Strong Decays of Excited Heavy Mesons In Chiral Perturbation Theory

Abstract

We construct an effective Lagrangian describing the interaction of soft pions and kaons with mesons containing a heavy quark and light degrees of freedom in an orbital $p$ wave. The formalism is easily extended to heavy mesons and baryons in arbitrary excited states. We calculate the leading contributions to the strong decays $\dtwo\to\dπ$, $\dtwo\to\dstarπ$ and $\done\to\dstarπ$. We confirm the relations between the rates previously obtained by Isgur and Wise using heavy quark symmetry, and find that the absolute widths are consistent with na\"ıve power counting. We also estimate the branching ratios for the two pion decays $\dtwo\to\dstarππ$, $\done\to\dstarππ$ and $\done\to\dππ$, which are dominated by pole graphs. Our predictions depend on the masses and widths of the as yet unseen scalar-pseudovector $p$-wave doublet. Heavy quark spin symmetry predicts $Γ(\dtwo\to\dstarππ): Γ(\done\to\dstarππ):Γ(\done\to\dππ)=3:1:2$, but this relation is badly violated in practice because $1/M$ effects arising purely from kinematics are large.