Semileptonic Decay of ${\Lambda }_b\to N(1520){\ell }^{-}{\bar{\nu }}_{\ell }$ from QCD Light-cone Sum Rules

Abstract

We investigate the complete set of vector and axial-vector form factors for the charged-current transition ${\Lambda }_b^0\to N(1520{)}^{+}$ using QCD light-cone sum rules (LCSRs) based on the light-cone distribution amplitudes (LCDAs) of the ${\Lambda }_b$ baryon, with the hard-scattering kernels evaluated at tree level. In the hadronic representation of the correlation function, we include the pole contributions of both the negative-parity $N(1520)$, with $J^P=3/2^{-}$, and the positive-parity $N(1720)$, with $J^P=3/2^{+}$. By matching a selected set of Lorentz structures, we derive sum rules that separate the $N(1520)$ contribution from the $N(1720)$ contribution within the adopted two-pole hadronic ansatz. After extrapolating the large-recoil LCSR results over the physical $q^2$ region using a pole-improved $z$ expansion truncated at linear order, we predict the differential branching fractions, the lepton forward-backward asymmetry, the charged-lepton polarization, and the $N(1520)$ polarization in ${\Lambda }_b^0\to N(1520{)}^{+}{\ell }^{-}{\bar{\nu }}_{\ell }$ ($\ell =e,\mu ,\tau$). The corresponding total branching fractions are ${\mathcal{B}}_{e,\mu ,\tau }=(12.4\pm 10.5,12.4\pm 10.5,5.0\pm 4.3)\times 10^{-5}$. Within the stated approximations, these results may serve as theoretical benchmarks for future experimental studies of this channel.

Comments: 26 pages,6 figures