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

We study the effect of sigma meson on the $D_1(2430) \to Dππ$ 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 $σ$-$π$-$π$ coupling constant to the I=0, $S$-wave $π$-$π$ scattering data. Then, we show how the differential decay width $dΓ(D_1 \to D(ππ)_{I = 0, L =0})/d m_{ππ}$ 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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