Novel sum rules for the three-point sector of QCD
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Regular Article - Theoretical Physics
Novel sum rules for the three-point sector of QCD A. C. Aguilar1,a , M. N. Ferreira1, J. Papavassiliou2 1 2
University of Campinas, UNICAMP, Institute of Physics “Gleb Wataghin”, Campinas, São Paulo 13083-859, Brazil Department of Theoretical Physics and IFIC, University of Valencia and CSIC, 46100 Valencia, Spain
Received: 11 June 2020 / Accepted: 8 September 2020 © The Author(s) 2020
Abstract 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.
1 Introduction In recent years, the fundamental n-point correlation (Green’s) functions of QCD [1] have been the subject of systematic scrutiny both through continuous methods, such as Schwinger–Dyson equations (SDEs) [2–13] and functional renormalization group [14,15], as well as by means of largevolume lattice simulations [16–23]. In this quest, the original intense activity dedicated to the gluon and ghost propagators (two-point sector) [24–51] has been complemented by an indepth exploration of the three-gluon vertex, Iαμν [52–64], a e-mail:
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the ghost-gluon vertex, μ [17,52,57,65–70], and, in part, the auxiliary ghost-gluon kernel, Hμν [69]. This concerted effort has catalyzed a vast array of new theoretical insights on the nonperturbative QCD dynamics, and has afforded a tighter grip on a number of complex phenomenological issues [71–80]. 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 [83–87]. 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
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