Form-factor-independent test of lepton universality in semileptonic heavy meson and baryon decays

Abstract

In the semileptonic decays of heavy mesons and baryons the lepton-mass dependence factors out in the quadratic ${\cos }^2\theta$ coefficient of the differential $\cos \theta$ distribution. We call the corresponding normalized coefficient the convexity parameter. This observation opens the path to a test of lepton universality in semileptonic heavy meson and baryon decays that is independent of form-factor effects. By projecting out the quadratic rate coefficient, dividing out the lepton-mass-dependent factor and restricting the phase space integration to the $\tau$ lepton phase space, one can define optimized partial rates which, in the Standard Model, are the same for all three $(e,\mu ,\tau )$ modes in a given semileptonic decay process. We discuss how the identity is spoiled by New Physics effects. We discuss semileptonic heavy meson decays such as ${\bar{B}}^0\to D^{(\ast )+}{\ell }^{-}{\bar{\nu }}_{\ell }$ and $B_c^{-}\to J/\psi ({\eta }_c){\ell }^{-}{\bar{\nu }}_{\ell }$, and semileptonic heavy baryon decays such as ${\Lambda }_b\to {\Lambda }_c{\ell }^{-}{\bar{\nu }}_{\ell }$ for each $\ell =e,\mu ,\tau$.

Comments: 14 pages, 4 figures, 3 tables. Some discussion and references added. Will be published in PRD