Nonperturbative Parameters of Inclusive $Λ_b$ Decays from Small Velocity Sum Rules

Abstract

We investigate the nonperturbative parameters entering the heavy quark expansion for the inclusive decay rates of the $Λ_b$ baryon, focusing on the kinetic term $\hatμ_π^2$ and the Darwin term $\hatρ_D^3$. Recent evaluations have yielded an unexpectedly large Wilson coefficient associated with the dimension-six Darwin operator, which motivates a more detailed examination of the associated hadronic matrix element. We constrain $\hatμ_π^2$ and $\hatρ_D^3$ using Small Velocity Sum Rules for the inclusive semileptonic decay $Λ_b \to X_c e^- \barν_e$. These sum rules relate moments of hadronic structure functions, computed via the Operator Product Expansion, to hadronic matrix elements of relevant exclusive transitions. Truncating the hadronic side to include the lowest-lying charmed baryon states with spin-parity $ J^P = 1/2^+, 1/2^-, 3/2^- $, we employ the corresponding lattice QCD form factors near zero recoil as inputs. By analysing zeroth and higher moments, we derive inequalities that define an allowed region in the $(\hatμ_π^2, \hatρ_D^3)$ plane. The derived constraints are consistent, within uncertainties, with estimates from spectroscopic relations and the nonrelativistic constituent quark model. This work refines the determination of key HQE parameters for $Λ_b$, with implications for precision predictions of heavy baryon lifetimes and inclusive decays of heavy baryons in general.