SCET sum rules for $Λ_b \to Λ\ell^+\ell^-$, $Λγ$ decays

Abstract

We construct light-cone sum rules for various types of effective form factors in the $Λ_b \to Λ\ell^+\ell^-$ and $Λ_b \to Λγ$ decays by analyzing vacuum-to-$Λ_b$ (or $γ^\ast$-to-$Λ_b$) correlation functions with the light $Λ$-baryon interpolating current. These form factors, defined via hadronic matrix elements within soft-collinear effective theory (SCET), enter the next-to-leading-power QCD factorization formulas for large-recoil transitions. Implementing the perturbative matching from $\text{SCET}_\text{I}$ to heavy quark effective theory, we determine the hard-collinear functions at next-to-leading-order accuracy. Based on light-cone sum rule predictions for the $Λ_b \to Λ$ form factors, we compute the $q^2$-dependent differential branching fraction, forward-backward asymmetry and dilepton longitudinal polarization fraction for $Λ_b \to Λ\ell^+\ell^-$ decay, as well as the branching fraction for $Λ_b \to Λγ$ decay.