Charm and Bottom Semileptonic Decays

Abstract

We review the present status of theoretical attempts to calculate the semileptonic charm and bottom decays and then present a calculation of these decays in the light--front frame at the kinematic point $q^2=0$. This allows us to evaluate the form factors at the same value of $q^2$, even though the allowed kinematic ranges for charm and bottom decays are very different. Also, at this kinematic point the decay is given in terms of only one form factor $A_0(0)$. For the ratio of the decay rates given by the E653 collaboration we show that the determination of the ratio of the Cabibbo--Kobayashi--Maskawa (CKM) matrix elements is consistent with that obtained from the unitarity constraint. At present, though, the unitarity method still has greater accuracy. Since comparisons of the semileptonic decays into $\rho$ and either electrons or muons will be available soon from the E791 Fermilab experiment, we also look at the massive muon case. We show that for a range of $q^2$ the $SU(3{)}_F$ symmetry breaking is small even though the contributions of the various helicity amplitudes becomes more complicated. For $B$ decays, the decay $B\to K^{\ast }\ell \bar{\ell }$ at $q^2=0$ involves an extra form factor coming from the photon contribution and so is not amenable to the same kind of analysis, leaving only the decay $B\to K^{\ast }\nu \bar{\nu }$ as a possibility. As the mass of the decaying particle increases we note that the $SU(3)$ symmetry becomes badly broken at $q^2=0$.

Latex, 19 pages, two figures are attached, a minor change in the manuscript related to this

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• Revisiting the form factors of $P\to V$ transition within the light-front quark models
• Tensor form factors of $P\to P,S,V$ and $A$ transitions within the standard and the covariant light-front approaches
• New Measurement of BR(D+ ->Rho0 Mu+ Nu) / BR(D+ ->K*0 Mu+ Nu) Branching Ratio