Form factors of $Λ_b^0 \to Λ_c(2595)^+$ within light-cone QCD sum rules

Abstract: In this work, we calculated the form factors of the weak decay process $\Lambda_b⁰ \to \Lambda_c(2595)<sup>+$, where the final charm baryon represents an excited state with spin-parity $\frac{1}{2}<sup>-$. Utilizing the light-cone QCD sum rules approach, we incorporated the contributions of the lowest two charm baryon states: the ground state $\Lambda_c$ with $J<sup>P=\frac{1}{2}<sup>+$ and the excited state $\Lambda_c(2595)<sup>+$ with $J<sup>P=\frac{1}{2}<sup>-$ in the hadronic representation of the $\Lambda_b \to \Lambda_c(2595)<sup>+$ transition correlation function. This approach allows us to extract the form factors of the $\Lambda_b⁰ \to \Lambda_c(2595)<sup>+$ from $\Lambda_b⁰ \to \Lambda_c<sup>+$ transition. During the light-cone QCD sum rules procedure, we employed the light-cone distribution amplitudes (LCDAs) of the $\Lambda_b$ baryon. Furthermore, by combining these form factors with the helicity amplitudes of the bottom baryon transition matrix elements, we calculated the differential decay widths for the processes $$\Lambda_b⁰ \to \Lambda_c(2595)<sup>+\ell<sup>-\bar{\nu}_\ell$$ and provided the optimal choice of the interpolating current for $\Lambda_c$ in this process. Additionally, within the lifetime of $\Lambda_b<sup>0$, we obtained the absolute branching fractions for the semileptonic decays $$\Lambda_b⁰ \to \Lambda_c(2595)⁺ \ell^- \bar{\nu}<em>\ell$$. With the branching fractions of $$\Lambda_b⁰ \to \Lambda_c(2595)⁺ \ell^- \bar{\nu}</em>\ell$$ calculated in this work, we also determined the parameter $R(\Lambda_c(2595)<sup>+)$ which tests the lepton flavor universality. This parameter is defined as the ratio of branching fractions $$Br(\Lambda_b⁰ \to \Lambda_c(2595)<sup>+\tau<sup>-\bar{\nu}_\tau)$$ and $$Br(\Lambda_b⁰ \to \Lambda_c(2595)<sup>+\mu<sup>-\bar{\nu}_\mu)$$. Our results provide a valuable theoretical test for these decay channels and offer insights into the LCDAs of bottom baryons, paving the way for further in-depth investigations.