Quark condensate for various heavy flavors

Antonov, Dmitri; Ribeiro, J. E. F. T.

doi:10.1140/epjc/s10052-012-2179-7

Cited by 12 publications

(30 citation statements)

References 21 publications

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“…Furthermore, as has been demonstrated in Ref. [39], for the case of exponential correlations of such interactions, they do not affect the value of the quark condensate. The question of whether this result is specific to the exponential ansatz for the correlation function g 2 F a µν (0)F b λρ (x) , or it holds for some other ansätze (such as, e.g., the Gaussian one) equally well, requires a separate study.…”

Section: Quark Condensate For Various Heavy Flavorssupporting

confidence: 62%

“…We will now follow Ref. [39] to calculate these corrections by using the approach proposed in Ref. [22].…”

Section: Quark Condensate For Various Heavy Flavorsmentioning

confidence: 99%

“…Referring the reader for details to Ref. [39], we present here the final result for the corresponding ratio…”

Section: Quark Condensate For Various Heavy Flavorsmentioning

confidence: 99%

“…Ref. [39]). In particular, we obtain J(1) 0.36, which means a 64%-decrease in the value of the quark condensate for m µ.…”

Section: Quark Condensate For Various Heavy Flavorsmentioning

confidence: 99%

“…The possibility for such a reduction is provided by the fact that the whole dependence on the non-Abelian gauge field in the effective action is encoded in the form of the area-and the perimeter-law terms entering Equation (30). The auxiliary Abelian field appears then in the course of the regularization of the area S of the minimal surface Σ C and the perimeter L of the contour C. Furthermore, while for L such a regularization is straightforward (owing to the one-dimensionality of the contour), for S one can rather adopt various parametrizations in terms of C, which all render the path integral in the effective action calculable [7][8][9]39,80]. From all such parametrizations, we find the one used in Ref.…”

Section: Electroweak Phase Transition As a Vacuum Instabilitymentioning

confidence: 99%

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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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Section: Quark Condensate For Various Heavy Flavorssupporting

confidence: 62%

“…We will now follow Ref. [39] to calculate these corrections by using the approach proposed in Ref. [22].…”

Section: Quark Condensate For Various Heavy Flavorsmentioning

confidence: 99%

“…Referring the reader for details to Ref. [39], we present here the final result for the corresponding ratio…”

Section: Quark Condensate For Various Heavy Flavorsmentioning

confidence: 99%

“…Ref. [39]). In particular, we obtain J(1) 0.36, which means a 64%-decrease in the value of the quark condensate for m µ.…”

Section: Quark Condensate For Various Heavy Flavorsmentioning

confidence: 99%

Section: Electroweak Phase Transition As a Vacuum Instabilitymentioning

confidence: 99%

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World-Line Formalism: Non-Perturbative Applications

Bellettre

2016

Universe

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Scalar gauge dynamics and Dark Matter

Buttazzo

Luzio

Ghorbani

et al. 2020

J. High Energ. Phys.

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We consider theories with one gauge group (SU, SO or Sp) and one scalar in a two-index representation. The renormalizable action often has accidental symmetries (such as global U(1) or unusual group parities) that lead to one or more stable states, providing Dark Matter candidates. We discuss the confined phase(s) of each theory and compute the two Higgs phases, finding no generic dualities among them. Discrete gauge symmetries can arise and accidental symmetries can be broken, possibly giving pseudo-Goldstone Dark Matter. Dark Matter candidates can have a complicated sub-structure characteristic of each group and can be accompanied by extra dark radiation.

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A semi-classical analogue of the relation between the chiral and the gluon QCD condensates

Ribeiro¹,

Antonov²

2015

Physics Letters B

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We present a semi-classical analogue of the relation between chiral and gluon QCD condensates, in which a condensation of a massless scalar field is provided by a classical field, instead of a quantum YangMills field. For the classical field, we choose a gravitational field of a spherically symmetric object. The size of such an object becomes then a classical-physics analogue of the QCD vacuum correlation length, whereas the squared curvature of the gravitational field plays the role of the gluon condensate. Finally, by iterating the emerging contribution to the trace of the energy-momentum tensor, we prove that the energy density of the object remains of the same order of magnitude, i.e. no instability of the system occurs.

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Quark condensate for various heavy flavors

Cited by 12 publications

References 21 publications

World-Line Formalism: Non-Perturbative Applications

World-Line Formalism: Non-Perturbative Applications

Scalar gauge dynamics and Dark Matter

A semi-classical analogue of the relation between the chiral and the gluon QCD condensates

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