Lepton polarization and sensitivity to the form factors in $Λ\to p\,\ell^-\barν_\ell$ with lattice QCD

We investigate the polarization of the charged lepton in the semileptonic hyperon decay $Λ\to p\,\ell^-\barν_\ell$ ($\ell=e,μ$) 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 $R_{μe}$. We show that the longitudinal polarization determines the ratio $g_1/f_1$ 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 $R_{μe}$ is nearly independent of $g_1/f_1$ and the weak magnetism. For comparison, we also use the QCD sum-rule form factors, whose $g_1/f_1$ 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 $q^2$ dependence of $R_{μe}$ 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 $R_{μe}$ can be measured at BESIII and the proposed Super Tau-Charm Facility, and $R_{μe}$ also at LHCb. These measurements can test the Standard Model and the lattice-QCD form factors.