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

Passera, M.; Sasaki, Kenji

doi:10.1103/physrevd.54.5763

Cited by 8 publications

(11 citation statements)

References 53 publications

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“…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]. Moreover, Pilaftsis applied the PT to the resonant CP violation a decade ago [245,246], and recently to resonant leptogenesis [247,248].…”

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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“…by simply exploiting the fundamental WI of Eq. (2.10), one can arrive at the set of diagrams of the RFG starting from the set of diagrams at any other value of ξ (see for example [30]), or even from the diagrams corresponding to non-covariant gauge-fixing schemes [31].…”

Section: Overview Of the One-loop Casementioning

confidence: 99%

Pinch technique at two loops: The case of massless Yang-Mills theories

Papavassiliou

2000

Phys. Rev. D

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The generalization of the pinch technique beyond one loop is presented. It is shown that the crucial physical principles of gauge-invariance, unitarity, and gauge-fixing-parameter independence are instrumental for accomplishing this task, and is explained how the aforementioned requirements single out at two loops exactly the same algorithm which has been used to define the pinch technique at one loop, without any additional assumptions. The two-loop construction of the pinch technique gluon self-energy, and quark-gluon vertex are carried out in detail for the case of mass-less YangMills theories, such as perturbative QCD. We present two different but complementary derivations. First we carry out the construction by directly rearranging two-loop diagrams. The analysis reveals that, quite interestingly, the well-known one-loop correspondence between the pinch technique and the background field method in the Feynman gauge persists also at two-loops. Since we use dimensional regularization the entire construction does not depend on the value of the space-time dimension d. The renormalization (when d = 4) is discussed in detail, and is shown to respect the aforementioned correspondence. Second, we present an absorptive derivation, exploiting the unitarity of the S-matrix and the underlying BRS symmetry; at this stage we deal only with tree-level and one-loop physical amplitudes. The gauge-invariant sub-amplitudes defined by means of this absorptive construction correspond precisely to the imaginary parts of the n-point functions defined in the full two-loop derivation, thus furnishing a highly nontrivial self-consistency check for the entire method. Various future applications are briefly discussed.

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“…It is only a typographical error and does not propagate to Eq. (25), and thus their conclusions are intact. I would like to thank Eric Braaten for providing me with this information.…”

Section: Summary and Discussionmentioning

confidence: 86%

“…The application of PT to QCD at high temperature was first made by Alexanian and Nair [24] to calculate the gap equation for the magnetic mass to one-loop order. The issue of gauge independence of several quantities in hot QCD was recently discussed from the PT point of view [25]. The paper is organized as follows.…”

Section: πmentioning

confidence: 99%

Gauge-independent resummed gluon self-energy in hot QCD

Sasaki¹

1997

Nuclear Physics B

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The pinch technique (PT) is applied to obtain the gauge-independent resummed gluon self-energy in a hot Yang-Mills gas. Calculation is performed at one-loop level in linear gauges which preserve rotational invariance and the resummed propagators and vertices are used. The effective gluon self-energy, which is obtained as the sum of the resummed gluon self-energy and the resummed pinch contributions, is not only gaugeindependent but also satisfies the transversality relation. Using this gauge-independent effective gluon self-energy, we calculate the damping rate for transverse gluons in the leading order and show that the result coincides with the one obtained by Braaten and Pisarski.

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

Cited by 8 publications

References 53 publications

Pinch technique: Theory and applications

Pinch technique: Theory and applications

Pinch technique at two loops: The case of massless Yang-Mills theories

Gauge-independent resummed gluon self-energy in hot QCD

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