Symmetry Of QCD Research Articles

Burgers-like equation for spontaneous breakdown of the chiral symmetry in QCD

We link the spontaneous breakdown of chiral symmetry in Euclidean QCD to the collision of spectral shock waves in the vicinity of zero eigenvalue of the Dirac operator. The mechanism, originating from complex Burgerʼs-like equation for viscid, pressureless, one-dimensional flows of eigenvalues, is similar to the recently observed weak-strong coupling phase transition in large Nc Yang–Mills theory. The spectral viscosity is proportional to the inverse size of the random matrix that replaces the Dirac operator in the universal (ergodic) regime. We obtain the exact scaling function and critical exponents of the chiral phase transition for the averaged characteristic polynomial for Nc⩾3 QCD. We reinterpret our results in terms of known properties of chiral random matrix models and lattice data.

FakingBs→μ+μ−

Recent evidence from observation of the flavor-changing neutral current decay B_s to mu+ mu- by the LHCb collaboration B(B_s to mu^+ mu^-) = (3.2 * 10^{-9}), is consistent with the latest standard model prediction B(B_s to mu^+ mu^-) = (3.23 +- 0.27) * 10^{-9}. While New Physics can still affect this decay amplitude, its contribution is certainly not the dominant one. We analyze branching ratios of the decays B_s to mu+ mu- X, with X = a photon or neutrino anti-neutrino pair, which can mimic B_s to mu+ mu- on portions of the parameter space where X is soft. We perform a model-independent standard model calculation of those processes incorporating heavy quark and chiral symmetries of QCD. We show that the considered contributions contribute to B_s to mu+ mu- at a sub-percent level.

Hadron spectroscopy from strangeness to charm and beauty

Quarks of different flavors have different masses, which will cause breaking of flavor symmetries of QCD. Flavor symmetries and their breaking in hadron spectroscopy play important role for understanding the internal structures of hadrons. Hadron spectroscopy with strangeness reveals the importance of unquenched quark dynamics. Systematic study of hadron spectroscopy with strange, charm and beauty quarks would be very revealing and essential for understanding the internal structure of hadrons and its underlying quark dynamics.

Intrinsic transverse momentum and parton correlations from dynamical chiral symmetry breaking

The dynamical breaking of chiral symmetry in QCD is caused by nonperturbative interactions on a scale rho ~ 0.3 fm, much smaller than the hadronic size R ~ 1 fm. These short-distance interactions influence the intrinsic transverse momentum distributions of partons and their correlations at a low normalization point. We study this phenomenon in an effective description of low-energy dynamics based on chiral constituent quark degrees of freedom, which refers to the large-N_c limit of QCD. The nucleon is obtained as a system of constituent quarks and antiquarks moving in a self-consistent classical chiral field (chiral quark-soliton model). The calculated distributions of constituent quarks/antiquarks are matched with QCD partons at the scale rho^{-2}. The p_T distribution of valence quarks is localized at p_T^2 ~ R^{-2} and roughly of Gaussian shape. The sea quark distribution exhibits a would-be power-like tail ~1/p_T^2 extending up to the chiral symmetry-breaking scale. Such behavior is seen in the flavor-singlet unpolarized and nonsinglet polarized sea. The high-momentum tails are the result of short-range correlations between sea quarks in the nucleon's light-cone wave function, analogous to NN correlations in nuclei. The nucleon wave function contains correlated pairs of transverse size rho << R with sigma- and pi-like quantum numbers, whose internal wave functions become identical at p_T^2 ~ rho^{-2} (restoration of chiral symmetry). These features are model-independent and represent an effect of dynamical chiral symmetry breaking on the nucleon's partonic structure. Our results have numerous implications for the P_T distributions of particles produced in hard scattering processes. The nonperturbative parton correlations predicted here could be observed in particle correlations between the current and target fragmentation regions of DIS.

QCD as High Energy Limit of the Scalar Strong Interaction Hadron Theory

This paper is an extension of the book of reference [1] below. QCD Lagrangian is derived from the same equations of motion for quarks used to construct the equations of motion for mesons and baryons in the scalar strong interaction hadron theory that accounts for many basic low energy data not covered by QCD. At high energies, the energetic quarks in a hadron can be far from each other and approximately free. Each quark is associated with a vector in an internal space characterizing its mass and charge. These spaces are interchangeable and provide a new symmetry equivalent to color symmetry in QCD. A quark in a meson has two “colors” and in a baryon three “colors”; the β function of QCD is 61%-92% greater in high energy interactions leading to baryons than that to mesons. This function enters the measurable running coupling constant and this prediction is testable against experiment. QCD, successful at high energies, is thus reconciled with the scalar strong interaction hadron theory and both complement each other.

Vafa-Witten theorem, vector meson condensates, and magnetic-field-induced electromagnetic superconductivity of vacuum

We show that the electromagnetic superconductivity of vacuum in strong magnetic field background is consistent with the Vafa-Witten theorem because the charged vector meson condensates lock relevant internal global symmetries of QCD with the electromagnetic gauge group.

Noise and ultraviolet divergences in the dynamics of the chiral condensate in QCD

The time evolution of the matter produced in high energy heavy-ion collisions seems to be well described by relativistic viscous hydrodynamics. In addition to the hydrodynamic degrees of freedom related to energy-momentum conservation, degrees of freedom associated with order parameters of broken continuous symmetries must be considered because they are all coupled to each other. Of particular interest is the coupling of degrees of freedom associated with the chiral symmetry of QCD. Quantum and thermal fluctuations of the chiral fields act as noise sources in the classical equations of motion, turning them into stochastic differential equations in the form of Ginzburg-Landau-Langevin (GLL) equations. Analytic solutions of GLL equations are attainable only in very special circumstances and extensive numerical simulations are necessary, usually by discretizing the equations on a spatial lattice. However, a not much appreciated issue in the numerical simulations of GLL equations is that ultraviolet divergences in the form of lattice-spacing dependence plague the solutions. The divergences are related to the well-known Rayleigh-Jeans catastrophe in classical field theory. In the present communication we present a systematic lattice renormalization method to control the catastrophe. We discuss the implementation of the method for a GLL equation derived in the context of a model for the QCD chiral phase transition and consider the nonequilibrium evolution of the chiral condensate during the hydrodynamic flow of the quark-gluon plasma.

Nonlinear boundary dynamics and chiral symmetry in holographic QCD

In a hard-wall model of holographic QCD, we find that nonlinear boundary dynamics are required in order to maintain the correct pattern of explicit and spontaneous chiral symmetry breaking beyond leading order in the pion fields. With the help of a field redefinition, we relate the requisite nonlinear boundary conditions to a standard Sturm-Liouville system. Observables insensitive to the chiral limit receive only small corrections in the improved description, and classical calculations in the hard-wall model remain surprisingly accurate.

On Particles Mass and the Universons Hypothesis

In the logic of the Universons assumption, we deduce the nature of De Broglie wave and periodic mass variation for particles. We verify consistency with quantum mechanics, in particular the Schrodinger equation. We analyze the hypothesis that elementary particle mass is momentum circulating at light speed. We discover resonance rules acting within elementary particles leading to a formula governing the quantization of masses. Applying this formula to the electrons, muons, tauons and quarks, we find resonances that match with current measurements. We deduce the energy of unknown massless sub–particles at the core of electrons, muons, and tauons. Geometrical constraints inherent to our formula lead to a possible explanation to only three generations of particles. Based on particles geometry, we verify the consistency of the deduced quarks structure with QCD and raise the hypothesis that color charge is magnetic. We verify consistency with QCD symmetry and find that P and CP symmetry are broken by the interaction, in agreement with weak force knowledge. Our logic leads to re–interpret the Dirac condition on magnetic monopole charge, explain why the detection of magnetic monopoles is so difficult and, when detected, why magnetic charge can depart from Dirac prediction. We deduce a possible root cause of gravitation, resulting in the Schwarzschild metric and probable non existence of dark matter.

Few-Body Physics in Chiral Effective Field Theory: Recent Developments

Chiral effective field theory provides a systematic tool to study few-nucleon dynamics based on the approximate and spontaneously broken chiral symmetry of QCD. I discuss applications of this method to nuclear forces and few-nucleon dynamics. Various related topics including recent advances in nuclear lattice simulations are also addressed.

On flavor symmetry in lattice quantum chromodynamics

Using a well established method to engineer non-abelian symmetries in superstring compactifications, we study the link between the point splitting method of Creutz et al. [PoS: Lattice 2010, 078 (2010) and Creutz et al. JHEP 041, 1012 (2010)] for implementing flavor symmetry in lattice QCD; and singularity theory in complex algebraic geometry. We show amongst others that Creutz flavors for naive fermions are intimately related with toric singularities of a class of complex Kahler manifolds that are explicitly built here. In the case of naive fermions of QCD2N, Creutz flavors are shown to live at the poles of real 2-spheres and carry quantum charges of the fundamental of [SU(2)]2N. We show moreover that the two Creutz flavors in Karsten-Wilczek model, with Dirac operator in reciprocal space of the form \documentclass[12pt]{minimal}\begin{document}$i\mathbf {\gamma }_{1}\mathrm{F}_{1}+i\mathbf {\gamma }_{2}\mathrm{F}_{2}+ i\mathbf {\gamma }_{3}\mathrm{F}_{3}+ \frac{i}{\sin \alpha }\mathbf {\gamma }_{^{4}}\mathrm{F}_{4}$\end{document}iγ1F1+iγ2F2+iγ3F3+isinαγ4F4, are related with the small resolution of conifold singularity that live at sin α = 0. Other related features are also studied.

Effective model approach to the dense state of QCD matter

The first-principle approach to the dense state of QCD matter, i.e. the lattice-QCD simulation at finite baryon density, is not under theoretical control for the moment. The effective model study based on QCD symmetries is a practical alternative. However the model parameters that are fixed by hadronic properties in the vacuum may have unknown dependence on the baryon chemical potential. We propose a new prescription to constrain the effective model parameters by the matching condition with the thermal Statistical Model. In the transitional region where thermal quantities blow up in the Statistical Model, deconfined quarks and gluons should smoothly take over the relevant degrees of freedom from hadrons and resonances. We use the Polyakov-loop coupled Nambu-Jona-Lasinio (PNJL) model as an effective description in the quark side and show how the matching condition is satisfied by a simple ansäatz on the Polyakov loop potential. Our results favor a phase diagram with the chiral phase transition located at slightly higher temperature than deconfinement which stays close to the chemical freeze-out points.

Pion Loops in Chiral Perturbation Theory and Light-Front Dynamics

From the approximate chiral symmetry of QCD, it is known that the pion loops in chiral perturbation theory play a vital role in understanding the nucleon’s long-range structure. We demonstrate the equivalence of the light-front, equal-time and covariant formulations for the interactions of nucleons with pions in chiral perturbation theory. In particular, we discuss the self-energy Σ of a nucleon dressed by pion loops with the pseudovector πNN coupling. It is shown that the leading nonanalytic behavior of Σ is equivalent whichever formulations are used for the derivation. We also discuss the relation between the mass shift and the wavefunction renormalization as well as the difference between the pseudovector and pseudoscalar theories.

πNtransition distribution amplitudes: Their symmetries and constraints from chiral dynamics

Baryon to meson transition distribution amplitudes (TDAs) extend the concept of generalized parton distributions. Baryon to meson TDAs appear as building blocks in the collinear factorized description of amplitudes for a class of hard exclusive reactions, prominent examples of which being hard exclusive meson electroproduction off a nucleon in the backward region and baryon-antibaryon annihilation into a meson and a lepton pair. We study the general properties of these objects following from the underlying symmetries of QCD. In particular, the Lorentz symmetry results in the polynomiality property of the Mellin moments in longitudinal momentum fractions. We present a detailed account of the isotopic and permutation symmetry properties of nucleon to pion (\pi N) TDAs. This restricts the number of independent leading twist \pi N TDAs to eight functions, providing description of all isotopic channels. Using chiral symmetry and the crossing relation between \pi N TDAs and \pi N generalized distribution amplitudes we establish soft pion theorems for \pi N TDAs, which determine the magnitude of \pi N TDAs. Finally, we build a simple resonance exchange model for \pi N TDAs considering N and \Delta(1232) exchange contributions into the isospin-1/2 and isospin-3/2 \pi N TDAs.

Chiral unitary approach to [formula omitted] scattering at low energies

We study the η′N interaction within a chiral unitary approach which includes πN, ηN and related pseudoscalar meson–baryon coupled channels. Since the SU(3) singlet does not contribute to the standard interaction and the η′ is mostly a singlet, the resulting scattering amplitude is very small and inconsistent with the experimental scattering length. The additional consideration of vector meson–baryon states into the coupled channel scheme, via normal and anomalous couplings of pseudoscalar to vector mesons, enhances substantially the η′N amplitude. We also exploit the freedom of adding to the Lagrangian a new term, allowed by the symmetries of QCD, which couples baryons to the singlet meson of SU(3). Adjusting the unknown strength to the η′N scattering length, we obtain predictions for the elastic η′N→η′N and inelastic η′N→ηN, πN, KΛ, KΣ cross sections at low η′ energies, and discuss their significance.

Chiral effective field theories of the strong interactions

Effective field theories of the strong interactions based on the approximate chiral symmetry of QCD provide a model-independent approach to low-energy hadron physics. We give a brief introduction to mesonic and baryonic chiral perturbation theory and discuss a number of applications. We also consider the effective field theory including vector and axial-vector mesons.

Medium Modifications of Hadron Properties and Partonic Processes

Chiral symmetry is one of the most fundamental symmetries in QCD. It is closely connected to hadron properties in the nuclear medium via the reduction of the quark condensate < q̄q >, manifesting the partial restoration of chiral symmetry. To better understand this important issue, a number of Jefferson Lab experiments over the past decade have focused on understanding properties of mesons and nucleons in the nuclear medium, often benefiting from the high polarization and luminosity of the CEBAF accelerator. In particular, a novel, accurate, polarization transfer measurement technique revealed for the first time a strong indication that the bound proton electromagnetic form factors in 4He may be modified compared to those in the vacuum. Second, the photoproduction of vector mesons on various nuclei has been measured via their decay to e+ e− to study possible in-medium effects on the properties of the ρ meson. In this experiment, no significant mass shift and some broadening consistent with expected collisional broadening for the ρ meson has been observed, providing tight constraints on model calculations. Finally, processes involving in-medium parton propagation have been studied. The medium modifications of the quark fragmentation functions have been extracted with much higher statistical accuracy than previously possible.

Chiral Random Matrix Theory and Chiral Perturbation Theory

Spontaneous breaking of chiral symmetry in QCD has traditionally been inferred indirectly through low-energy theorems and comparison with experiments. Thanks to the understanding of an unexpected connection between chiral Random Matrix Theory and chiral Perturbation Theory, the spontaneous breaking of chiral symmetry in QCD can now be shown unequivocally from first principles and lattice simulations. In these lectures I give an introduction to the subject, starting with an elementary discussion of spontaneous breaking of global symmetries.

Confinement, chiral symmetry, and the lattice

Confinement, chiral symmetry, and the latticeTwo crucial properties of QCD, confinement and chiral symmetry breaking, cannot be understood within the context of conventional Feynman perturbation theory. Non-perturbative phenomena enter the theory in a fundamental way at both the classical and quantum levels. Over the years a coherent qualitative picture of the interplay between chiral symmetry, quantum mechanical anomalies, and the lattice has emerged and is reviewed here.

The Role of Δ-Resonance in Chiral Few Nucleon Forces

Description of light nuclei and low energy nuclear reactions can be given in a model-independent way by using chiral effective field theory of QCD. In this framework nuclear forces are described by pion and nucleon (Delta) rather than fundamental quark degrees of freedom in harmony with the symmetries of QCD. In this manuscript we will discuss state-of-the-art nuclear forces derived within this framework and present preliminary results on the three-body forces calculated up to next-to-next-to-next-to-leading order in chiral effective field theory with explicit Delta degrees of freedom.