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 $\cos^2\theta$ 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 $\ell=e,\mu,\tau$.