The chiral limit of a fermion-scalar $(1/2)^+$ system in covariant gauges

Abstract

The homogeneous Bethe-Salpeter equation (BSE) of a (1/2)$^+$ bound system, that has both fermionic and bosonic degrees of freedom, that we call a {\em mock nucleon}, is studied in Minkowski space, in order to analyse the chiral limit in covariant gauges. After adopting an interaction kernel built with a one-particle exchange, the $\chi$-BSE is numerically solved by means of the Nakanishi integral representation and light-front projection. Noteworthy, the chiral limit induces a scale-invariance of the model and consequently generates a wealth of striking features: i) it reduces the number of non trivial Nakanishi weight functions to only one; ii) the form of the surviving weight function has a factorized dependence on the two relevant variables, compact and non-compact one; iii) the coupling constant becomes an explicit function of the real exponent governing the power-law fall-off of the non trivial Nakanishi weight function. The thorough investigation at large transverse-momentum of light-front Bethe-Salpeter amplitudes, obtained with massive constituents, provides a confirmation of the expected universal power-law fall-off, with exponents predicted by our non-perturbative framework. Finally, one can shed light on the exponents that govern the approach to the upper extremum of the longitudinal-momentum fraction distribution function of the {\em mock nucleon}, when the coupling constant varies.