Extraction of the D^*Dπ coupling from D^* decays

The decays D^* -> D\pi and D^* -> D\gamma are well described by heavy meson chiral perturbation theory. With the recent measurement of Br(D^{*+} -> D^+ \gamma), the D^{*0}, D^{*+}, and D_s^* branching fractions can be used to extract the D^*D\pi and D^*D\gamma couplings $g$ and $\beta$. The D^* -> D\gamma decays receive important corrections at order $\sqrt{m_q}$ and, from the heavy quark magnetic moment, at order $1/m_c$. Here all the decay rates are computed to one-loop, to first order in $m_q$ and $1/m_c$, including the effect of heavy meson mass splittings, and the counterterms at order $m_q$. A fit to the experimental data gives two possible solutions, g=0.27^{+.04}_{-.02}^{+.05}_{-.02}, \beta=0.85^{+.2}_{-.1}^{+.3}_{-.1} GeV^{-1} or g=0.76^{+.03}_{-.03}^{+.2}_{-.1}, \beta=4.90^{+.3}_{-.3}^{+5.0}_{-.7} GeV^{-1}. The first errors are experimental, while the second are estimates of the uncertainty induced by the counterterms. (The experimental limit \Gamma_{D^{*+}} < 0.13 MeV excludes the $g=0.76$ solution.) Predictions for the D^* and B^* widths are given.