Possible relevance of the softening of the sigma meson to $\eta$ decay into 3$\pi$ in the nuclear medium

TL;DR

This study explores how the softening of the sigma meson in nuclear matter significantly enhances the decay widths of eta mesons into three pions, offering a potential new probe for chiral symmetry restoration.

Contribution

It demonstrates that sigma meson softening in nuclear medium increases eta decay widths, providing a novel experimental signature for chiral symmetry restoration in nuclear physics.

Findings

Decay widths increase by a factor of 4 to 10 in nuclear medium.

Moderate density dependence for eta to 3pi0 decay compared to eta to pi+pi-pi0.

Sigma meson softening causes cancellation effects in 3pi0 decay.

Abstract

We investigate the role of the softening of the scalar-isoscalar (sigma) meson in the $\eta\rightarrow\pi^+\pi^-\pi^0$ and $3\pi^0$ decay widths in the symmetric nuclear medium using a linear sigma model. Our calculation shows that these decay widths in the nuclear medium increase by up to a factor of four to ten compared with those in the free space mainly depending on the mass of the sigma meson in the free space, which is an input parameter of the model. The enhancements are considerable even at a half of the normal nuclear density. Thus, the $\eta$ decay into $3\pi$ could be a possible new probe for the chiral restoration in the nuclear medium. We find that the density dependence of the $\eta\rightarrow3\pi^0$ decay is moderate in comparison with that of $\eta\rightarrow\pi^+\pi^-\pi^0$, although the former width is greater than the latter one at a given density. This is because the softening of the sigma meson causes cancellation of the terms appearing from the Bose symmetry in the $\eta\rightarrow3\pi^0$ decay. The difference between the density dependences should be helpful for experimental confirmation of the findings of the present study.