Self-consistency of off-shell Slavnov-Taylor identities in QCD

Gracey, J.A.; Kißler, Henry; Kreimer, Dirk

doi:10.1103/physrevd.100.085001

Cited by 17 publications

(13 citation statements)

References 71 publications

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“…As is well-known, the fundamental Slavnov-Taylor identities (STIs) [81,82] impose crucial constraints between the two-and three-point sectors of the theory [83][84][85][86][87]. In the present study, we offer a novel point of view inspired by these profound relations, which, for the special kinematic conditions that we consider, give rise to two relatively simple sum rules.…”

Section: Introductionmentioning

confidence: 91%

Novel sum rules for the three-point sector of QCD

2020

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For special kinematic configurations involving a single momentum scale, certain standard relations, originating from the Slavnov-Taylor identities of the theory, may be interpreted as ordinary differential equations for the “kinetic term” of the gluon propagator. The exact solutions of these equations exhibit poles at the origin, which are incompatible with the physical answer, known to diverge only logarithmically; their elimination hinges on the validity of two integral conditions that we denominate “asymmetric” and “symmetric” sum rules, depending on the kinematics employed in their derivation. The corresponding integrands contain components of the three-gluon vertex and the ghost-gluon kernel, whose dynamics are constrained when the sum rules are imposed. For the numerical treatment we single out the asymmetric sum rule, given that its support stems predominantly from low and intermediate energy regimes of the defining integral, which are physically more interesting. Adopting a combined approach based on Schwinger–Dyson equations and lattice simulations, we demonstrate how the sum rule clearly favors the suppression of an effective form factor entering in the definition of its kernel. The results of the present work offer an additional vantage point into the rich and complex structure of the three-point sector of QCD.

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Section: Introductionmentioning

confidence: 91%

Novel sum rules for the three-point sector of QCD

2020

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“…saturates the relevant STIs, while the 8 See also [106,110] for a variety of relevant properties of the four-gluon vertex.…”

Section: Lmentioning

confidence: 99%

Gluon mass scale through nonlinearities and vertex interplay

et al. 2019

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We present a novel analysis of the gluon gap equation, where its full nonlinear structure is duly taken into account. In particular, while in previous treatments the linearization of this homogeneous integral equation introduced an indeterminacy in the scale of the corresponding mass, the current approach determines it uniquely, once the value of the gauge coupling at a given renormalization point is used as input. A crucial ingredient for this construction is the "kinetic term" of the gluon propagator, whose form is not obtained from the complicated equation governing its evolution, but is rather approximated by suitable initial Ansätze, which are subsequently improved by means of a systematic iterative procedure. The multiplicative renormalization of the central equation is carried out following an approximate method, which is extensively employed in the studies of the standard quark gap equation. This approach amounts to the effective substitution of the vertex renormalization constants by kinematically simplified form factors of the three-and four-gluon vertices. The resulting numerical interplay, exemplified by the infrared suppression of the three-gluon vertex and the mild enhancement of the four-gluon vertex, is instrumental for obtaining positive-definite and monotonically decreasing running gluon masses. The resulting gluon propagators, put together from the gluon masses and kinetic terms obtained with this method, match rather accurately the data obtained from large-volume lattice simulations.

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“…Using this in the variation of (43) we get the gauge variation of the exponent divided into three term. The contribution independent of the external source, J, coincides with (22) from the scalar case according to…”

Section: B Variation Of the Propagatormentioning

confidence: 99%

“…The utility of these transformations is well illustrated by the restrictions imposed on the non-perturbative three-point vertex for it to be compatible with the LKF transformation of the fermion propagator [39][40][41]. Unfortunately, despite their importance in restraining the structure of gauge theory interactions, the LKF transformations have been studied far less than the more familiar constraints arising from the Ward-Takahashi / Slavanov-Taylor identities [42,43]. However, the LKF transformations for the particular case of the propagator have been examined to varying degrees of detail.…”

Section: Introductionmentioning

confidence: 99%

The Generalised LKF Transformations for Arbitrary $N$-point Fermion Correlators

Ahmadiniaz,

Edwards,

Nicasio

et al. 2020

Preprint

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We examine the non-perturbative gauge dependence of arbitrary configuration space fermion correlators in quantum electrodynamics (QED). First, we study the dressed electron propagator (allowing for emission or absorption of any number of photons along a fermion line) using the first quantised approach to quantum field theory and analyse its gauge transformation properties induced by virtual photon exchange. This is then extended to the N -point functions where we derive an exact, generalised version of the fully non-perturbative Landau-Khalatnikov-Fradkin (LKF) transformation for these correlators. We discuss some general aspects of application in perturbation theory and investigate the structure of the LKF factor about D = 2 dimensions.

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Self-consistency of off-shell Slavnov-Taylor identities in QCD

Cited by 17 publications

References 71 publications

Novel sum rules for the three-point sector of QCD

Novel sum rules for the three-point sector of QCD

Gluon mass scale through nonlinearities and vertex interplay

The Generalised LKF Transformations for Arbitrary $N$-point Fermion Correlators

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