Purely leptonic charm decays

Let us assume that leptonic charm decays proceed via (13.1.1), i.e. neglecting the other contributions listed in Section 13.2.1. We show in Fig. 13.14 examples of Cabibbo allowed and suppressed decays. 

To get an estimate for the leptonic decay rates, note that vector boson effects are unimportant, so that from Section 1.2 the Feynman amplitude for the pseudo-scalar P — decay will be given by (0 means vacuum) 

To the extent that SU(4) p is not too badly broken a rough estimate of leptonic charm decay can be obtained by assuming /,r — //c — /d — fOs-Taking A4p in (13.2.4), summing over the spins of the leptons and using the definitions (13.2.5) one gets for the process P — (P = 

The pion decay can be used to set the scale using the experimental value 3.84 x lO s one gets U 0.131 GeV. The phase space factor [1 — (w /mp)] is already 0.91 for K decay and becomes 

As can be seen from (13.2.6), decays into will totally dominate over decays into e+i/g because of the very large mass ratio (m /me). The decay rate Df T Ur (heavy lepton) is expected to be about 16 times larger than Df iX Vix but is unfortunately very difficult to observe. 

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As we shall soon see, the total decay rate of D and (into hadrons) can be estimated to be of the order of 10 — 10 s so that the purely leptonic decay rate of charm mesons leads to branching ratios which are, at most, of order 10 — 10 and can, therefore, be neglected. Indeed up to the present, none of the leptonic decays has been observed (on this question, the Particle Data Group (1992) reports BR( > — ... 

Estimates can be made, however, if we use the free quark-parton model and assume that partons convert into hadrons with unit probability. A very rough estimate for the inclusive semi-leptonic D decay can be obtained along the lines given previously [eqn (13.2.2)] if we forget all complications coming from non-spectator diagrams and assume that the light quark behaves purely like a spectator while the charm quark decay proceeds as if it were a free particle. In this case one has... 

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