Charm and beauty content of the pion and kaon in the Flavor U(5) Nambu-Jona-Lasinio model

TL;DR

This paper investigates how heavy charm and beauty quarks influence light meson properties within a flavor-dependent NJL model, revealing minor effects on observables despite large variations in heavy quark masses.

Contribution

It introduces a flavor-dependent U(5) NJL model incorporating heavy quark effects and analyzes their impact on light meson properties, a novel approach in this context.

Findings

Charm and beauty quark contributions to pion and kaon masses are small.

Light quark observables are minimally affected by heavy quark mass variations.

Pion mass can vary up to 20%, while kaon mass varies around 2% with heavy quark mass changes.

Abstract

We consider a U(5)-Nambu-Jona-Lasinio model with flavor-dependent couplings constants obtained from quark-antiquark polarization to investigate the role of the heavy quarks for light constituent quarks and mesons. A quantum mixing, due to the different representations of the flavor group needed to defined quarks and mesons, lead to charm and beauty sea quark contributions to properties of the light quark sector. For a given fitting procedure for the parameters of the model, the charm and beauty quark effective masses are freely varied from very small values to very large values (infinite). The effect of these variations on pion and kaon observables, such as masses, weak decay constants and condensates, is calculated. Although the pion mass can vary (seemingly too much) up to $20\%$ for a very large variation of heavy quark effective masses, their contributions for the kaon mass are at most of the order of $2\%$ and all the other variables and observables, including up and down quark constituent masses, vary at most around $1\%$.