Charmed baryon semileptonic decays in a relativistic three-quark model

RESUMO

We study the spin-$1/2\to1/2$ semileptonic decays of singly charmed baryons ($\Lambda_c^+$, $\Xi_c^{0,+}$, and $\Omega_c^0$) into the light baryon octet within a relativistic three-quark model. The constituent quark masses and spatial wave functions are determined by the baryon mass spectrum. For the physical $\Xi_c$ states, the light flavor $\mathrm{SU}(3)$ breaking ($m_s > m_{u,d}$) naturally induces a coherent mixing between the flavor antitriplet and flavor sextet configurations, which is completely fixed by the mass eigenstates. Consequently, no adjustable parameters are introduced in calculating the weak transition amplitudes. Using these wave functions, we calculate the $c\to s,d$ helicity amplitudes with the Bakamjian--Thomas boost, including the spatial Jacobian and the Wigner rotations of the constituent spins. The branching fractions, $q^2$ distributions, longitudinal polarizations, and form factors are then obtained from these amplitudes. For the $\Lambda_c^+\to\Lambda\ell^+\nu_\ell$ and $\Lambda_c^+\to n\ell^+\nu_\ell$ modes, our branching fractions and form factors are in good agreement with the experimental data and Lattice QCD results. For $\Xi_c^0\to\Xi^-e^+\nu_e$, we obtain branch ratio $\mathcal B_{\ell} \simeq 4.0~\%$, which is consistent with recent Lattice QCD calculations but lies well above the current experimental average. Clarifying the origin of this discrepancy calls for further dedicated efforts from both experimental and theoretical sides. For the $\Omega_c^0\to\Xi^-\ell^+\nu_\ell$ decay, the spin-$1$ $ss$ spectator yields a positive longitudinal polarization of the final $\Xi^-$, in contrast to the negative polarizations in the predominantly antitriplet decay modes. Our predictions for the $q^2$ spectra, angular asymmetries, and final baryon polarizations may provide useful references for future measurements of singly charmed baryon semileptonic decays.