$\Lambda_b \to p, N^\ast(1535)$ Form Factors from QCD Light-Cone Sum Rules

In this work we calculate the transition form factors of $\Lambda_b$ decaying into proton and $N^*(1535)$ ($J^P={1/2}^+$ and ${1/2}^-$ respectively), within the framework of light-cone sum rules with the distribution amplitudes (DAs) of $\Lambda_b$-baryon. In the hadronic representation of the correlation function, we have isolated both the proton and the $N^*(1535)$ states so that the $\Lambda_b \rightarrow p, N^*(1535)$ form factors can be evaluated simultaneously. Due to the less known properties of baryons, we investigate three interpolating currents of the light baryons and five parametrization models for DAs of $\Lambda_b $. Numerically, our predictions on the $\Lambda_b \rightarrow p$ form factors and the branching fractions of $\Lambda_b\to p\ell \nu$ from the Ioffe or the tensor currents are consistent with the Lattice simulation and the results from the light-baryon sum rules, as well as the experimental data of $Br(\Lambda_b^0\to p\mu^-\bar\nu)$. The predictions on the form factors of $\Lambda_b \rightarrow N^*(1535)$ are very sensitive to the choice of the interpolating currents so that the relevant measurement could be helpful to clarify the properties of baryons.