Abstract
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 $a\approx 0.11\:{\rm fm},\:0.085\:{\rm fm}$ 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 $\Lambda_c \to n\, e^+ \nu_e$ and $\Lambda_c \to n\, \mu^+ \nu_\mu$ 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.
Highlights
This paper reports a lattice QCD calculation of the form factors describing the matrix elements hNjq ΓcjΛci, where q denotes the up or down quark field, N denotes the proton or neutron, and Γ ∈ fγμ; γμγ5; σμνg
The Λc → n vector and axial vector form factors govern the charged-current decays Λc → nlþνl, whose rates are proportional to jVcdj2
Rare charm decays provide an opportunity to search for new fundamental physics, but this is more challenging than in the bottom sector due to the dominance of long-distance contributions from nonlocal matrix elements in most or all of the kinematic range [except for some observables that vanish in the standard model (SM)]
Summary
This paper reports a lattice QCD calculation of the form factors describing the matrix elements hNjq ΓcjΛci, where q denotes the up or down quark field, N denotes the proton or neutron, and Γ ∈ fγμ; γμγ; σμνg. The Λc → p form factors play a role in the rare charm decays Λc → plþl−, Λc → pγ, and others. Rare charm decays provide an opportunity to search for new fundamental physics, but this is more challenging than in the bottom sector due to the dominance of long-distance contributions from nonlocal matrix elements in most or all of the kinematic range [except for some observables that vanish in the standard model (SM)]. Recent theoretical studies of mesonic rare charm decays such.
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