Proceedings Series


Vol. 6 (2013), No. 1, pp. 1 – 384

LIGHT CONE Cracow 2012 Modern Approaches to Nonperturbative Gauge Theories and Their Applications

Kraków, Poland; July 9–13, 2012

Diffractive Proton–Proton Scattering in Holographic QCD

abstract

We further analyze the holographic dipole–dipole scattering amplitude developed in  G. Basar et al. , Phys. Rev. D85, 105005 (2012) and A. Stoffers, I. Zahed, arXiv:1205.3223 [hep-ph]. Gribov diffusion at strong coupling yields the scattering amplitude in a confining background. We compare the holographic result for the differential cross section to diffractive proton–proton scattering data.


Three-field Potential for Soft-wall AdS/QCD

abstract

The AdS/CFT correspondence may offer new and useful insights into the non-perturbative regime of strongly coupled gauge theories such as Quantum Chromodynamics. Soft-wall AdS/QCD models have reproduced the linear trajectories of meson spectra by including background dilaton and chiral condensate fields. Efforts to derive these background fields from a scalar potential have so far been unsuccessful in satisfying the UV boundary conditions set by the AdS/CFT dictionary while reproducing the IR behavior needed to obtain the correct chiral symmetry breaking and meson spectra. We present a three-field scalar parametrization that includes the dilaton field and the chiral and glueball condensates. This model is consistent with linear trajectories for the meson spectra and the correct mass-splitting between the vector and axial-vector mesons. We also present the resulting meson trajectories.


Some Approaches to GPDs in AdS/QCD

abstract

We discuss a way to get some generalized parton distributions (GPDs) of quarks using AdS/QCD models. The approach is based on a matching procedure of sum rules relating the electromagnetic form factors to GPDs and AdS modes.


Emergent AdS/QCD

abstract

We elaborate on the correspondence between a non-conformal 4d quantum field theory over the Minkowski space — e.g. quantum chromodynamics or an extension of the standard model that breaks the electroweak symmetry dynamically — and a 5d description over an AdS spacetime. Among other things, we are tracing contributions that break the conformal symmetry in the 4d theory to the warping of the 5d geometry, which resembles the soft-wall model.


Relations Between Anomalous and Even-parity Sectors in AdS/QCD

abstract

We derive the \({\cal O}(p^6)\) Chiral Perturbation Theory Lagrangian in the massless quark limit for a class of gravity dual models of Quantum Chromodynamics with the chiral symmetry broken through boundary conditions. The odd \({\cal O}(p^6)\) couplings are related to the \({\cal O}(p^4)\) low-energy constants (LECs) in the even-parity sector. Some combinations of even \({\cal O}(p^6)\) couplings are found to be universal and independent of the peculiarities of the model. These relations turn out to be the manifestation at low energies of a broader relation between anomalous and even-parity amplitudes.


Nucleon Structure Including High Fock States in Soft-wall Holographic Approach

abstract

We present a detailed analysis of nucleon form factors in a holographic soft-wall model. This approach is based on an action which describes hadrons with broken conformal invariance and incorporates confinement through the presence of a background dilaton field. For \(N_c=3\), we describe the nucleon structure in a superposition of a three valence quark state with high Fock states including an adjustable number of partons (quarks, antiquarks and gluons) via studying the dynamics of 5D fermion fields of different scaling dimension in anti-de Sitter (ADS) space. According to the gauge/gravity duality the 5D fermion fields of different scaling dimension correspond to the Fock state components with a specific number of partons.


Fluid/Gravity Correspondence and Holographic Mixed Gauge-Gravitational Anomaly

abstract

We study, in the framework of the fluid/gravity correspondence, the anomaly induced current of a magnetic field and a vortex in a relativistic fluid. We use a holographic model with pure gauge and mixed gauge-gravitational Chern–Simons terms in the action, and confirm the results obtained within the Kubo formulae formalism [K. Landsteiner, E. Megías, F. Pena-Benitez, Rev. Lett. 107, 021601 (2011); K. Landsteiner, E. Megías, L. Melgar, F. Pena-Benitez J. High Energy Phys. 09, 121 (2011). The results are obtained in several frames, and we study the relation between these frames and the boundary conditions when solving the dynamical equations.


Non-equilibrium Dynamics of QGP in AdS/CFT Framework

abstract

Recently developed numerical method in AdS/CFT correspondence allows for simulation of strongly coupled non-equilibrium expanding \({\mathcal N}=4\) SYM fluid. This system serves as a testbed for RHIC and LHC quark-gluon plasma research, as well as a well-defined toy model of strongly coupled, non-perturbative non-Abelian gauge theory at finite temperature. Application of numerical tools allowed to gain some insight into the process of transition to hydrodynamic regime and also gave a few surprisingly simple characteristics of hydronization and thermalization process.


Relativistic Bound States at Born Level

abstract

Theoretical and phenomenological studies indicate that the QCD coupling \(\alpha _{\rm s}(Q^2)\) freezes in the infrared. Hadrons may then be described by a perturbative expansion around “Born” states bound only by a confining potential. A linear potential results from the QCD equations of motion when Gauss’ law for \(A^0\) is solved with \(F_{\mu \nu }^a F^{\mu \nu }_a \neq 0\) as boundary condition. The \({\cal O} (\alpha _{\rm s}^0)\) Born states are Poincaré covariant and can serve as \(|{\rm in}\rangle \) and \(\langle {\rm out}|\) states of scattering amplitudes. Their Dirac-type wave functions include \(f\bar f\) creation/annihilation effects giving sea-like partons at low \({x_{\rm Bj}}\).


How to Construct Self/Anti-self Charge Conjugate States for Higher Spins? Significance of the Spin Bases, Mass Dimension, and All That

abstract

We construct self/anti-self charge conjugate (Majorana-like) states for the \((1/2,0)\oplus (0,1/2)\) representation of the Lorentz group, and their analogs for higher spins within the quantum field theory. The problems of the basis rotations and that of the selection of phases in the Dirac-like and Majorana-like field operators are considered. The discrete symmetries properties (\(P, C, T\)) are studied. The corresponding dynamical equations are presented. In the \((1/2,0)\oplus (0,1/2)\) representation they obey the Dirac-like equation with eight components, which has been first introduced by Markov. Thus, the Fock space for corresponding quantum fields is doubled (as shown by Ziino). The particular attention has been paid to the questions of chirality and helicity (two concepts which are frequently confused in the literature) for Dirac and Majorana states, and to the normalization (“the mass dimension”). We further review several experimental consequences which follow from the previous works of M. Kirchbach et al. on neutrinoless double beta decay, and G.J. Ni et al. on meson lifetimes. The results are generalized for spins 1, 3/2 and 2.


Worldline Techniques and QCD Observables

abstract

This report attempts to capture the essential workings of gauge links (Wilson lines) inside gauge-invariant formulations of parton distribution functions in QCD and gain some deeper insight into their key (renormalization) properties. We show, in particular, that the one-loop anomalous dimension of the Cherednikov–Stefanis quark TMD PDF is in the lightcone gauge \(A^+=0\), combined with the Mandelstam–Leibbrandt pole prescription, the same as that obtained in the special covariant gauge \(a=-3\), leaving no uncancelled rapidity singularities.


Gluon Confinement and the Two IR Solutions

abstract

We examine the two solutions (massive and scaling) for the covariant Yang–Mills Dyson–Schwinger equations within stochastic quantization, and find that the scaling solution does not survive outside Landau gauge. We also see that the (rainbow) massive solution has less Faddeev–Popov effective action. Finally, we argue that gluon confinement has only been marginally established in experiment and suggest further empirical work.


Progress in Euclidean Relativistic Few-body Quantum Mechanics

abstract

We discuss recent progress in the Euclidean formulation of relativistic few-body quantum mechanics.


Hadron Resonances, Large \(N_c\) and the Half-width Rule

abstract

We suggest using the half-width rule to make an estimate of the \(1/N_c\) errors in hadronic models containing resonances. We show simple consequences ranging from the analysis of meson Regge trajectories, the hadron resonance gas at finite temperature and generalized hadronic form factors.


Quark Transverse Momentum Distributions Inside a Nucleon: a Light-front Hamiltonian Dynamics Study

abstract

Through an impulse approximation analysis of single spin Sivers and Collins asymmetries in the Bjorken limit, the possibility to extract the quark transverse-momentum distributions in the neutron from semi-inclusive deep inelastic electron scattering off polarized \(^3\)He is illustrated. The analysis is generalized to finite momentum transfers in a light-front Poincaré covariant framework, defining the light-front spin-dependent spectral function of a \(J=1/2\) system. The definition of the light-front spin-dependent spectral function for constituent quarks in the nucleon allows us to show that, within the light-front dynamics, only three of the six leading twist \(T\)-even transverse-momentum distributions are independent.


Intrinsic Transverse Momentum and Parton Correlations From Nonperturbative Short-range Interactions

abstract

We summarize recent progress in understanding the effects of nonperturbative short-range interactions in QCD on the nucleon’s partonic structure at a low scale: (a) Sea quarks have intrinsic transverse momenta up to the chiral symmetry-breaking scale \(\rho ^{-1} \sim 0.6\) GeV, much larger than those of valence quarks. (b) Sea quarks in the nucleon light-cone wave function exist partly in correlated pairs of transverse size \(\rho \) with sigma and pi-like quantum numbers and a distinctive spin structure (\(L = 1\) components). The effects are demonstrated in an effective model of the low-energy dynamics resulting from chiral symmetry breaking in QCD. They have numerous implications for the \(P_{\rm T}\) distribution of hadrons in semi-inclusive DIS and multiparton processes in high-energy \(pp\) collisions.


Ideas of Four-fermion Operators in Hadron Physics

abstract

Four-fermion operators have been utilized in the past to link the quark-exchange processes in the interaction of hadrons with the effective meson-exchange amplitudes. In this paper, we apply the similar idea of Fierz rearrangement to the electromagnetic processes and focus on the electromagnetic form factors of nucleon and electron. We explain the motivation of using four-fermion operators and discuss the advantage of this method in computing electromagnetic processes.


Quark Orbital Angular Momentum

abstract

For transversely polarized nucleons the distribution of quarks in the transverse plane is transversely shifted and that shift can be described in terms of Generalized Parton Distributions (GPDs). This observation provides a ‘partonic’ derivation of the Ji-relation for the quark angular momentum in terms of GPDs. Wigner distributions are used to show that the difference between the Jaffe–Manohar definition of quark orbital angular momentum and that of Ji is equal to the change of orbital angular momentum due to the final state interactions as the struck quark leaves the target in a DIS experiment.


Issues in the GPD Formulation of DVCS

abstract

Virtual Compton scattering (VCS) can be used to explore the structure of hadrons. In the domain of large energy and momentum transfers, VCS is complementary to deep-inelastic scattering. If the kinematics is collinear, generalized parton distributions (GPDs) are widely used to describe VCS. This formulation satisfies electromagnetic gauge invariance only approximately. We propose to analyze experimental data in terms of Coulomb form factors, which occur in a gauge invariant formulation of Compton scattering, do not depend on the kinematics and can be related to GPDs in the deeply virtual limit.


Emphasizing the Different Trends of the Existing Data for the \(\gamma ^*\gamma \to \pi ^0\) Transition Form Factor

abstract

The new data on the \(\gamma ^*\gamma \to \pi ^0\) transition form factor of the Belle Collaboration are analyzed in comparison with those of BaBar (including the older data of CELLO and CLEO) using an approach based on light-cone sum rules. Performing a 2-, and a 3-parametric fit to these data, we found that the Belle and the BaBar data have no overlap at the \(1\sigma \) level. While the Belle data agree with our predictions, the Babar data are in conflict with them.


Axial Anomaly and Light Cone Distributions

abstract

Axial anomaly leads to exact sum rules for transition form factors providing the important constraints to respective distribution amplitudes. This rigorous NPQCD approach is valid even if QCD factorization is broken. The status of possible small non-OPE corrections to continuum in comparison to BaBar and Belle data is discussed.


Form Factors of Pseudoscalar Mesons in a Model with Unitarity and Regge Exchanges

abstract

We consider the transition and electromagnetic pseudoscalar form factors in a wide range of energy-momentum transfer, \(s\). We employ dispersion relations to connect the time-like and space-like region. We find that hadronic resonances give sizable contributions in the currently available range of \(s\). For the asymptotic contribution, we propose a model that operates with reggeized fermion exchanges.


The Meson-exchange Induced Light-by-light Contribution to \((g-2)_\mu \) Within the Nonlocal Chiral Quark Model

abstract

The current status of the muon anomalous magnetic moment (AMM) problem is briefly presented. The corrections to the muon AMM coming from the effects of hadronic light-by-light (LbL) scattering due to light quark–antiquark exchange in pseudoscalar and scalar channels are estimated within the nonlocal chiral quark model (N\(\chi \)QM). Within this approach the full kinematic dependence on the photon and meson virtualities are taken into account. As a result, the meson exchange contributions to the muon AMM calculated within N\(\chi \)QM are, in general, smaller than the contributions obtained within other models. The contribution from the scalar channel is positive and small, but stabilizes the combined with pseudoscalar channel result with respect to variation of the model parameters.


String Percolation and the First LHC Data

abstract

The results of string percolation on multiplicities and elliptic flow in \(AA\) and \(pp\) collisions are compared with LHC data showing a good agreement. We show that the dependence of the shear viscosity over entropy density ratio on the temperature, presents a minimum close to the critical temperature remaining small in the range of the RHIC and LHC energies.


Transport Properties of a Pion Gas

abstract

Through elliptic and higher-Fourier component flow measurements in ultra-relativistic heavy-ion collisions at RHIC and the LHC it is found that the shear viscosity-to-entropy ratio is very low, indicating that strong-interaction matter is a nearly perfect fluid. In this presentation, I discuss recent results for \(\eta /s\) in hadronic matter at vanishing baryo-chemical potential within kinetic theory. Using the Nambu-Jona–Lasinio model, special attention is paid to effects arising from the restoration of spontaneously broken chiral symmetry with increasing temperature.


New Hadrons with Heavy Quarks

abstract

We discuss several highly accurate theoretical predictions for masses of baryons containing the \(b\) quark which have been recently confirmed by experimental data. Proper treatment of the color-magnetic hyperfine interaction in QCD is crucial for obtaining these results. Several predictions are given for additional properties of heavy baryons. We also discuss the two charged exotic resonances \(Z_b\) with quantum numbers of a \((b \bar b u \bar d)\) tetraquark, very recently reported by Belle in the channel \([{\mit \Upsilon }(nS) \pi ^+,\ n=1,2,3]\). Among possible implications are deeply bound \(I{=0}\) counterparts of the \(Z_b\)’s and existence of a \({\mit \Sigma }_b^+{\mit \Sigma }_b^-\) dibaryon, a beauteron.


Two-particle Correlations from High Energy QCD

abstract

Angular correlations in two-gluon inclusive production are argued to be a generic feature of high energy/high density QCD. I, first, briefly review the wavefunction approach to high energy collisions and then, consider single and double inclusive gluon production within the formalism.


Pion–photon Transition Distribution Amplitudes in Non-local Chiral Quark Model

abstract

We study the pion–photon transition distribution amplitudes (TDAs) within semibosonized Nambu–Jona-Lasinio model with momentum dependent constituent quark mass. In order to satisfy the Ward–Takahashi identities, we use the non-local currents. We analyse the axial and vector channels and find that our TDAs satisfy polynomiality and the normalization requirement due to the axial anomaly. We calculate the related form factors (for \(\pi ^{\pm }\rightarrow e^{\pm }\nu \gamma \) decay) and find that the value of the axial form factor at zero momentum transfer is shifted towards the experimental value due to the non-locality of the model. We also analyse the pion–photon transition form factor for \(\pi ^{0}\rightarrow \gamma ^{*}\gamma \) and compare it with data.


Gluon Wavefunctions and Amplitudes on the Light-front

abstract

We investigate the tree level multi-gluon components of the gluon light cone wavefunctions in the light cone gauge keeping the exact kinematics of the gluon emissions. We focus on the components with all helicities identical to the helicity of the incoming gluon. The recurrence relations for the gluon wavefunctions are derived. In the case when the virtuality of the incoming gluon is neglected, the exact form of the multi-gluon wavefunction as well as the fragmentation function is obtained. Furthermore, we analyze the 2 to \(N\) tree-level gluon scattering in the framework of light-front perturbation theory and we demonstrate that the amplitude for this process can be obtained from the 1 to \(N+1\) gluon wavefunction. Finally, we demonstrate that our results for selected helicity configurations are equivalent to the Parke–Taylor amplitudes.


Some Aspects of Final States and QCD Evolution Equations

abstract

One of the approaches to study such effects like parton saturation in final states at the LHC is to combine physics of the BK and the CCFM evolution equations. We report on recently obtained resummed form of the BK equation and nonlinear extension of the CCFM equation — the KGBJS equation.


Optimizing Polar Angle Asymmetry Observables at Colliders

abstract

Angular asymmetries are simple, intuitive, model-independent observables used to identify spins of new elementary particles. In the case of Drell–Yan-like boson resonances, we generalize the well-known center-edge angular asymmetry to optimize spin identification when only a limited sample of events is available. By choosing simple weight functions \(W(\theta )\) in integrals over the polar angle \(\theta \), such as \(W = \cos ^n \theta \), we can improve spin discrimination significantly in production and decays of spin-0, spin-1, and spin-2 bosons. The power \(n\) can be tuned in particular cases, but \(n=2\) (\(n=1\)) works well for any forward–backward symmetric (non-symmetric) decay to massless particles.


all authors

A. Kusina, T. Stavreva, S. Berge, F.I. Olness, I. Schienbein, K. Kovařík, T. Ježo, J.Y. Yu, K. Park

Strange Quark PDF Uncertainty and Its Implications for \(W/Z\) Production at the LHC

abstract

We investigate the impact of parton distribution functions (PDFs) uncertainties on \(W/Z\) production at the LHC, concentrating on the strange quark PDF. Additionally, we examine the extent to which precise measurements at the LHC can provide additional information on the proton flavor structure.


QCD and Light-front Holography

abstract

The eigenvalues of the light-front QCD Hamiltonian, quantized at fixed light-front time \(\tau = t+z/c\), predict the hadronic mass spectrum and the corresponding eigensolutions provide the light-front wavefunctions which describe hadron structure. More generally, we show that the valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a single-variable relativistic equation of motion, analogous to the nonrelativistic radial Schrödinger equation, with an effective confining potential \(U\) which systematically incorporates the effects of higher quark and gluon Fock states. We outline a method for computing the required potential from first principles in QCD. The holographic mapping of gravity in AdS space to QCD, quantized at fixed light-front time, yields the same light-front Schrödinger equation; in fact, the soft-wall AdS/QCD approach provides a model for the light-front potential which is color-confining and reproduces well the light-hadron spectrum. One also derives via light-front holography a precise relation between the bound-state amplitudes in the fifth dimension of AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. The elastic and transition form factors of the pion and the nucleons are found to be well described in this framework. The light-front AdS/QCD holographic approach thus gives a frame-independent first approximation of the color-confining dynamics, spectroscopy, and excitation spectra of relativistic light-quark bound states in QCD.


Confinement, Chiral Symmetry Breaking and the Mass Generation of Hadrons

abstract

A key question to QCD is what mechanism generates the hadron mass in the light quark sector, where both confinement and chiral symmetry breaking are in the game. Are confinement and chiral symmetry breaking in the vacuum uniquely interconnected? Can hadrons survive chiral symmetry restoration? If yes, what happens with their mass and what symmetries beyond the chiral symmetry are there? We review our recent insights. In particular, in a dynamical lattice simulation we artificially restore chiral symmetry by removing the low-lying Dirac modes of the valence quark propagators, which is a well defined procedure and keep gluodynamics intact. Hadrons survive this artificial chiral restoration and their mass is surprisingly large. All hadrons fall into chiral multiplets and some of them are degenerate, i.e. the spectrum reveals some higher symmetry, that includes the chiral symmetry as a subgroup. The U\((1)_A\) symmetry does not get restored after removal of the chiral modes from the valence quarks.


Anomalous Quark–Gluon Chromomagnetic Interaction and Helicity Amplitudes of High Energy \(\rho \)-meson Electroproduction

abstract

In this article, we present some results of our investigation of the influence of instanton induced anomalous quark chromomagnetic moment on spin properties of electroproduced \(\rho \)-meson. The full set of helicity amplitudes has been calculated. It is shown that the existence of a large anomalous chromomagnetic moment of quark gives a tiny contribution to spin-flip amplitudes, but it is important for non-spin-flip amplitudes.


all authors

J.P. Vary, X. Zhao, A. Ilderton, H. Honkanen, P. Maris, S.J. Brodsky

Basis Light-front Quantization: a New Approach to Non-perturbative Scattering and Time-dependent Production Processes

abstract

Hamiltonian light-front quantum field theory constitutes a framework for deriving invariant masses, correlated parton amplitudes of self-bound systems and time-dependent scattering amplitudes. By choosing the light-front gauge and adopting an orthonormal basis function representation, we obtain a large, sparse, Hamiltonian matrix for mass eigenstates that is solvable by adapting ab initio no-core methods of nuclear many-body theory. In the continuum limit, the infinite matrix limit, we recover full covariance. There is considerable freedom in the choice of the orthonormal and complete set of basis functions with key considerations being convenience and convergence properties. We adopt a two-dimensional harmonic oscillator basis for transverse modes that corresponds with eigensolutions of the soft-wall anti-de Sitter/quantum chromodynamics (AdS/QCD) model obtained from light-front holography. We outline our approach and present preliminary results for non-linear Compton scattering, evaluated non-perturbatively, where a strong (possibly time-dependent) laser field excites an electron that emits a photon.


String Picture of 1+1 Dimensional QED in Light-front Formulation

abstract

We study quantum electrodynamics in 1+1 dimensions in the light-front frame using numerical methods. We analyze confinement and charge screening which are key features of this system. By direct analysis of wavefunctions of bound states in two-parton sector we determine the string tension. In four-parton sector we introduce inclusive distributions and inspect structure of energy eigenstates. We conclude that they are composed of two weakly interacting \(f\bar f\) pairs. These four-particle states are responsible for the screening. Finally, we study time evolution of a fermion–antifermion state separated by a specific distance. We demonstrate that for sufficient separation it decays into a multiparton state and the number of particles in the product depends on separation of particles.


Neutrino Oscillations in Hamiltonian Dynamics

abstract

Quantum mechanical description of neutrino oscillations can be developed in terms of the Gell-Mann–Goldberger formal theory of scattering [M. Gell-Mann, M.L. Goldberger, Phys. Rev. 91, 398 (1953)] provided that the theory is slightly extended [S.D. Głazek, A.P. Trawiński, Phys. Rev. D85, 125001(2012)]. The extension is needed because Gell-Mann and Goldberger considered only a very short period of time after a long incoming beam-preparation process ends and before a long outgoing transition-rate counting process starts, while in the case of neutrino oscillations the corresponding period of time is much longer than the beam-preparation and transition rate-counting processes. Besides the standard form of Hamiltonian dynamics, a slightly extended formal theory of scattering can also be defined in the so-called front form of Hamiltonian dynamics. The front form was distinguished by Dirac as particularly interesting in the context of particle physics [P.A.M. Dirac, Rev. Mod. Phys. 21, 392 (1949); P.A.M. Dirac, The Mathematical Foundations of Quantum Theory, ed. A.R. Marlow, Academic Press, 1978, pp. 1–8]. We present here an example of a description of neutrino oscillations in the front-form version of the required scattering theory [S.D. Głazek, A.P. Trawiński, Phys. Rev. D87, 025002 (2013)].


Light-front Quark Model Update on Mass Spectrum Calculations for Ground State Pseudoscalar and Vector Mesons

abstract

We present an update on our light-front quark model constrained by the variational principle for the QCD-motivated effective Hamiltonian. By smearing out the Dirac delta function in the hyperfine interaction and taking a larger harmonic oscillator basis in our trial wave function, we improved our model predictions for both mass spectra and decay constants of ground state pseudoscalar and vector mesons.


New Operator Solution of the Schwinger Model in a Covariant Gauge and Axial Anomaly

abstract

Massless QED (1+1) — the Schwinger model — is studied in a covariant gauge. The main new ingredient is an operator solution of the Dirac equation expressed directly in terms of the fields present in the Lagrangian. This allows us to study in detail residual symmetry of the covariant gauge. For comparison, we analyze first an analogous solution in the Thirring–Wess model and its implication for the axial anomaly arising from the necessity to correctly define products of fermion operators via point-splitting. In the Schwinger model, one has to define the currents in a gauge-invariant (GI) way. Certain problems with their usual derivation are identified, that obscure the origin of the massive gauge boson. We show how to define the truly GI interacting currents, reformulate the theory in a finite volume and clarify role of the gauge zero mode in the axial anomaly and in the Schwinger mechanism. A transformation to the Coulomb gauge representation is suggested along with ideas about how to correctly obtain other properties of the model.


Elementary Example of Mass Mixing Dynamics Without Involvement of the Vacuum

abstract

Most relativistic quantum field theories of interest appear to involve the unsolved problem of constructing a ground state, called vacuum. An elementary example of the vacuum problem appears in a theory in which the entire interaction is reduced to a mass-mixing term. This example can be solved using a new renormalization group procedure for effective particles and the relativistic solution is obtained without any need to solve the vacuum problem. This contribution briefly reviews the vacuum problem and explains how the new procedure works around it in the example.


Nakanishi Representation Onto the Null Plane and the Solution of the Bethe–Salpeter Equation

abstract

The Nakanishi perturbative integral representation of the 4D Bethe–Salpeter amplitude is used to solve the bound state problem in the Minkowski space. The main step to derive workable equations for Nakanishi weight function is provided by the projection onto the null-plane of the 4D Bethe–Salpeter Equation. We present a homogeneous equation for the Nakanishi weight-function for the ladder approximation of a bosonic model obtained by using uniqueness of the Nakanishi weight function. We provide numerical results and compare with another solution method.


Towards Finite Field Theory: The Taylor–Lagrange Regularization Scheme

abstract

We recall a natural framework to deal with local field theory in which bare amplitudes are completely finite. We first present the main general properties of this scheme, the so-called Taylor–Lagrange regularization scheme. We then investigate the consequences of this scheme on the calculation of perturbative radiative corrections to the Higgs mass within the Standard Model. Important consequences for the renormalization group equations are finally discussed.


Bound State Calculations in QED and QCD Using Basis Light-front Quantization

abstract

In order to describe self-bound systems, one needs a nonperturbative approach. We discuss the relativistic bound state equations of QED and QCD formulated in Basis Light-Front Quantization. In this approach, the light-front direction is discretized, and two-dimensional harmonic oscillator basis functions are used for the transverse direction. At present, the Fock-space in our calculations is limited to the minimal Fock sector, but the extension to an arbitrary number of (anti-)fermions and gauge bosons is in principle straightforward. We present initial results for the energies and distribution functions of two-body bound states obtained within this approach and discuss convergence issues.


Lorentz Symmetry for the Light-front Wightman Functions

abstract

New results for the Wightman function near the light-front hypersurface are presented. Mainly they disagree with the existing literature and suggest a substantial reformulation of the LF theory.


Solution of Bethe–Salpeter Equation in the Minkowski Space for the Scattering States

abstract

The Bethe–Salpeter equation for the scattering states in the Minkowski space is solved for spinless particles and ladder kernel. The off-mass-shell scattering amplitude is computed for the first time.


The Infrared Fixed Point of Landau Gauge Yang–Mills Theory

abstract

Over the last decade, the infrared behavior of Yang–Mills theory in the Landau gauge has been scrutinized with the help of Dyson–Schwinger equations and lattice calculations. In this contribution, we describe a technically simple approach to the deep infrared regime via Callan–Symanzik renormalization group equations in an epsilon expansion. This approach recovers, in an analytical and systematically improvable way, all the solutions previously found as solutions of the Dyson–Schwinger equations and singles out the solution favored by lattice calculations as the infrared-stable fixed point (for space-time dimensions above two).


Towards a Self-consistent Solution of the Landau Gauge Quark-Gluon Vertex Dyson–Schwinger Equation

abstract

The quark-gluon vertex in Landau gauge QCD is investigated in the Dyson–Schwinger approach. The aim is to obtain a fully self-consistent solution of the quark propagator and the quark-gluon vertex Dyson–Schwinger equation (DSE) in the vacuum using the gluon propagator as input from other calculations. The truncation scheme used in an earlier study is systematically improved and the first decisive step towards a full solution is presented. First results for the quark propagator with a fully dressed quark-gluon vertex in a truncation that incorporates all twelve vertex tensor-structures are shown.


A Dual Order Parameter From Fundamentally Colour Charged Matter

abstract

The center phase transition of QCD and of fundamentally charged scalar QCD at non-vanishing temperature is investigated within a Dyson–Schwinger approach. The temperature dependence of the scalar/quark propagator is studied with generalized boundary conditions. A novel order parameter for the center phase transition is established which still exhibits a considerable dependence on the scalar/quark-gluon vertex.


Lorentz Symmetry and Gauge Dependence in the Zwanziger Model of Two-potential QED

abstract

Zwanziger model of quantum electrodynamics (QED) introduces two independent vector gauge fields: \(A_\mu \) and \(B_\mu \), which allows for the local form of interaction and the electromagnetic duality transformation. This formulation is based on a fixed space-like 4-vector \(n^\nu \), which appears in the definition of the electromagnetic field strength tensor \(F_{\mu \nu }\). One finds a gauge invariant differential condition on the Wightman function \(\langle 0 | A_\mu (x) B_\nu (y) | 0 \rangle \). For a a free field, due to Peierls’s formula, this condition has no dependence on \(n^\mu \). One proves that this condition is inconsistent with the Lorentz covariance for vector fields, thus there is no Lorentz covariant Wightman function \(\langle 0 | A_\mu (x) B_\nu (y) | 0 \rangle \) in any gauge. Therefore, one may freely take different choices for the equal-time and the light-front formulations.


Electroweak Hadron Structure Within a Point-form Approach

abstract

We present a relativistic point-form approach for the calculation of electroweak form factors of few-body bound states. As an example, the transition form factors for the semileptonic weak decay \(B\to D^*e\bar \nu _e\) are discussed and it is sketched how they can be extracted unambiguously from the invariant transition amplitude that describes the process. It is shown how these form factors go over into one universal function, the Isgur–Wise function, in the heavy-quark limit, \(m_Q\to \infty \), and comparison with the available experimental data is made.


Flavor Analysis of Baryon Electromagnetic Form Factors

abstract

We report some sample results from a detailed study of the electromagnetic structure of baryons with flavors \(u\), \(d\), and \(s\). The individual flavor contributions to the elastic electromagnetic form factors are calculated along a relativistic constituent-quark model and compared to experimental data as well as results from lattice quantum chromodynamics. In the region of momentum transfers up to \(\sim \)4 GeV\(^2\), the form factor properties are well reproduced with valence-quark degrees of freedom only.


On Analytic Solutions of Multi-parton ’t Hooft Equations

abstract

Recent progress in understanding the structure of QCD\(_2\) with adjoint matter is reported. In particular, the analytic solutions of the most singular (in infrared) part of the QCD equations are constructed in arbitrary Fock sector of the theory.


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