Endpoint Relations for Baryons

Abstract

Following our earlier work we establish kinematic endpoint relations for baryon decays using the Wigner-Eckart theorem and apply them to $\frac{1}{2} \to \frac{1}{2}$ and $\frac{1}{2} \to \frac{3}{2}$ baryon transitions. We provide angular distributions at the kinematic endpoint which hold for the generic $d=6$ model-independent effective Hamiltonian. Moreover, we explicitly verify the endpoint relations using an explicit form factor parametrisation and clarify constraints on helicity based form factors to evidence endpoint relations. Our results provide guidance for phenomenological parameterisations, consistency checks for theory computations and experiment. Results are applicable to ongoing and future new physics searches at LHCb, BES III and Belle II with rare semileptonic-, dineutrino-and charged-modes, which include $\Lambda_b \to \Lambda^{(*)} \ell \ell, \Lambda_b \to \Lambda^{(*)} \nu \nu$, $\Omega_b \to \Omega \ell \ell$, $\Lambda_c \to p \ell \ell$, $\Sigma \to p \ell \ell$ and $\Lambda_b \to \Lambda_c^{(*)} \ell \nu$