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.

37 pages, 12 figures