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

In the semileptonic decays of heavy mesons and baryons the lepton-mass dependence factors out in the quadratic $cos^2theta$ coefficient of the differential $costheta$ 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 $bar{B}^0 to D^{(ast)+} ell^- bar u_ell$ and $B_c^- to J/psi (eta_c)ell^- bar u_ell$, and semileptonic heavy baryon decays such as $Lambda_b to Lambda_c ell^- bar u_ell$ for each $ell=e,mu,tau$.