$\Lambda_b \to \Lambda$ Form Factors from Light-Cone Sum Rules with $\Lambda$-Baryon Distribution Amplitudes

Abstract

We compute the $\Lambda_b \to \Lambda$ transition form factors using light-cone sum rules based on $\Lambda$-baryon distribution amplitudes, including contributions up to twist--6. The analysis is performed for pseudoscalar, vector, and axial-vector $b\to s$ currents and for different choices of the $\Lambda_b$ interpolating current. We find that only the pseudoscalar interpolating current leads to numerically stable and phenomenologically viable form factors. The resulting form factors are parametrised using a $z$-expansion and applied to the rare decay $\Lambda_b \to \Lambda \ell^+ \ell^-$, yielding predictions for branching ratios in the low-$q^2$ region.