The decays $\Lambda_{b,c}\to N^*\, l\,\nu$ in QCD

TL;DR

This paper calculates the form factors and decay widths of $ ext{Lambda}_{b,c} o N^* l u$ decays using light-cone sum rules, comparing two methods and models to identify the most reliable approach and highlight the importance of experimental measurements.

Contribution

It introduces a comparative analysis of two different interpolating currents and models for $ ext{Lambda}_{b,c} o N^*$ decays within the light-cone sum rule framework, identifying the most reliable method.

Findings

The axial-vector like current with structures of highest $p_+$ powers yields the most reliable results.

Predicted decay widths depend significantly on the chosen model and parameters.

Even rough experimental measurements can discriminate between different distribution amplitude models.

Abstract

We present an exploratory study of the $\Lambda_{c,b}\to N^*$-form factors and the semileptonic decay width within the framework of light-cone sum rules. We use two different methods and two different interpolating currents for the $\Lambda_{c,b}$. As interpolating currents we choose an axial-vector like and a pseudoscalar like current. Our results show that the procedure of eliminating negative parity partners is not well suited for the case at hand and that the second approach using structures with highest powers of $p_+$ with an axial-vector like interpolating current gives the most reliable results. Our predictions are based on the models obtained in \cite{Anikin:2015ita,Braun:2014wpa}. The largest uncertainty comes from the uncertainty of the twist 4 parameters $\eta_{10},\,\eta_{11}$ and we take the spread between the two models in \cite{Anikin:2015ita} as a measure for this. We get \begin{eqnarray} \Gamma(\Lambda_b\to N^*(1535) l \nu)&=&\left(0.0058^{+0.0010}_{-0.0009}\right)\cdot\left(\dfrac{V_{ub}}{3.5\cdot10^{-3}}\right)^2,\quad\mbox{LCSR(1)} \nonumber \Gamma(\Lambda_b\to N^*(1535) l \nu)&=&\left(0.00070^{+0.00012}_{-0.00011}\right)\cdot\left(\dfrac{V_{ub}}{3.5\cdot10^{-3}}\right)^2,\quad\mbox{LCSR(2)} \nonumber \Gamma(\Lambda_c\to N^*(1535) l \nu)&=&\left(0.0064^{+0.0012}_{-0.0011}\right)\cdot \left(\dfrac{V_{cd}}{0.225}\right)^2,\quad\mbox{LCSR(1)}\nonumber \Gamma(\Lambda_c\to N^*(1535) l \nu)&=&\left(0.00077^{+0.00016}_{-0.00014}\right)\cdot \left(\dfrac{V_{cd}}{0.225}\right)^2,\quad\mbox{LCSR(2)}\nonumber \end{eqnarray} as predictions for the respective decay widths, where LCSR(1) and LCSR(2) refer to the two different models of the distribution amplitudes of the $N^*$. It is seen that even a rough measurement of these decays will greatly help to discriminate different models.