Can Large $u, d$ Quark Masses be Inferred from the $D_s \to n π$ decay rate?

Abstract

The $D_s \rightarrow n π$ measured branching could lead to information on $u, d$ quark masses if it is dominated by the (helicity suppressed) $D_s \rightarrow u \bar d$ annihilation channel. The data would then suggest anomalously high $m_u \approx m_d \approx 30$MeV masses. We find however that $D_s \rightarrow u {\bar d} g$ can explain $\sum Br(D_s \rightarrow n π)$ with zero up and down quark masses. We also argue that the present $D_s \rightarrow n π$ data may not even convincingly imply any annihilation process whatsoever.