Puzzle in the Charmed $D_s$ meson decays into pions: Could the light quarks be not so light?

Abstract

The inclusive decay rate into pions of the charmed $D_s$ meson is surprisingly larger than estimates expected from the $W$ annihilation, adopting commonly used values of current-algebra up and down quark masses. We then go beyond this tree diagram and consider possible QCD effects that might cause such a large rate. There are two; the first one is related to the spectator decay $ c{\bar s} \rightarrow s{\bar s} + u {\bar d}$ followed by $ s {\bar s} \rightarrow d{\bar d}~,~ u{\bar u}$ via two-gluon exchange box diagram. The second one is a gluon emission in weak annihilation for which the usual helicity suppression is vitiated: $D_s\rightarrow W+g$ followed by $ W\rightarrow u {\bar d},~ g\rightarrow d{\bar d},~u{\bar u}$. These two contributions, however, turn out to be insufficient to explain data, implying that the puzzle could be understood if the up, down quarks have higher mass values. Furthermore, on the basis of experimental informations on the spectral function $\rho_{3\pi}(Q^2)$ deduced from the exclusive $ D_s \rightarrow 3\pi$ mode, the QCD sum rules also point to a higher mass for light quarks.