Form factors of \(\varLambda _b^0 \rightarrow \varLambda _c(2595)^+\) within light-cone QCD sum rules

In this work, we calculated the form factors of the weak decay process \(\varLambda _b^0 \rightarrow \varLambda _c(2595)^+\), where the final charm baryon represents an excited state with spin-parity \(\frac{1}{2}^-\). Utilizing the light-cone QCD sum rules approach, we incorporated the contributions of the lowest two charm baryon states: the ground state \(\varLambda _c\) with \(J^P=\frac{1}{2}^+\) and the excited state \(\varLambda _c(2595)^+\) with \(J^P=\frac{1}{2}^-\) in the hadronic representation of the \(\varLambda _b \rightarrow \varLambda _c(2595)^+\) transition correlation function. This approach allows us to extract the form factors of the \(\varLambda _b^0 \rightarrow \varLambda _c(2595)^+\) from \(\varLambda _b^0 \rightarrow \varLambda _c^+\) transition. During the light-cone QCD sum rules procedure, we employed the light-cone distribution amplitudes (LCDAs) of the \(\varLambda _b\) 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 \(\varLambda _b^0 \rightarrow \varLambda _c(2595)^+\ell ^-\bar{\nu }_\ell \) and provided the optimal choice of the interpolating current for \(\varLambda _c\) in this process. Additionally, within the lifetime of \(\varLambda _b^0\), we obtained the absolute branching fractions for the semileptonic decays \(\varLambda _b^0 \rightarrow \varLambda _c(2595)^+ \ell ^- \bar{\nu }_\ell \). With the branching fractions of \(\varLambda _b^0 \rightarrow \varLambda _c(2595)^+ \ell ^- \bar{\nu }_\ell \) calculated in this work, we also determined the parameter \(\mathcal {R}(\varLambda _c(2595)^+)\) which tests the lepton flavor universality. This parameter is defined as the ratio of branching fractions \(\mathcal {B}r(\varLambda _b^0 \rightarrow \varLambda _c(2595)^+\tau ^-\bar{\nu }_\tau )\) and \(\mathcal {B}r(\varLambda _b^0 \rightarrow \varLambda _c(2595)^+\mu ^-\bar{\nu }_\mu )\). 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.