The impact of transverse Slavnov-Taylor identities on dynamical chiral symmetry breaking

Abstract We extend earlier studies of transverse Ward-Fradkin-Green-Takahashi identities in QED, their usefulness to constrain the transverse fermion-boson vertex and their importance for multiplicative renormalizability, to the equivalent gauge identities in QCD. To this end, we consider transverse...

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Autores principales:	Luis Albino, Adnan Bashir, Bruno El-Bennich, Eduardo Rojas, Fernando E. Serna, Roberto Correa da Silveira
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2021
Materias:	Gauge Symmetry Nonperturbative Effects Lattice QCD Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
Acceso en línea:	https://doaj.org/article/7da1493897b44edea279d231d229098b
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spelling	oai:doaj.org-article:7da1493897b44edea279d231d229098b2021-12-05T12:24:54ZThe impact of transverse Slavnov-Taylor identities on dynamical chiral symmetry breaking10.1007/JHEP11(2021)1961029-8479https://doaj.org/article/7da1493897b44edea279d231d229098b2021-11-01T00:00:00Zhttps://doi.org/10.1007/JHEP11(2021)196https://doaj.org/toc/1029-8479Abstract We extend earlier studies of transverse Ward-Fradkin-Green-Takahashi identities in QED, their usefulness to constrain the transverse fermion-boson vertex and their importance for multiplicative renormalizability, to the equivalent gauge identities in QCD. To this end, we consider transverse Slavnov-Taylor identities that constrain the transverse quark-gluon vertex and derive its eight associated scalar form factors. The complete vertex can be expressed in terms of the quark’s mass and wave-renormalization functions, the ghost-dressing function, the quark-ghost scattering amplitude and a set of eight form factors. The latter parametrize the hitherto unknown nonlocal tensor structure in the transverse Slavnov-Taylor identity which arises from the Fourier transform of a four-point function involving a Wilson line in coordinate space. We determine the functional form of these eight form factors with the constraints provided by the Bashir-Bermudez vertex and study the effects of this novel vertex on the quark in the Dyson-Schwinger equation using lattice QCD input for the gluon and ghost propagators. We observe significant dynamical chiral symmetry breaking and a mass gap that leads to a constituent mass of the order of 500 MeV for the light quarks. The flavor dependence of the mass and wave-renormalization functions as well as their analytic behavior on the complex momentum plane is studied and as an application we calculate the quark condensate and the pion’s weak decay constant in the chiral limit. Both are in very good agreement with their reference values.Luis AlbinoAdnan BashirBruno El-BennichEduardo RojasFernando E. SernaRoberto Correa da SilveiraSpringerOpenarticleGauge SymmetryNonperturbative EffectsLattice QCDNuclear and particle physics. Atomic energy. RadioactivityQC770-798ENJournal of High Energy Physics, Vol 2021, Iss 11, Pp 1-39 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Gauge Symmetry Nonperturbative Effects Lattice QCD Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
spellingShingle	Gauge Symmetry Nonperturbative Effects Lattice QCD Nuclear and particle physics. Atomic energy. Radioactivity QC770-798 Luis Albino Adnan Bashir Bruno El-Bennich Eduardo Rojas Fernando E. Serna Roberto Correa da Silveira The impact of transverse Slavnov-Taylor identities on dynamical chiral symmetry breaking
description	Abstract We extend earlier studies of transverse Ward-Fradkin-Green-Takahashi identities in QED, their usefulness to constrain the transverse fermion-boson vertex and their importance for multiplicative renormalizability, to the equivalent gauge identities in QCD. To this end, we consider transverse Slavnov-Taylor identities that constrain the transverse quark-gluon vertex and derive its eight associated scalar form factors. The complete vertex can be expressed in terms of the quark’s mass and wave-renormalization functions, the ghost-dressing function, the quark-ghost scattering amplitude and a set of eight form factors. The latter parametrize the hitherto unknown nonlocal tensor structure in the transverse Slavnov-Taylor identity which arises from the Fourier transform of a four-point function involving a Wilson line in coordinate space. We determine the functional form of these eight form factors with the constraints provided by the Bashir-Bermudez vertex and study the effects of this novel vertex on the quark in the Dyson-Schwinger equation using lattice QCD input for the gluon and ghost propagators. We observe significant dynamical chiral symmetry breaking and a mass gap that leads to a constituent mass of the order of 500 MeV for the light quarks. The flavor dependence of the mass and wave-renormalization functions as well as their analytic behavior on the complex momentum plane is studied and as an application we calculate the quark condensate and the pion’s weak decay constant in the chiral limit. Both are in very good agreement with their reference values.
format	article
author	Luis Albino Adnan Bashir Bruno El-Bennich Eduardo Rojas Fernando E. Serna Roberto Correa da Silveira
author_facet	Luis Albino Adnan Bashir Bruno El-Bennich Eduardo Rojas Fernando E. Serna Roberto Correa da Silveira
author_sort	Luis Albino
title	The impact of transverse Slavnov-Taylor identities on dynamical chiral symmetry breaking
title_short	The impact of transverse Slavnov-Taylor identities on dynamical chiral symmetry breaking
title_full	The impact of transverse Slavnov-Taylor identities on dynamical chiral symmetry breaking
title_fullStr	The impact of transverse Slavnov-Taylor identities on dynamical chiral symmetry breaking
title_full_unstemmed	The impact of transverse Slavnov-Taylor identities on dynamical chiral symmetry breaking
title_sort	impact of transverse slavnov-taylor identities on dynamical chiral symmetry breaking
publisher	SpringerOpen
publishDate	2021
url	https://doaj.org/article/7da1493897b44edea279d231d229098b
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The impact of transverse Slavnov-Taylor identities on dynamical chiral symmetry breaking

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