Transition form factors of the \(\Lambda _b \rightarrow \Lambda (1520)\) in QCD light-cone sum rules

Abstract

In this work, we investigate the transition form factors for \(\Lambda _b\rightarrow {\Lambda (1520)}\) within the framework of light-cone sum rules (LCSR), using the light-cone distribution amplitudes (LCDAs) of the \(\Lambda _b\)-baryon. In the hadronic representation of the correlation function, we carefully select the appropriate Lorentz structures and isolate the contributions from both the \(\Lambda (1520)(J^P=(3/2)^-)\) and the \(\Lambda (1890)(J^P=(3/2)^+),\) ensuring that the form factors for \(\Lambda _b\rightarrow {\Lambda (1520)}\) can be calculated unambiguously. We also provide predictions for various physical observables in the decay \(\Lambda _b\rightarrow {\Lambda (1520)}l^+l^-,\) including the differential branching fraction, the lepton-side forward–backward asymmetry, the longitudinal polarization fraction, and the CP-averaged normalized angular observable. Our prediction for the differential branching fraction of \(\Lambda _b\rightarrow {\Lambda (1520)}\mu ^+\mu ^-\) is in good agreement with the LHCb measurement within the uncertainties.