DOCSLIB.ORG

Swimming with Quarks

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Swimming with Quarks SWIMMING WITH QUARKS M. R. Pennington Institute for Particle Physics Phenomenology, University of Durham, Durham DH1 3LE, U.K. Abstract. These six lectures, given at the XI Mexican School of Particles and Fields held at Xalapa in August 2004, are on the subject of strong coupling QCD. How this colours and shapes the hadron world in terms of (i) the hadron spectrum, (ii) chiral symmetry breaking, (iii) dynamical mass generation and (iv) confinement, are the topics discussed. 1. The quark model and beyond QCD is the theory of the strong interactions. It describes the forces between quarks and gluons that make up the hadron world. It may appear that lectures about hadrons describe ancient history, like the world of nuclei before we knew about protons and neutrons. However, there is an essential difference. Hadrons are what we observe in detectors. Though we often like to describe what is going on in terms of quarks and gluons, it is hadrons that either collide or are the result of collisions (or both) and not elementary quarks and gluons. In describing proton collisions at the LHC we imagine quarks and gluons interacting and these may in turn produce an elementary Higgs. However, though quarks and gluons may well interact perturbatively over distance scales of 10−18 m., we must not forget that as they travel over bigger distances away from the hard scattering process they have to dress themselves into the protons, pions and kaons that trigger detectors. How quarks and gluons are bound into hadrons is a long distance, strong coupling problem. It involves the regime of QCD that makes this theory and the interaction it describes far more interesting than QED. It provides the challenge for our understanding. Strong coupling QCD is responsible for the spectrum of hadrons, particularly those of light flavour. It is responsible for confinement and for the chiral symmetry breaking that shapes the light hadron world reflected in experiment. These are the topics of the present lectures. QCD has its beginnings in the spectrum of hadrons and the quark model representation of these [1]-[5]. This is our first strong coupling problem. The bound state problem we learnt about at our mother's knee is that of atoms. We know that the spectrum of light, emitted as an excited atom decays, directly reflects the fact that atoms are composed of charged objects, nuclei and electrons, with an electromagnetic force holding them together. Thus the spectrum of the system teaches us about the constituents of the system and the forces that bind them together. This is equally true of the spectrum of hadrons. Let us concentrate on mesons and recall the simple structure of some of the lightest of these [4]. Quarks have spin 1/2. Consequently a quark and antiquark can only form a system of intrinsic spin S = 0 or 1. The quark and antiquark can have relative orbital angular momentum, L , Figure 1. The multiplet of the nine lightest vector mesons on the left. The implicit horizontal axis is the z -component of isospin and the vertical axis is strangeness. ρ0; !; φ are at the origin. The main hadronic decay of each of these vector states is to pseudoscalar mesons as displayed on the right, where the length of the arrow denotes the energy released in that transition. which combines with S vectorially as usual in quantum mechanics to give the spin of the meson J , where J = L + S . This then fixes the parity and charge conjugation of the meson to be P = ( 1)L+1 ; C = ( 1)L+S : (1) − − Let us first consider the quark model states with S = 1; L = 0 . This gives the vector mesons with J P C = 1−− . With three light flavours, u; d; s we have nine vector mesons. We expect these to be divided into a flavour octet and flavour singlet, since: 3 3 = 8 1 : (2) ⊗ ⊕ The quantum numbers of the nine observed states are shown in Fig. 1. The two states in the middle of the multiplet with I = 0 , the ! and φ , are however not members of an octet and a singlet, respectively, but they magically mix so that they correspond to states of definite quark flavour. We learn this from their decays and from their masses, Fig. 1. The states decay overwhelmingly into pseudoscalar mesons by the creation of uu and dd pairs from the vacuum. This explains why the strange vector state the K ∗(890) decays to Kπ and the ρ to ππ , as shown in Fig. 2. The I = 0 octet and singlet states would both decay to 3 pions ( G -parity forbids the decay to 2 pions ). While the ! does decay to 3 pions, and has a mass very close to the ρ reflecting their composition of u and d quarks, the φ overwhelmingly decays to KK despite much greater phase space for its 3π mode, Fig. 1, and an ss composition is inferred. This is intimately related to the mass differences m(φ) m(K∗) m(K∗) m(!) 120 MeV ; − ' − ' which reflect the mass difference between the s quark and the u and d . For a state made of ss quarks to decay to 3π requires the initial strange quarks to annihilate and for all the quarks Figure 2. Quark line diagrams illustrating how the creation of uu and dd pairs allows the vector mesons, K∗; ρ, φ to decay into two pseudoscalar mesons. of the final state to be created from the vacuum. We learn that such a process is suppressed. This is known as the OZI rule. The fact that the ρ0 , ! and φ have composition 1 uu dd ; ss ; (3) p2 is confirmed by their decay rate to e+e− . As illustrated in Fig. 3, in this decay the quarks annihilate to form a virtual photon that then couples to an e+e− pair. Since the coupling of the photon to quarks is proportional to their charge, these decay rates are a measure of the square of the mean charge of the constituent quarks. If all other factors are equal for each Figure 3. Feynman graph of the neutral vector meson, V , decaying into e+e− , illustrating how the matrix element for this process is proportional to the average charge of the constituent quarks in the meson. meson, then Γ(ρ0 e+e−) : Γ(φ e+e−) : Γ(! e+e−) = ! ! ! 1 2 1 2 1 2 1 2 1 2 : : + = 9 : 2 : 1 :(4) p 3 3 3 p 3 3 2 − − − 2 − Experiment agrees with this very well. Exactly, the same structure of an ideally mixed nonet shown in Fig. 1 applies to the tensor 0 mesons where the quarks combine with S = 1; L = 1 . There the heaviest, the f2(1525) (the spin-2 analogue of the φ ) overwhelmingly decays to KK . The f2(1270) composed of u and d quarks can decay to KK too by the creation of an ss pair, but strange quarks being Figure 4. Feynman graph for a qq tensor meson, T , to decay into two photons. The square of its modulus gives the decay rate. heavier than u and d quarks, this has reduced probability. These assignments can be tested this time in their decay rate to two photons. A spin-2 meson naturally couples to two spin-1 photons. This rate is related to the square of the mean charge squared of the constituent quarks as illustrated in Fig. 4 by Γ(T γγ) α2 e2 2 Π ; (5) ! ∼ h q i T where ΠT is the probability that the quarks in a tensor meson, T , annihilate. In the non- relativistic quark model this is proportional to (0) 2 , where (0) is the wavefunction at the origin. If all these factors are the same for eachjneutralj tensor meson, then for an ideally mixed multiplet 0 Γ(f2(1270) γγ) : Γ(a2(1320) γγ) : Γ(f2(1525) γγ) = 25 : 9 : 2 : ! ! ! Experiment very approximately reproduces this with 25 : (10 1) : (1 1) . That this is not more exact is a combination of imperfect experiments and the fact that the masses of the states are only roughly equal so there are inevitably corrections to the naive non-relativistic quark model. This is highlighted by the application of the same formula, Eq. (5), to pseudoscalar mesons: π; η; η0 , for which experiment gives the ratio 1 : 50 : 600 . But Hayne and Isgur [6] 3 proposed that the naive result of Eq. (5) should be corrected by a factor of MP , where MP is the mass of the pseudoscalar meson. For the π; η; η0 this contributes factors of 1 : 67 : 357 multiplying the quark charges, bringing far better agreement with experiment. What does QCD add to this picture of qq mesons? We believe confinement requires that hadronic states should be colour singlets. This means their wavefunctions must be symmetric under permutations of the colours. Then the ρ+ instead of being simply ud has a colour wavefunction: + 1 ρ = uR dR + uG dG + uB dB + ; (6) j i pNc j · · · i where R (red), G (green), B (blue), label the Nc colours. While the number of colours matters little for mesons, for baryons ·it· ·is a different matter. A colour singlet wavefunction for a state of three quarks demands that each comes in a different colour. So a proton, made of uud quarks, has a singlet wavefunction 1 p = uR uG dB + uG uB dR + uB uR dG uR uB dG uB uG dR uG uR dB : (7) j i p6 j − − − i While the wavefunction is symmetric under permutations of the colours, it is odd under the interchange of any pair.
Load more

Recommended publications
  • Mesons Modeled Using Only Electrons and Positrons with Relativistic Onium Theory Ray Fleming Rayrfleming@Gmail.Com
    All mesons modeled using only electrons and positrons with relativistic onium theory Ray Fleming rayrfleming@gmail.com All mesons were investigated to determine if they can be modeled with the onium model discovered by Milne, Feynman, and Sternglass with only electrons and positrons. They discovered the relativistic positronium solution has the mass of a neutral pion and the relativistic onium mass increases in steps of me/α and me/2α per particle which is consistent with known mass quantization. Any pair of particles or resonances can orbit relativistically and particles and resonances can collocate to form increasingly complex resonances. Pions are positronium, kaons are pionium, D mesons are kaonium, and B mesons are Donium in the onium model. Baryons, which are addressed in another paper, have a non-relativistic nucleon combined with mesons. The results of this meson analysis shows that the compo- sition, charge, and mass of all mesons can be accurately modeled. Of the 220 mesons mod- eled, 170 mass estimates are within 5 MeV/c2 and masses of 111 of 121 D, B, charmonium, and bottomonium mesons are estimated to within 0.2% relative error. Since all mesons can be modeled using only electrons and positrons, quarks and quark theory are unnecessary. 1. Introduction 2. Method This paper is a report on an investigation to find Sternglass and Browne realized that a neutral pion whether mesons can be modeled as combinations of (π0), as a relativistic electron-positron pair, can orbit a only electrons and positrons using onium theory. A non-relativistic particle or resonance in what Browne companion paper on baryons is also available.
    [Show full text]
  • The Muon G-2 Discrepancy: Errors Or New Physics?
    The muon g-2 discrepancy: errors or new physics? † M. Passera∗, W. J. Marciano and A. Sirlin∗∗ ∗Istituto Nazionale Fisica Nucleare, Sezione di Padova, I-35131, Padova, Italy †Brookhaven National Laboratory, Upton, New York 11973, USA ∗∗Department of Physics, New York University, 10003 New York NY, USA Abstract. After a brief review of the muon g 2 status, we discuss hypothetical errors in the Standard Model prediction that could explain the present discrepancy with the− experimental value. None of them looks likely. In particular, an hypothetical + increase of the hadroproduction cross section in low-energy e e− collisions could bridge the muon g 2 discrepancy, but is shown to be unlikely in view of current experimental error estimates. If, nonetheless, this turns out to− be the explanation of the discrepancy, then the 95% CL upper bound on the Higgs boson mass is reduced to about 130 GeV which, in conjunction with the experimental 114.4 GeV 95% CL lower bound, leaves a narrow window for the mass of this fundamental particle. Keywords: Muon anomalous magnetic moment, Standard Model Higgs boson PACS: 13.40.Em, 14.60.Ef, 12.15.Lk, 14.80.Bn SM 11 INTRODUCTION aµ = 116591778(61) 10− . The difference with the EXP× 11 experimental value aµ = 116592080(63) 10− [1] The anomalousmagnetic momentof the muon, aµ ,isone EXP SM 11 × is ∆aµ = aµ aµ =+302(88) 10− , i.e., 3.4σ (all of the most interesting observables in particle physics. errors were added− in quadrature).× Similar discrepan- Indeed, as each sector of the Standard Model (SM) con- HLO cies are found employing the aµ values reported in tributes in a significant way to its theoretical prediction, Refs.
    [Show full text]
  • Effective Field Theories, Reductionism and Scientific Explanation Stephan
    To appear in: Studies in History and Philosophy of Modern Physics Effective Field Theories, Reductionism and Scientific Explanation Stephan Hartmann∗ Abstract Effective field theories have been a very popular tool in quantum physics for almost two decades. And there are good reasons for this. I will argue that effec- tive field theories share many of the advantages of both fundamental theories and phenomenological models, while avoiding their respective shortcomings. They are, for example, flexible enough to cover a wide range of phenomena, and concrete enough to provide a detailed story of the specific mechanisms at work at a given energy scale. So will all of physics eventually converge on effective field theories? This paper argues that good scientific research can be characterised by a fruitful interaction between fundamental theories, phenomenological models and effective field theories. All of them have their appropriate functions in the research process, and all of them are indispens- able. They complement each other and hang together in a coherent way which I shall characterise in some detail. To illustrate all this I will present a case study from nuclear and particle physics. The resulting view about scientific theorising is inherently pluralistic, and has implications for the debates about reductionism and scientific explanation. Keywords: Effective Field Theory; Quantum Field Theory; Renormalisation; Reductionism; Explanation; Pluralism. ∗Center for Philosophy of Science, University of Pittsburgh, 817 Cathedral of Learning, Pitts- burgh, PA 15260, USA (e-mail: shart@pitt.edu) (correspondence address); and Sektion Physik, Universit¨at M¨unchen, Theresienstr. 37, 80333 M¨unchen, Germany. 1 1 Introduction There is little doubt that effective field theories are nowadays a very popular tool in quantum physics.
    [Show full text]
  • Arxiv:2009.05616V2 [Hep-Ph] 18 Oct 2020 ± ± Bution from the Decays K → Π A2π (Considered in [1]) 2 0 0 Mrα Followed by the Decay A2π → Π Π [7]
    Possible manifestation of the 2p pionium in particle physics processes Peter Lichard Institute of Physics and Research Centre for Computational Physics and Data Processing, Silesian University in Opava, 746 01 Opava, Czech Republic and Institute of Experimental and Applied Physics, Czech Technical University in Prague, 128 00 Prague, Czech Republic 0 We suggest a few particle physics processes in which excited 2p pionium A2π may be observed. They include the e+e− ! π+π− annihilation, the V 0 ! π0`+`− and K± ! π±`+`− (` = e; µ) decays, and the photoproduction of two neutral pions from nucleons. We analyze available exper- imental data and find that they, in some cases, indicate the presence of 2p pionium, but do not provide definite proof. I. INTRODUCTION that its quantum numbers J PC = 1−− prevent it from decaying into the positive C-parity π0π0 and γγ states. The first thoughts about an atom composed of a pos- It must first undergo the 2p!1s transition to the ground state. The mean lifetime of 2p pionium itive pion and a negative pion (pionium, or A2π in the present-day notation) appeared almost sixty years ago. τ = 0:45+1:08 × 10−11 s: (1) Uretsky and Palfrey [1] assumed its existence and ana- 2p −0:30 lyzed the possibilities of detecting it in the photoproduc- is close to the value which comes for the π+π− atom tion off hydrogen target. Up to this time, such a process assuming a pure Coulomb interaction [8]. After reaching has not been observed. They also hypothesized about the 0 0 the 1s state, a decay to two π s quickly follows: A2π ! possibility of decay K+ ! π+A , which has recently 0 0 2π A2π + γ ! π π γ.
    [Show full text]
  • Finite-Volume and Magnetic Effects on the Phase Structure of the Three-Flavor Nambu–Jona-Lasinio Model
    PHYSICAL REVIEW D 99, 076001 (2019) Finite-volume and magnetic effects on the phase structure of the three-flavor Nambu–Jona-Lasinio model Luciano M. Abreu* Instituto de Física, Universidade Federal da Bahia, 40170-115 Salvador, Bahia, Brazil † Emerson B. S. Corrêa Faculdade de Física, Universidade Federal do Sul e Sudeste do Pará, 68505-080 Marabá, Pará, Brazil ‡ Cesar A. Linhares Instituto de Física, Universidade do Estado do Rio de Janeiro, 20559-900 Rio de Janeiro, Rio de Janeiro, Brazil Adolfo P. C. Malbouisson§ Centro Brasileiro de Pesquisas Físicas/MCTI, 22290-180 Rio de Janeiro, Rio de Janeiro, Brazil (Received 15 January 2019; revised manuscript received 27 February 2019; published 5 April 2019) In this work, we analyze the finite-volume and magnetic effects on the phase structure of a generalized version of Nambu–Jona-Lasinio model with three quark flavors. By making use of mean-field approximation and Schwinger’s proper-time method in a toroidal topology with antiperiodic conditions, we investigate the gap equation solutions under the change of the size of compactified coordinates, strength of magnetic field, temperature, and chemical potential. The ’t Hooft interaction contributions are also evaluated. The thermodynamic behavior is strongly affected by the combined effects of relevant variables. The findings suggest that the broken phase is disfavored due to both the increasing of temperature and chemical potential and the drop of the cubic volume of size L, whereas it is stimulated with the augmentation of magnetic field. In particular, the reduction of L (remarkably at L ≈ 0.5–3 fm) engenders a reduction of the constituent masses for u,d,s quarks through a crossover phase transition to the their corresponding current quark masses.
    [Show full text]
  • Sub Atomic Particles and Phy 009 Sub Atomic Particles and Developments in Cern Developments in Cern
    1) Mahantesh L Chikkadesai 2) Ramakrishna R Pujari mahantesh.chikkadesai@gmail.com ramakrishnapujari123@gmail.com Mobile no: +919480780580 Mobile no: +917411812551 Phy 009 Sub atomic particles and Phy 009 Sub atomic particles and developments in cern developments in cern Electrical and Electronics Electrical and Electronics KLS’s Vishwanathrao deshpande rural KLS’s Vishwanathrao deshpande rural institute of technology institute of technology Haliyal, Uttar Kannada Haliyal, Uttar Kannada SUB ATOMIC PARTICLES AND DEVELOPMENTS IN CERN Abstract-This paper reviews past and present cosmic rays. Anderson discovered their existence; developments of sub atomic particles in CERN. It High-energy subato mic particles in the form gives the information of sub atomic particles and of cosmic rays continually rain down on the Earth’s deals with basic concepts of particle physics, atmosphere from outer space. classification and characteristics of them. Sub atomic More-unusual subatomic particles —such as particles also called elementary particle, any of various self-contained units of matter or energy that the positron, the antimatter counterpart of the are the fundamental constituents of all matter. All of electron—have been detected and characterized the known matter in the universe today is made up of in cosmic-ray interactions in the Earth’s elementary particles (quarks and leptons), held atmosphere. together by fundamental forces which are Quarks and electrons are some of the elementary represente d by the exchange of particles known as particles we study at CERN and in other gauge bosons. Standard model is the theory that laboratories. But physicists have found more of describes the role of these fundamental particles and these elementary particles in various experiments.
    [Show full text]
  • Properties of Baryons in the Chiral Quark Model
    Properties of Baryons in the Chiral Quark Model Tommy Ohlsson Teknologie licentiatavhandling Kungliga Tekniska Hogskolan¨ Stockholm 1997 Properties of Baryons in the Chiral Quark Model Tommy Ohlsson Licentiate Dissertation Theoretical Physics Department of Physics Royal Institute of Technology Stockholm, Sweden 1997 Typeset in LATEX Akademisk avhandling f¨or teknologie licentiatexamen (TeknL) inom ¨amnesomr˚adet teoretisk fysik. Scientific thesis for the degree of Licentiate of Engineering (Lic Eng) in the subject area of Theoretical Physics. TRITA-FYS-8026 ISSN 0280-316X ISRN KTH/FYS/TEO/R--97/9--SE ISBN 91-7170-211-3 c Tommy Ohlsson 1997 Printed in Sweden by KTH H¨ogskoletryckeriet, Stockholm 1997 Properties of Baryons in the Chiral Quark Model Tommy Ohlsson Teoretisk fysik, Institutionen f¨or fysik, Kungliga Tekniska H¨ogskolan SE-100 44 Stockholm SWEDEN E-mail: tommy@theophys.kth.se Abstract In this thesis, several properties of baryons are studied using the chiral quark model. The chiral quark model is a theory which can be used to describe low energy phenomena of baryons. In Paper 1, the chiral quark model is studied using wave functions with configuration mixing. This study is motivated by the fact that the chiral quark model cannot otherwise break the Coleman–Glashow sum-rule for the magnetic moments of the octet baryons, which is experimentally broken by about ten standard deviations. Configuration mixing with quark-diquark components is also able to reproduce the octet baryon magnetic moments very accurately. In Paper 2, the chiral quark model is used to calculate the decuplet baryon ++ magnetic moments. The values for the magnetic moments of the ∆ and Ω− are in good agreement with the experimental results.
    [Show full text]
  • Relationship of Pionium Lifetime with Pion Scattering Lengths In
    RELATIONSHIP OF PIONIUM LIFETIME WITH PION SCATTERING LENGTHS IN GENERALIZED CHIRAL PERTURBATION THEORY H. SAZDJIAN Groupe de Physique Th´eorique, Institut de Physique Nucl´eaire, Universit´eParis XI, F-91406 Orsay Cedex, France E-mail: sazdjian@ipno.in2p3.fr The pionium lifetime is calculated in the framework of the quasipotential-constraint theory approach, including the sizable electromagnetic corrections. The framework of generalized chiral perturbation theory allows then an analysis of the lifetime value as a function of the ππ S-wave scattering lengths with isospin I = 0, 2, the latter being dependent on the quark condensate value. The DIRAC experiment at CERN is expected to measure the pionium lifetime with a 10% accuracy. The pionium is an atom made of π+π−, which decays under the effect of strong interactions into π0π0. The physical interest of the lifetime is that it gives us information about the ππ scattering lengths. The nonrelativistic formula of the lifetime was first obtained by Deser et al. 1: 0 2 2 1 16π 2∆mπ (a0 − a0) 2 =Γ0 = 2 |ψ+−(0)| , ∆mπ = mπ+ − mπ0 , (1) τ0 9 s mπ+ mπ+ where ψ+−(0) is the wave function of the pionium at the origin (in x-space) 0 2 and a0, a0, the S-wave scattering lengths with isospin 0 and 2, respectively. The evaluation of the relativistic corrections to this formula can be done in a systematic way in the framework of chiral perurbation theory (χPT ) 2, in the presence of electromagnetism 3. There arise essentially two types of correction. arXiv:hep-ph/0012228v1 18 Dec 2000 (i) The pion-photon radiative corrections, which are similar to those met in conventional QED.
    [Show full text]
  • International Centre for Theoretical Physics
    INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS OUTLINE OF A NONLINEAR, RELATIVISTIC QUANTUM MECHANICS OF EXTENDED PARTICLES Eckehard W. Mielke INTERNATIONAL ATOMIC ENERGY AGENCY UNITED NATIONS EDUCATIONAL, SCIENTIFIC AND CULTURAL ORGANIZATION 1981 MIRAMARE-TRIESTE IC/81/9 International Atomic Energy Agency and United Nations Educational Scientific and Cultural Organization 3TERKATIOHAL CENTRE FOR THEORETICAL PHTSICS OUTLINE OF A NONLINEAR, KELATIVXSTTC QUANTUM HECHAHICS OF EXTENDED PARTICLES* Eckehard W. Mielke International Centre for Theoretical Physics, Trieste, Italy. MIRAHABE - TRIESTE January 198l • Submitted for publication. ABSTRACT I. INTRODUCTION AMD MOTIVATION A quantum theory of intrinsically extended particles similar to de Broglie's In recent years the conviction has apparently increased among most theory of the Double Solution is proposed, A rational notion of the particle's physicists that all fundamental interactions between particles - including extension is enthroned by realizing its internal structure via soliton-type gravity - can be comprehended by appropriate extensions of local gauge theories. solutions of nonlinear, relativistic wave equations. These droplet-type waves The principle of gauge invarisince was first formulated in have a quasi-objective character except for certain boundary conditions vhich 1923 by Hermann Weyl[l57] with the aim to give a proper connection between may be subject to stochastic fluctuations. More precisely, this assumption Dirac's relativistic quantum theory [37] of the electron and the Maxwell- amounts to a probabilistic description of the center of a soliton such that it Lorentz's theory of electromagnetism. Later Yang and Mills [167] as well as would follow the conventional quantum-mechanical formalism in the limit of zero Sharp were able to extend the latter theory to a nonabelian gauge particle radius.
    [Show full text]
  • A Pionic Hadron Explains the Muon Magnetic Moment Anomaly
    A Pionic Hadron Explains the Muon Magnetic Moment Anomaly Rainer W. Schiel and John P. Ralston Department of Physics and Astronomy University of Kansas, Lawrence, KS 66045 Abstract A significant discrepancy exists between experiment and calcula- tions of the muon’s magnetic moment. We find that standard formu- las for the hadronic vacuum polarization term have overlooked pio- + nic states known to exist. Coulomb binding alone guarantees π π− states that quantum mechanically mix with the ρ meson. A simple 2-state mixing model explains the magnetic moment discrepancy for 2 a mixing angle of order α 10− . The relevant physical state is pre- ∼ + dicted to give a tiny observable bump in the ratio R( s ) of e e− an- nihilation at a low energy not previously searched. The burden of proof is reversed for claims that conventional physics cannot explain the muon’s anomalous moment. 1. Calculations of the muon’s magnetic moment do not currently agree arXiv:0705.0757v2 [hep-ph] 1 Oct 2007 with experiment. The discrepancy is of order three standard deviations and quite important. Among other things, uncertainties of the anomalous moment feed directly to precision tests of the Standard Model, including the Higgs mass, as well as providing primary constraints on new physics such as supersymmetry. In terms of the Land´e g factor, the “anomaly” aµ = ( g 2 )/2 experimentally observed in muons has become the quintessen- tial precision− test of quantum electrodynamics ( QED ). The current world average for aµ is [1, 2]: experimental 10 a = ( 11659208.0 6.3 ) 10− . µ ± × 1 The Standard Model theoretical prediction [3] for aµ is theory 10 a = ( 11659180.4 5.1 ) 10− .
    [Show full text]
  • Decay Widths and Energy Shifts of Ππ and Πk Atoms
    Physics Letters B 587 (2004) 33–40 www.elsevier.com/locate/physletb Decay widths and energy shifts of ππ and πK atoms J. Schweizer Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland Received 20 January 2004; accepted 2 March 2004 Editor: W.-D. Schlatter Abstract + − ± ∓ We calculate the S-wave decay widths and energy shifts for π π and π K atoms in the framework of QCD + QED. The evaluation—valid at next-to-leading order in isospin symmetry breaking—is performed within a non-relativistic effective field theory. The results are of interest for future hadronic atom experiments. 2004 Published by Elsevier B.V. PACS: 03.65.Ge; 03.65.Nk; 11.10.St; 12.39.Fe; 13.40.Ks Keywords: Hadronic atoms; Chiral perturbation theory; Non-relativistic effective Lagrangians; Isospin symmetry breaking; Electromagnetic corrections 1. Introduction [4–6] and with the results from other experiments [7]. Particularly interesting is the fact that one may deter- × Nearly fifty years ago, Deser et al. [1] derived the mine in this manner the nature of the SU(2) SU(2) formulae for the decay width and strong energy shift spontaneous chiral symmetry breaking experimentally of pionic hydrogen at leading order in isospin symme- [8]. New experiments are proposed for CERN PS and try breaking. Similar relations also hold for π+π− [2] J-PARC in Japan [9]. In order to determine the scat- and π−K+ atoms, which decay predominantly into tering lengths from such experiments, the theoretical 2π0 and π0K0, respectively. These Deser-type rela- expressions for the decay width and the strong en- tions allow to extract the scattering lengths from mea- ergy shift must be known to an accuracy that matches surements of the decay width and the strong energy the experimental precision.
    [Show full text]
  • Light-Front Holographic QCD and Emerging Confinement
    SLAC–PUB–15972 Light-Front Holographic QCD and Emerging Confinement Stanley J. Brodsky SLAC National Accelerator Laboratory, Stanford University, Stanford, CA 94309, USA Guy F. de T´eramond Universidad de Costa Rica, San Jos´e, Costa Rica Hans G¨unter Dosch Institut f¨ur Theoretische Physik, Philosophenweg 16, D-6900 Heidelberg, Germany Joshua Erlich College of William and Mary, Williamsburg, VA 23187, USA arXiv:1407.8131v2 [hep-ph] 13 Feb 2015 sjbth@slac.stanford.edu, gdt@asterix.crnet.cr, h.g.dosch@thphys.uni-heidelberg.de, jxerli@wm.edu (Invited review article to appear in Physics Reports) This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-76SF00515 and HEP. Abstract In this report we explore the remarkable connections between light-front dynamics, its holographic mapping to gravity in a higher-dimensional anti-de Sitter (AdS) space, and conformal quantum mechanics. This approach provides new insights into the origin of a fundamental mass scale and the physics underlying confinement dynamics in QCD in the limit of massless quarks. The result is a relativistic light-front wave equation for arbitrary spin with an effective confinement potential derived from a conformal action and its embedding in AdS space. This equation allows for the computation of essen- tial features of hadron spectra in terms of a single scale. The light-front holographic methods described here gives a precise interpretation of holographic variables and quan- tities in AdS space in terms of light-front variables and quantum numbers.
    [Show full text]