretical calculations connecting the measurements to the QCD Lagrangian.
    [Show full text]
  • The Determination of the Strong Coupling Constant Arxiv
    The Determination of the Strong Coupling Constant G¨unther Dissertori Institute for Particle Physics, ETH Zurich, Switzerland June 18, 2015 Abstract The strong coupling constant is one of the fundamental parame- ters of the standard model of particle physics. In this review I will briefly summarise the theoretical framework, within which the strong coupling constant is defined and how it is connected to measurable observables. Then I will give an historical overview of its experimen- tal determinations and discuss the current status and world average value. Among the many different techniques used to determine this coupling constant in the context of quantum chromodynamics, I will focus in particular on a number of measurements carried out at the Large Electron Positron Collider (LEP) and the Large Hadron Col- lider (LHC) at CERN. arXiv:1506.05407v1 [hep-ex] 17 Jun 2015 A contribution to: The Standard Theory up to the Higgs discovery - 60 years of CERN L. Maiani and G. Rolandi, eds. 1 1 Introduction The strong coupling constant, αs, is the only free parameter of the lagrangian of quantum chromodynamics (QCD), the theory of strong interactions, if we consider the quarkp masses as fixed. As such, this coupling constant, or equivalently gs = 4παs, is one of the three fundamental coupling constants of the standard model (SM) of particle physics. It is related to the SU(3)C colour part of the overall SU(3)C × SU(2)L × U(1)Y gauge symmetry of the SM. The other two constants g and g0 indicate the coupling strengths relevant for weak isospin and weak hypercharge, and can be rewritten in terms of 0 the Weinberg mixing angle tan θW = g =g and the fine-structure constant 2 α = e =(4π), where the electric charge is given by e = g sin θW.
    [Show full text]