Confinement and chiral symmetry breaking in heavy-light quark systems

Bicudo, Pedro; Brambilla, Nora; Ribeiro, Emílio; Vairo, Antonio

doi:10.1016/s0370-2693(98)01220-9

Cited by 40 publications

(56 citation statements)

References 25 publications

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“…[18] already exhibited χRS. Here we solve the numerical equations again, in order to improve the numerical precision and perform tests of our χRS theorem.…”

Section: χRs In Chiral Invariant Quark Models For Antistatic-ligmentioning

confidence: 97%

“…Since the static antiquark -light quark system only has a single light propagator in lattice QCD, it is a conceptually simple hadronic system [17,18]. It is very convenient to study open problems in hadrons such as the quark spin crisis [19], hybrid excitations [20] in the spectrum, sug-…”

Section: B the Conceptual Simplicity Of Static-light Mesonsmentioning

confidence: 99%

“…[18]. This model is derived directly form QCD in the local coordinate gauge, also known as Balitski gauge, but it is only approximate due to the truncation of the DysonSchwinger equations.…”

Section: χRs In Chiral Invariant Quark Models For Antistatic-ligmentioning

confidence: 99%

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Chiral symmetry restoration in static-light mesons: A chiral restoration theorem, the quark running mass m(k) , and chiral restoration signals in the lattice QCD spectra

Bicudo

2016

Phys. Rev. D

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Chiral symmetry restoration high in the hadron spectra is expected but it remains to be confirmed both in lattice QCD computations and in experiments. Recently, a theorem was derived, relating chiral symmetry restoration high in the hadron spectra to the spontaneous generation of the dynamical quark mass in QCD. We refine the theorem in the case of static-light mesons. Utilizing chiral quark model computations and lattice QCD results for the spectrum of mesons composed by a static antiquark and a light quark, we explore chiral symmetry restoration in the spectrum and the quark running mass m(k).

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“…[18] already exhibited χRS. Here we solve the numerical equations again, in order to improve the numerical precision and perform tests of our χRS theorem.…”

Section: χRs In Chiral Invariant Quark Models For Antistatic-ligmentioning

confidence: 97%

Section: B the Conceptual Simplicity Of Static-light Mesonsmentioning

confidence: 99%

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Chiral symmetry restoration in static-light mesons: A chiral restoration theorem, the quark running mass m(k) , and chiral restoration signals in the lattice QCD spectra

Bicudo

2016

Phys. Rev. D

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“…A clear indication in favor of this statement stems from the following relation that holds between the order parameters of these two phenomena, which are the chiral and the chromo-electric gluon condensates, ψ ψ and (gE a i ) 2 [83][84][85]:…”

Section: A Semi-classical Analogue Of the Relation Between The Qcd Comentioning

confidence: 99%

“…The infra-red behavior of the running coupling, defined by Equation (79), stems from the replacement of the free-gluon polarization operator, Equation (84), by that of a confined gluon,…”

Section: Yang-mills Running Coupling With An Ir-stable Fixed Pointmentioning

confidence: 99%

World-Line Formalism: Non-Perturbative Applications

Bellettre

2016

Universe

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This review addresses the impact on various physical observables which is produced by confinement of virtual quarks and gluons at the level of the one-loop QCD diagrams. These observables include the quark condensate for various heavy flavors, the Yang-Mills running coupling with an infra-red stable fixed point, and the correlation lengths of the stochastic Yang-Mills fields. Other non-perturbative applications of the world-line formalism presented in the review are devoted to the determination of the electroweak phase-transition critical temperature, to the derivation of a semi-classical analogue of the relation between the chiral and the gluon QCD condensates, and to the calculation of the free energy of the gluon plasma in the high-temperature limit. As a complementary result, we demonstrate Casimir scaling of k-string tensions in the Gaussian ensemble of the stochastic Yang-Mills fields.Keywords: the world-line formalism; Wilson loops; analytic calculations of path integrals with the minimal-area surfaces; theoretical foundations of the stochastic vacuum model; confinement and chiral-symmetry breaking in QCD; gluonic bound states; Casimir scaling; the Yang-Mills running coupling; thermodynamics of the gluon plasma; electroweak phase transition Quark Condensate for Various Heavy FlavorsAs is well known, because of confinement in QCD, quarks and gluons do not exist as individual particles, but appear only in the form of bound states (for recent reviews, see [1,2]). The latter include mesons, baryons (as well as other possible quark bound states, such as tetra-and pentaquarks), glueballs, and the so-called hybrids consisting of a quark, an antiquark, and one or several gluons. Each bound state can be represented as an average of a certain operator over the Euclidean QCD vacuum. Since the vacuum state is gauge-invariant, only the gauge-invariant operators yield non-vanishing results once averaged over it. (This statement can be viewed as a corollary of the so-called Elitzur theorem [3,4], which states that a local gauge symmetry cannot be broken spontaneously.) For local composite operators, such asψψ or (F a µν ) 2 , gauge invariance holds automatically, and the mean values of these operators yield the QCD condensates [5,6]. Nevertheless, the quark and the gluon bound states are in general represented by the field operators which are defined at different points of the Euclidean space, so that a phase factor (also called a parallel transporter or a Schwinger string) interpolating between these points is required in order to provide gauge invariance of the full non-local operator. That is, the non-local gauge-invariant operators have, e.g., the formψ i (x)Φ ij xxwhere Φ ij xx and Φ ab xx are the phase factors transforming under the fundamental and the adjoint representations of SU(N), respectively, with i, j = 1, . . . , N and a, b = 1, . . . , N 2 − 1. (Throughout this review, we denote the number of colors by N.) Thus, the phase factors provide long-range correlations of color between individual quark...

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Quark running mass and vacuum energy density in truncated Coulomb gauge QCD for five orders of magnitude of current masses

Bicudo

2011

Nuclear Physics A

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We study in detail the effect of the finite current quark mass on chiral symmetry breaking, in the framework of truncated Coulomb gauge QCD with a linear confining quark-antiquark potential. In the chiral limit of massless current quarks, the breaking of chiral symmetry is spontaneous. But for a finite current quark mass, some dynamical symmetry breaking continues to add to the explicit breaking caused by the quark mass. Moreover, using as order parameter the mass gap, i. e. the quark mass at vanishing moment or the quark condensate, a finite quark mass transforms the chiral symmetry breaking from a phase transition into a crossover. For the study of the QCD phase diagram it thus is relevant to determine how the current quark mass affects chiral symmetry breaking. Since the current quark masses of the six standard flavours u, d, s, c, b, t span over five orders of magnitude from 1.5 MeV to 171 GeV, we develop an accurate numerical method to study the running quark mass gap and the quark vacuum energy density from very small to very large current quark masses. IntroductionChiral symmetry breaking has been studied in detail with chiral invariant and confining quark models in the chiral limit of a vanishing current quark mass m 0 . For a finite current quark mass m 0 = 0, studies exist with an approximate Email address: bicudo@ist.utl.pt (P. Bicudo).

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Confinement and chiral symmetry breaking in heavy-light quark systems

Cited by 40 publications

References 25 publications

Chiral symmetry restoration in static-light mesons: A chiral restoration theorem, the quark running mass m(k) , and chiral restoration signals in the lattice QCD spectra

Chiral symmetry restoration in static-light mesons: A chiral restoration theorem, the quark running mass m(k) , and chiral restoration signals in the lattice QCD spectra

World-Line Formalism: Non-Perturbative Applications

Quark running mass and vacuum energy density in truncated Coulomb gauge QCD for five orders of magnitude of current masses

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