On the $D^0$ -- $D_s$ lifetime difference and $τ\to 7π+ ν_τ$ decays

In this paper we discuss some aspects of inclusive decays of charmed mesons and also decays of the $τ$ lepton into $ν_τ+ 7π$. We find that phase space effects are likely to explain the observed lifetime ratio $τ(D_s^+) / τ(D^0)$ = 1.17. In particular one need not appeal to a large annihilation contribution in the inclusive $D^0$ decay which, being absent in $D_s^+$ decays could also contribute to the enhanced $D^0$ decay rate relative to that of the $D_s^+$. Examining a separate problem, we find that the rate for $τ\to ν_τ+ 7π$ is almost completely dominated by the tiny phase space for the final eight particle state. Using an effective chiral Lagrangian to estimate the matrix element yields a branching ratio into the channel of interest far smaller than the present upper bound.

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