Endpoint Relations for Baryons

TL;DR

This paper derives and verifies kinematic endpoint relations for baryon decays, providing angular distributions and constraints useful for phenomenology and new physics searches at major experiments.

Contribution

It establishes model-independent endpoint relations for baryon transitions and verifies them with form factor parametrizations, aiding phenomenological analyses.

Findings

Derived angular distributions at kinematic endpoints.

Verified endpoint relations with explicit form factor models.

Provided constraints on helicity form factors.

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 $\Lambda_b \to \Lambda_c^{(*)} \ell \nu$