Linking continuum and lattice quark mass functions via an effective charge

Lei Chang,Yu-Bin Liu,Yi-Bo Yang,Khépani Raya,J Rodríguez-Quintero

doi:10.1103/physrevd.104.094509

Abstract

The quark mass function is computed both by solving the quark propagator Dyson-Schwinger equation and from lattice simulations implementing overlap and Domain-Wall fermion actions for valence and sea quarks, respectively. The results are confronted and seen to produce a very congruent picture, showing a remarkable agreement for the explored range of current-quark masses. The effective running-interaction is based on a process-independent charge rooted on a particular truncation of the Dyson-Schwinger equations in the gauge sector, establishing thus a link from there to the quark sector and inspiring a correlation between the emergence of gluon and hadron masses.

Highlights

The non-Abelian nature of QCD leads to fascinating consequences in nuclear and hadronic physics, such as quark-gluon confinement and the emergence of hadron masses [1,2]
As it has been stated above, the main aim of this paper is confronting the quark mass function derived both from the Dyson-Schwinger equations (DSEs) gap equation, capitalizing on the running interaction featured by the effective charge given in Eq (10), and from lattice QCD (lQCD)
A gap equation running interaction has been defined on the ground of a phenomenological effective charge, which in its turn shares the IR behavior, and the vanishing-momentum saturation, with the processindependent effective charge defined within the framework of the PT-BFM truncation of gauge-field DSEs

Summary

INTRODUCTION

The non-Abelian nature of QCD leads to fascinating consequences in nuclear and hadronic physics, such as quark-gluon confinement and the emergence of hadron masses [1,2]. We will proceed further on this track and focus on a scheme for the DSEs truncation based on a combination of the pinch technique [3,4,5,29] and background field method [30] (PT-BFM) Within this framework, the connection of gauge and matter sectors of QCD, linking the emergence of gluon and hadron masses [2] depends on a sensible definition of the running interaction for the quark propagator DSE, widely dubbed as the gap equation. We solve the gap equation in the chiral limit and, evaluating the pion decay constant and the quark condensate in this limit, verify the Gell-Mann-OakesRenner formula [39]

THE GAP EQUATION AND THE EFFECTIVE CHARGE

EFFECTIVE CHARGE AND QCD EVOLUTION OF THE PION PDF

THE QUARK MASS FROM LATTICE QCD

THE QUARK MASS FUNCTION FROM THE GAP EQUATION

CONCLUSION