New results on the baryon decay Lambda_b -> Lambda_c ell nu in Heavy Quark Effective Theory

TL;DR

This paper derives new theoretical sum rules for form factors in Lambda_b to Lambda_c semileptonic decay within Heavy Quark Effective Theory, providing bounds and correlations useful for interpreting upcoming experimental data at LHCb.

Contribution

It formulates a sum rule for the subleading form factor A(w) at order 1/m_Q, revealing relations between leading and subleading Isgur-Wise functions in baryon decays.

Findings

Derived a sum rule for A(w) involving only specific intermediate states.

Established a lower bound for the correction at zero recoil in terms of form factor derivatives.

Identified a non-trivial correlation between the leading and subleading Isgur-Wise functions.

Abstract

The baryon differential spectrum of the baryon decay $\Lambda_b \to \Lambda_c \ell \bar{\nu}_\ell$ will be measured in detail at LHCb. We obtain new results on the form factors in the heavy quark expansion of Heavy Quark Effective Theory that can be useful in the interpretation of the data. We formulate a sum rule for the elastic subleading form factor $A(w)$ at order $1/m_Q$, that originates from the Lagrangian perturbation $\mathcal{L}_{kin}$. In the sum rule appear only the intermediate states $(j^P, J^P) = (0^+, {1 \over 2}^+)$, entering also in the $1/{m_Q^2}$ correction to the axial form factor $G_1(w)$, that contributes to the differential rate at zero recoil $w = 1$. This result, together with another sum rule in the forward direction for $|G_1(1)|^2$, allows us to obtain a lower bound for the correction at zero recoil $- \delta_{1/{m_Q^2}}^{(G_1)}$ in terms of the derivative $A'_1(1)$ and the slope $\rho^2_\Lambda$ and curvature $\sigma^2_\Lambda$ of the elastic Isgur-Wise function $\xi_{\Lambda}(w)$. Another theoretical implication is that $A'(1)$ must vanish for some relation between $\rho^2_\Lambda$ and $\sigma^2_\Lambda$, as well as for $\rho^2_\Lambda \to 0$, establishing a non-trivial correlation between the leading IW function $\xi_{\Lambda}(w)$ and the subleading one $A(w)$. A phenomenological estimation of these two functions allows to obtain a lower bound on $- \delta_{1/{m_Q^2}}^{(G_1)}$.