SCET sum rules for $\Lambda_b \to \Lambda \ell^+\ell^-$, $\Lambda \gamma$ decays

Abstract

We construct light-cone sum rules for various types of effective form factors in the $\Lambda_b \to \Lambda \ell^+\ell^-$ and $\Lambda_b \to \Lambda \gamma$ decays by analyzing vacuum-to-$\Lambda_b$ (or $\gamma^\ast$-to-$\Lambda_b$) correlation functions with the light $\Lambda$-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 $\Lambda_b \to \Lambda$ form factors, we compute the $q^2$-dependent differential branching fraction, forward-backward asymmetry and dilepton longitudinal polarization fraction for $\Lambda_b \to \Lambda \ell^+\ell^-$ decay, as well as the branching fraction for $\Lambda_b \to \Lambda \gamma$ decay.