Two-loop electroweak corrections to the ρ parameter beyond the leading approximation

Papavassiliou, Joannis; Philippides, Kostas; Sasaki, Kenji

doi:10.1103/physrevd.53.3942

Cited by 11 publications

(14 citation statements)

References 36 publications

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“…In order to understand the origin of the problems associated with the subleading contributions, one should first establish the mechanism that enforces the good behavior of the leading contributions-in particular their UV finiteness [150]. If we denote the leading (fermionic) contributions (both at one and two loops) to the W W and ZZ self-energies by Π (ℓ)µν W W (q) and Π (ℓ)µν ZZ (q), respectively (the label ℓ stands for "leading"), and use the important fact that …”

Section: The Universal Part Of the ρ Parameter Beyond One Loopmentioning

confidence: 99%

“…Of course, as the reader must have realized by now, this unpleasant trade-off between gaugeindependence and process-independence is completely artificial, and can be easily avoided by defining ∆ un beyond one loop in terms of the physical PT self-energies, namely [150] un , and in particular (5.84), (5.91), and (5.92) are valid both for leading and subleading contributions. Evidently, the PT restores the mechanism for the cancellation of the UV divergences, and guarantees at the same time the gauge-and process-independence of the final answer.…”

Section: ) Then It Is Elementary To Establish Thatmentioning

confidence: 99%

“…(2.112), together with the additional general formula 150) we obtain for the case of two massless gluons in the final state 151) and thus (2.149) becomes…”

Section: The Fundamental S-t Cancellationmentioning

confidence: 99%

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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: The Universal Part Of the ρ Parameter Beyond One Loopmentioning

confidence: 99%

Section: ) Then It Is Elementary To Establish Thatmentioning

confidence: 99%

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Pinch technique: Theory and applications

2009

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“…with C χ = 1 and C H = i, and 12) where (−1) S is 1 (respectively, −1) when S = χ (respectively, S = H), and S = H (respectively, S = χ) when S = χ (respectively, S = H).…”

Section: Discussionmentioning

confidence: 99%

“…For quantizing the theory, a gauge fixing term must be added to the classical Lagrangian L cl SM . To avoid tree-level mixing between gauge and scalar fields, a renormalizable R ξ gauge of the 't Hooft type is most commonly chosen; this is specified by one gauge parameter for each gauge-boson, and defined through the linear gauge fixing functions 12) yielding to the R ξ gauge fixing Lagrangian…”

Section: The Electroweak Lagrangianmentioning

confidence: 99%

Electroweak pinch technique to all orders

Binosi¹

2004

J. Phys. G: Nucl. Part. Phys.

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Abstract. The generalization of the pinch technique to all orders in the electroweak sector of the Standard Model within the class of the renormalizable 't Hooft gauges, is presented. In particular, both the all-order PT gauge-boson-and scalar-fermions vertices, as well as the diagonal and mixed gauge-boson and scalar self-energies are explicitly constructed. This is achieved through the generalization to the Standard Model of the procedure recently applied to the QCD case, which consist of two steps: (i) the identification of special Green's functions, which serve as a common kernel to all self-energy and vertex diagrams, and (ii) the study of the (on-shell) SlavnovTaylor identities they satisfy. It is then shown that the ghost, scalar and scalar-gaugeboson Green's functions appearing in these identities capture precisely the result of the pinching action at arbitrary order. It turns out that the aforementioned Green's functions play a crucial role, their net effect being the non-trivial modification of the ghost, scalar and scalar-gauge-boson diagrams of the gauge-boson-or scalar-fermions vertex we have started from, in such a way as to dynamically generate the characteristic ghost and scalar sector of the background field method. The pinch technique gaugeboson and scalar self-energies are also explicitly constructed by resorting to the method of the background-quantum identities.

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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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Two-loop electroweak corrections to the ρ parameter beyond the leading approximation

Cited by 11 publications

References 36 publications

Pinch technique: Theory and applications

Pinch technique: Theory and applications

Electroweak pinch technique to all orders

Gauge-independent resummed gluon self-energy in hot QCD

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