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 ${\mathrm{cos}}^{2}\ensuremath{\theta}$ coefficient of the differential $\mathrm{cos}\ensuremath{\theta}$ 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 $\ensuremath{\tau}$ lepton phase space, one can define optimized partial rates which, in the Standard Model, are the same for all three $(e,\ensuremath{\mu},\ensuremath{\tau})$ 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 ${\overline{B}}^{0}\ensuremath{\rightarrow}{D}^{(*)+}{\ensuremath{\ell}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\ell}}$ and ${B}_{c}^{\ensuremath{-}}\ensuremath{\rightarrow}J/\ensuremath{\psi}({\ensuremath{\eta}}_{c}){\ensuremath{\ell}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\ell}}$ and semileptonic heavy baryon decays such as ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}{\ensuremath{\ell}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\ell}}$ for each $\ensuremath{\ell}=e$, $\ensuremath{\mu}$, $\ensuremath{\tau}$.