Dynamical regimes of the QCD string with quarks

Dubin, A. Yu.; Kaǐdalov, A. B.; Simonov, Yu. A.

doi:10.1007/bf02734022

Cited by 7 publications

(13 citation statements)

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“…The last example that we quote here is a derivation starting from formulation in Euclidean space [39][40][41][42] in order to continue further into Minkowski space with light cone variables by making inverse Wick rotation. As a result, in straight line approximation, the effective ultra relativistic Hamiltonian is quadratic.…”

Section: Front-form Methodsmentioning

confidence: 99%

Universality of Effective Potentials in Models of Mesons

Trawiński

2015

Few-Body Syst

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Many simple pictures of hadrons have been inspired by QCD. They are formulated in the instantform (IF) of dynamics as well as in the front-form (FF). One can observe that nearly all considerations in the IF lead to the conclusion that the potential between quarks and antiquarks should be linear at large distances. In contrast, the FF formulation favors a quadratic potential. We discuss examples and show that the linear IF confinement potential corresponds to the quadratic FF potential. An important tool in our discussion is the WKB method which allows one to relate the maximum distances of separation between quarks within mesons in different models.

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Section: Front-form Methodsmentioning

confidence: 99%

Universality of Effective Potentials in Models of Mesons

Trawiński

2015

Few-Body Syst

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“…In general, the corresponding world-line integral cannot be calculated analytically, because finding the minimal surface for an arbitrary contour z µ (τ) in D > 2 dimensions is too complicated. For this reason, effective parametrizations of the minimal surface have been invented in the literature [7][8][9] in order to construct the minimal-area functional in terms of z µ (τ). Owing to the fact that the Wilson-loop average is fully defined in terms of the geometric characteristics of the contour z µ (τ), this approach has an advantageous feature of being able to reduce the calculation of vacuum amplitudes in QCD to the calculation of the world-line integrals in an effective Abelian gauge theory, or even in quantum mechanics.…”

Section: Quark Condensate For Various Heavy Flavorsmentioning

confidence: 99%

“…Furthermore, the Wilson-loop average W[z µ ] can be again represented through Equation (8) as an integral over an auxiliary antisymmetric-tensor field B µν . The variational derivatives in Equation (14) recover then this field, so that the emerging B µν -integral reads…”

Section: Quark Condensate For Various Heavy Flavorsmentioning

confidence: 99%

“…We use further the so-called non-backtracking approximation Σ √ f 2 , where f ≡ 1 2 s 0 dτ(z ×ż). This approximation is widely used in order to simplify the parametrizations of minimal surfaces allowing for an analytic calculation of the corresponding world-line integrals [7][8][9]. (In general, 1 2 s 0 dτ |z ×ż| can be larger than √ f 2 .…”

Section: Free Energy Of the Gluon Plasma In The High-temperature Limitmentioning

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.…”

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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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Two-point gauge invariant quark Green's functions with polygonal phase factor lines

Sazdjian

2014

Nuclear Physics B - Proceedings Supplements

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6 pages, PDFLatex uses elsarticle class. Invited talk at the Conference Light Cone: Relativistic Hadronic and Particle Physics, 10-15 December 2012, Delhi, IndiaPolygonal lines are used for the paths of the gluon field phase factors entering in the definition of gauge invariant quark Green's functions. This allows classification of the Green's functions according to the number of segments the polygonal lines contain. Functional relations are established between Green's functions with polygonal lines with different numbers of segments. An integrodifferential equation is obtained for the quark two-point Green's function with a path along a single straight line segment where the kernels are represented by a series of Wilson loop averages along polygonal contours. The equation is exactly and analytically solved in the case of two-dimensional QCD in the large-$N_c$ limit. The solution displays generation of an infinite number of dynamical quark masses accompanied with branch point singularities that are stronger than simple poles. An approximation scheme, based on the counting of functional derivatives of Wilson loops, is proposed for the resolution of the equation in four dimensions

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Dynamical regimes of the QCD string with quarks

Cited by 7 publications

References 2 publications

Universality of Effective Potentials in Models of Mesons

Universality of Effective Potentials in Models of Mesons

World-Line Formalism: Non-Perturbative Applications

Two-point gauge invariant quark Green's functions with polygonal phase factor lines

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