Effect of sigma meson on the $D_1(2430) \to D\pi\pi$ decay

TL;DR

This paper investigates how the sigma meson influences the decay process of D_1(2430) into D and two pions, using an effective Lagrangian that respects chiral and heavy quark symmetries, aiming to shed light on the sigma meson's internal structure.

Contribution

The study constructs a chiral and heavy quark symmetry-preserving effective Lagrangian including the sigma meson with different quark configurations, and analyzes its impact on decay widths.

Findings

Fitted sigma meson mass and coupling to pion scattering data.

Showed the decay width dependence on sigma meson quark structure.

Provided a method to probe sigma meson structure through decay analysis.

Abstract

We study the effect of sigma meson on the $D_1(2430) \to D\pi\pi$ decay by constructing an effective Lagrangian preserving the chiral symmetry and the heavy quark symmetry. The sigma meson is included through a linear sigma model, in which both the $q\bar{q}$ and $qq\bar{q}\bar{q}$ states are incorporated respecting their different $U(1)_{A}$ transformation properties. We first fit the sigma meson mass and $\sigma$-$\pi$-$\pi$ coupling constant to the I=0, $S$-wave $\pi$-$\pi$ scattering data. Then, we show how the differential decay width $d\Gamma(D_1 \to D(\pi\pi)_{I = 0, L =0})/d m_{\pi\pi}$ depends on the quark structure of the sigma meson. We find that our study, combing with the future data, can give a clue to understand the sigma meson structure.