Study of Light Scalar Meson Structure in $D_1$ decay

TL;DR

This paper investigates the quark structure of the sigma meson through $D_1$ meson decay, using an effective Lagrangian based on chiral and heavy quark symmetries, predicting decay widths related to the meson's quark content.

Contribution

It introduces a model combining $qar{q}$ and $qqar{q}ar{q}$ states for light scalar mesons within chiral symmetry, and predicts decay widths sensitive to the sigma meson's quark composition.

Findings

Decay width increases with higher $qar{q}$ content in sigma.

Predicted $D_1 o D\pi\pi$ decay width can be tested experimentally.

Model incorporates chiral partners and respects U(1)$_A$ transformation properties.

Abstract

We study the quark structure of the sigma meson through the decay of $D_1(2430)$ meson by constructing an effective Lagrangian for charmed mesons interacting with light mesons based on the chiral symmetry and heavy quark symmetry. Within the linear realization of the chiral symmetry, we include the P-wave charmed mesons ($D_1(2430)$, $D_0(2400)$) as the chiral partners of ($D^\ast$, $D$), and the light scalar mesons as the chiral partner of the pseudoscalar mesons. In the light meson sector, both the $q\bar{q}$ and $qq\bar{q}\bar{q}$ states are incorporated respecting their different U(1)$_A$ transformation properties. We predict the $D_1 \to D\pi\pi$ decay width with two pions in the $I=0,\,l=0$ channel, which can be tested in the future experiment. We find that the width increases with the percentage of the $q\bar{q}$ content in the sigma meson.