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The decays of the ground-state charmed baryon $Lambda_c$ are now close to being completely mapped out. In this paper we discuss some remaining open questions, whose answers can help shed light on weak processes contributing to those decays, on calculations of such quantities as transition form factors in lattice QCD, and on missing decay modes such as $Lambda_c to Lambda^* ell^+ u_ell$, where $Lambda^*$ is an excited resonance. The discussion is in part a counterpart to a previous analysis of inclusive $D_s$ decays.
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An earlier analysis of observed and anticipated $Lambda_c$ decays [M. Gronau and J. L. Rosner, Phys. Rev. D {bf 97}, 116015 (2018)] is provided with a table of inputs and a figure denoting branching fractions. This addendum is based on the 2018 Particle Data Group compilation and employs a statistical isospin model to estimate branching fractions for as-yet-unseen decay modes.
We study the semileptonic decays of $Lambda_c^+ to Lambda(n)ell^+ u_{ell}$ in two relativistic dynamical approaches of the light-front constituent quark model (LFCQM) and MIT bag model (MBM). By considering the Fermi statistic between quarks and determining spin-flavor structures in baryons along with the helicity formalism in the two different dynamical models, we calculate the branching ratios (${cal B}$s) and averaged asymmetry parameters ($alpha$s) in the decays. Explicitly, we find that ${cal B}( Lambda_c^+ to Lambda e^+ u_{e})=(3.36pm0.87,3.48)%$ and ${alpha}( Lambda_c^+ to Lambda e^+ u_{e})=(-0.97pm0.03,-0.83)$ in (LFCQM, MBM), in comparison with the data of ${cal B}( Lambda_c^+ to Lambda e^+ u_{e})=(3.6pm0.4)%$ and ${alpha}( Lambda_c^+ to Lambda e^+ u_{e})=-0.86pm 0.04$ given by the Particle Data Group, respectively. We also predict that ${cal B}( Lambda_c^+ to n e^+ u_{e})=(0.57pm0.15, 3.6pm1.5)times 10^{-3}$ and ${alpha}( Lambda_c^+ to n e^+ u_{e})=(-0.98pm0.02,-0.96pm0.04)$ in LFCQM with two different scenarios for the momentum distributions of quarks in the neutron, and ${cal B}( Lambda_c^+ to n e^+ u_{e})= 0.279times 10^{-2}$ and ${alpha}( Lambda_c^+ to n e^+ u_{e})=-0.87$ in MBM, which could be tested by the ongoing experiments at BESIII, LHCb and BELLEII.
We analyze the mixing between $Sigma^0$ and $Lambda^0$ based on the baryon masses. We distinguish the contributions from QCD and QED in the baryon mass splittings. We find that the mixing angle between $Sigma^0$ and $Lambda^0$ is $(2.07pm 0.03)times 10^{-2} $, which leads to the decay branching fraction and up-down asymmetry of $Lambda_c^+ to Sigma^0 e^+ u_e$ to be ${cal B}(Lambda_c^+ to Sigma^0 e^+ u_e)=(1.5pm 0.2)times 10^{-5}$ and $alpha(Lambda_c^+ to Sigma^0 e^+ u_e)=-0.86pm 0.04$, respectively. Moreover, we obtain that $Delta {cal B}equiv {cal B}(Lambda_c^+to Sigma^0 pi^+) - {cal B}(Lambda_c^+to Sigma^+pi^0)=(3.8pm 0.5)times 10^{-4}$ and $Delta alpha equivalpha(Lambda_c^+to Sigma^0 pi^+) -alpha(Lambda_c^+to Sigma^+pi^0)=(-1.6pm 0.7)times10^{-2}$, which should vanish without the mixing.
I describe the theoretical progress in the study of semileptonic tree-level B decays, and its interplay with recent experimental results. In particular, I focus on two anomalies: the ratios $R(D^{(*)})=displaystylefrac{{cal B}(B to D^{(*)} tau bar u_tau)}{{cal B}(B to D^{(*)} ell bar u_ell)}$ and the inclusive versus exclusive determination of $|V_{cb}|$. I review a few explanations proposed for such anomalies, and discuss tests to shed light on their origin.
A lattice QCD determination of the $Lambda_c to N$ vector, axial vector, and tensor form factors is reported. The calculation was performed with $2+1$ flavors of domain wall fermions at lattice spacings of $aapprox 0.11:{rm fm},:0.085:{rm fm}$ and pion masses in the range $230:{rm MeV} lesssim m_pi lesssim 350$ MeV. The form factors are extrapolated to the continuum limit and the physical pion mass using modified $z$ expansions. The rates of the charged-current decays $Lambda_c to n, e^+ u_e$ and $Lambda_c to n, mu^+ u_mu$ are predicted to be $left( 0.405 pm 0.016_{,rm stat} pm 0.020_{,rm syst} right)|V_{cd}|^2 :{rm ps}^{-1}$ and $left( 0.396 pm 0.016_{,rm stat} pm 0.020_{,rm syst} right)|V_{cd}|^2 :{rm ps}^{-1}$, respectively. The phenomenology of the rare charm decay $Lambda_c to p, mu^+ mu^-$ is also studied. The differential branching fraction, the fraction of longitudinally polarized dimuons, and the forward-backward asymmetry are calculated in the Standard Model and in an illustrative new-physics scenario.
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