On the form factors of semileptonic baryon decays in Heavy Quark Effective Theory

TL;DR

This paper derives sum rules and bounds for form factors in semileptonic Lambda_b to Lambda_c decays within Heavy Quark Effective Theory, highlighting the relationship between leading and subleading Isgur-Wise functions.

Contribution

It introduces a sum rule for the subleading elastic IW function A(w) and establishes a correlation between A(w) and the leading IW function xi(w), providing new theoretical constraints.

Findings

Derived a sum rule for the subleading IW function A(w)

Established a lower bound on the correction to G1(w)

Proved that A'(1) must vanish when xi(w) slope saturates its lower bound

Abstract

We study consequences of the non-forward amplitude for the semileptonic baryon decay Lambda_b into Lambda_c which will be measured in detail at LHCb. We obtain a sum rule for the subleading elastic Isgur-Wise (IW) function A(w) that originates from the kinetic part of the O(1/mQ) effective Lagrangian perturbation. In the sum rule appear only the intermediate states J^P=1/2+, the same that contribute to the O(1/mQ)^2 correction to the axial-vector form factor G1(w) involved in the differential decay rate at zero recoil w=1. This allows us to obtain a lower bound on the correction -delta^(G1)_(1/mQ^2) in terms of A(w) and the shape of the leading elastic IW function xi(w). Another theoretical implication is that A'(1) must vanish in the limit where the slope of the xi(w) saturates its lower bound. A strong correlation between the leading IW function and the subleading one A(w) is thus established in the case of the baryons.