Gauge-independent resummed gluon self-energy in hot QCD

Sasaki, Kenji

doi:10.1016/s0550-3213(97)00068-0

Cited by 10 publications

(8 citation statements)

References 61 publications

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“…Let us mention a few. There have been several application in the area of finite temperature field theory, starting with the early work by Cornwall and collaborators [162,191], the calculation of the plasmon decay constant by Nadkarni [240], the gauge-independent thermal β function computed by Sasaki [241,242], and the work on magnetic screening for the quark-gluon plasma by Alexanian and Nair [243]. In addition, the explicit one-loop PT calculations in the context of the Coulomb and temporal axial gauges have been presented by Passera and Sasaki in [244].…”

Section: Discussionmentioning

confidence: 99%

Pinch technique: Theory and applications

2009

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We review the theoretical foundations and the most important physical applications of the Pinch Technique (PT). This general method allows the construction of off-shell Green's functions in non-Abelian gauge theories that are independent of the gauge-fixing parameter and satisfy ghost-free Ward identities. We first present the diagrammatic formulation of the technique in QCD, deriving at one loop the gauge independent gluon self-energy, quark-gluon vertex, and three-gluon vertex, together with their Abelian Ward identities. The generalization of the PT to theories with spontaneous symmetry breaking is carried out in detail, and the profound connection with the optical theorem and the dispersion relations are explained within the electroweak sector of the Standard Model. The equivalence between the PT and the Feynman gauge of the Background Field Method (BFM) is elaborated, and the crucial differences between the two methods are critically scrutinized. A variety of field theoretic techniques needed for the generalization of the PT to all orders are introduced, with particular emphasis on the Batalin-Vilkovisky quantization method and the general formalism of algebraic renormalization. The main conceptual and technical issues related to the extension of the technique beyond one loop are described, using the twoloop construction as a concrete example. Then the all-order generalization is thoroughly examined, making extensive use of the field theoretic machinery previously introduced; of central importance in this analysis is the demonstration that the PT-BFM correspondence persists to all orders in perturbation theory. The extension of the PT to the non-perturbative domain of the QCD Schwinger-Dyson equations is presented systematically, and the main advantages of the resulting self-consistent truncation scheme are discussed. A plethora of physical applications relying on the PT are finally reviewed, with special emphasis on the definition of gauge-independent off-shell form-factors, the construction of non-Abelian effective charges, the gauge-invariant treatment of resonant transition amplitudes and unstable particles, and finally the dynamical generation of an effective gluon mass.

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Section: Discussionmentioning

confidence: 99%

Pinch technique: Theory and applications

2009

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“…Hence it is not consistent to stop the calculation at one-loop order for soft internal momenta, and the resummed propagator and the vertices [14] must be used to obtain the complete leading contribution. The PT algorithm still works even when we use the resummed propagator and the vertices [26]. It can be shown that the resummed effective gluon self-energy obtained in the framework of PT is gauge-independent and that, using this effective gluon self-energy, we can obtain the correct thermal β function in the leading order.…”

Section: Summary and Discussionmentioning

confidence: 99%

Gluon self-energy in the Coulomb and temporal axial gauges via the pinch technique

Passera

Sasaki

1996

Phys. Rev. D

Self Cite

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The S-matrix pinch technique is used to derive an effective gluon selfenergy to one-loop order, when the theory is quantized in the Coulomb gauge (CG) and in the temporal axial gauge (TAG). When the pinch contributions are added, the gluon self-energies calculated in CG and TAG turn out to be identical and coincide with the result previously obtained with covariant gauges. The issue of gauge independence of several quantities in hot QCD is discussed from the pinch technique point of view. It is also pointed out that the spurious singularities which appear in TAG calculations cancel out once the pinch contributions are combined.

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“…This means, the coupling constant has a strong dependence on the vertex function [15,16]. Also, the dependence of coupling constant on the gauge was investigated in [17,18]. Braaten and Pisarski [19] introduced significant ideas like hard thermal loops and, using it, they presented resummation of QCD thermal perturbation theory.…”

Section: Introductionmentioning

confidence: 99%

Running coupling constant in thermal $ϕ^4$ theory up to two loop order

Arjun,

Vinodkumar,

Bannur

2021

Preprint

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Using the imaginary time formalism in thermal field theory, we derive running coupling constant and running mass in two loop order. In the process, we express the imaginary time formalism of Feynman diagrams as the summation of non-thermal quantum field theory (QFT) Feynman diagrams with coefficients that depend on temperature and mass. Renormalization constants for thermal φ 4 theory were derived using simple diagrammatic analysis. Our model links the nonthermal QFT and the imaginary time formalism by assuming both have the same mass scale µ and coupling constant g. When these results are combined with the renormalization group equations (RGE) and applied simultaneously to thermal and non-thermal proper vertex functions, coupling constant and running mass with implicit temperature dependence are obtained. We evaluated pressure for scalar particles in two loop orders at zero external momentum limit by substituting the running mass result in the quasi-particle model.

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Gauge-independent resummed gluon self-energy in hot QCD

Cited by 10 publications

References 61 publications

Pinch technique: Theory and applications

Pinch technique: Theory and applications

Gluon self-energy in the Coulomb and temporal axial gauges via the pinch technique

Running coupling constant in thermal $ϕ^4$ theory up to two loop order

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