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

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.

14 pages, 5 figures

References in corpus (4)

• A Theory of Scalar Mesons
• Note on a sigma model connection with instanton dynamics
• Two chiral nonet model with massless quarks
• Properties of light resonances from unitarized Chiral perturbation theory: Nc behavior and quark mass dependence

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• Comparative study of the scalar- and tensor-meson production in the reaction $\gamma {\gamma }^{\ast }(Q^2)\to \eta {\pi }^0$
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