Electroweak properties of pions in a nuclear medium

TL;DR

This paper investigates how the properties of pions, such as decay constants and charge form factors, change within nuclear matter using the NJL model and quark-meson coupling model, revealing density-dependent modifications.

Contribution

It provides a detailed analysis of in-medium pion properties, including decay constants, form factors, and charge radius, using combined theoretical models.

Findings

Pion decay constant decreases with density.

Pion charge radius increases by about 20% at normal nuclear density.

Pion mass remains insensitive to density up to 1.25 times normal nuclear density.

Abstract

The charge form factor and weak decay constant of the pion as well as the pion-quark coupling constant in symmetric nuclear matter are explored in the framework of the Nambu--Jona-Lasinio model, where the pion is described as a bound state of dressed quark-antiquark pair obtained by the Bethe-Salpeter equation. For the in-medium current quark properties, we adopt the quark-meson coupling model, which describes successfully many hadron properties in a nuclear medium. The pion decay constant and the pion-quark coupling constant are found to decrease with increasing density as well as the magnitude of the light quark condensate. But the pion mass is found to be insensitive to density up to $1.25$ times the normal nuclear density. The pion charge form factor in the space-like region is also explored and is found to have a similar $Q^2$ dependence as the form factor in vacuum showing $1/Q^2$-behavior in large $Q^2$ region, where $Q^2$ is the negative of the four-momentum transfer squared. The modifications of the charge radius of the charged pion in nuclear matter are then estimated and the root-mean-square radius at the normal nuclear density is predicted to be larger than that in vacuum by about 20\%.