Dispersive analysis of $\Lambda_b \to \Lambda(1520)$ local form factors

TL;DR

This paper develops a model-independent dispersive approach to analyze $ ext{Lambda}_b o ext{Lambda}(1520)$ form factors, constrained by lattice QCD and other theoretical bounds, enabling precise predictions for decay observables.

Contribution

It introduces a dispersive parametrization of the form factors constrained by lattice QCD, endpoint relations, and SCET, providing a comprehensive framework for $ ext{Lambda}_b o ext{Lambda}(1520)$ decays.

Findings

Predicted differential branching ratios and asymmetries for $ ext{Lambda}_b o ext{Lambda}(1520) ext{l}^+ ext{l}^-$ decays.

Validated the dispersive approach with lattice QCD data and theoretical constraints.

Provided a reproducible Python notebook for the analysis.

Abstract

We perform an analysis of $\Lambda_b\to\Lambda(1520)$ local form factors. We use dispersive techniques to provide a model-independent parametrisation of the form factors that can be used in the whole kinematic region. We use lattice QCD data to constrain the free parameters in the form factors expansion, which is further constrained by endpoint relations, dispersive bounds, and SCET relations. We analyse different scenarios, where we expand the form factors up to different orders, and their viability. Finally, we use our results to obtain predictions for some observables in $\Lambda_b\to\Lambda(1520)\ell^+\ell^-$ decays, as the differential branching ratio, the forward-backwards lepton asymmetry and the branching ratio of $\Lambda_b\to\Lambda(1520)\gamma$. Finally, we provide a python notebook based on the software EOS to reproduce our result.