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

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.