Heavy Meson Masses in Chiral Perturbation Theory with Heavy Quark Symmetry

Abstract

The $SU(3)$ and hyperfine mass splittings of mesons containing a single heavy quark are computed to one-loop order in chiral perturbation theory with heavy quark spin symmetry. Electromagnetic contributions of order $\alpha_em$ are included. The observed values of the mass splittings are consistent with the one-loop chiral perturbation theory calculation. The $d-u$ hyperfine splitting $(D^{* +} - D^+) - (D^{*0} - D^0)$ is equal to $(m_d - m_u)/ m_s$ times the $s-d$ hyperfine splitting $(D_s^{* +} - D_s^+) - (D^{*+} - D^+)$ upto electromagnetic contributions. The small observed value of the $s-d$ hyperfine splitting implies that the $d-u$ hyperfine splitting is completely dominated by electromagnetic mass contributions.