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

Details Effect of sigma meson on the $D_1(2430) \to Dππ$ decay Effect of sigma meson on the $D_1(2430) \to Dππ$ decay

2012-03-16

arxiv.org/abs/1203.3632v1

Physics

High Energy Physics

High Energy Physics - Phenomenology

14 pages, 5 figures

Scientific paper

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.

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