Lepton polarization and sensitivity to the form factors in Λ→ p\,⁻ν_ with lattice QCD

We investigate the polarization of the charged lepton in the semileptonic hyperon decay Λ→ p\,⁻ν_ (=e,μ) within the Standard Model, using the form factors obtained from lattice QCD. We compute the longitudinal, transverse and normal polarization of the lepton, the forward-backward asymmetry of each lepton spin state, and the lepton flavor universality ratio Rμe. We show that the longitudinal polarization determines the ratio g₁/f₁ of the axial-vector to vector couplings, and that the forward-backward asymmetries of the electron and of negative-helicity muons determine the weak magnetism. The asymmetry of positive-helicity muons is fixed by kinematics up to a small dependence on the second-class form factors, whereas Rμe is nearly independent of g₁/f₁ and the weak magnetism. For comparison, we also use the QCD sum-rule form factors, whose g₁/f₁ and weak magnetism are opposite in sign to experiment and lattice QCD, and find very different values for the observables that depend on them. Moreover, the q² dependence of Rμe fixes the longitudinal polarization of the muon, which can thus be measured from the decay rates, without measuring the muon spin. The normal polarization is generated by the electromagnetic final-state interaction and provides the Standard Model reference for searches for time-reversal violation. The electron forward-backward asymmetry and Rμe can be measured at BESIII and the proposed Super Tau-Charm Facility, and Rμe also at LHCb. These measurements can test the Standard Model and the lattice-QCD form factors.