Two-Pion Decay Widths of Excited Charm Mesons

The widths for $\pi\pi$ decay of the L=1 charm mesons are calculated by describing the pion coupling to light constituents quarks by the lowest order chiral interaction. The wavefunctions of the charm mesons are obtained as solutions to the covariant Blankenbecler-Sugar equation. These solutions correspond to an interaction Hamiltonian modeled as the sum of a linear scalar confining and a screened one-gluon exchange (OGE) interaction. This interaction induces a two-quark contribution to the amplitude for two-pion decay, which is found to interfere destructively with the single quark amplitude. For the currently known L=1 $D$ mesons, the total $\pi\pi$ decay widths are found to be $\sim 1$ MeV for the $D_1(2420)$ and $\sim 3$ MeV for the $D^*_2(2460)$ if the axial coupling of the constituent quark is taken to be $g_A^q=1$. The as yet undiscovered spin singlet $D_1^*$ state is predicted to have a larger width of 7 - 10 MeV for $\pi\pi$ decay.