Semileptonic decay form factors of $\Xi_b^0 \rightarrow \Xi_c^+\ell\bar{\nu}_{\ell}$ in HQET

Abstract

Heavy-to-heavy semileptonic decays, particularly the bottom-to-charm quark transitions, are essential for testing the Standard Model (SM) and extracting the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements. These decays have been extensively studied using various theoretical approaches. In this work, we investigate the semileptonic decay $\Xi_b^0 \rightarrow \Xi_c^+\ell\bar{\nu}_{\ell}$ (where $\ell = e$, $\tau$) using a phenomenological quark model. We compute the ground-state masses of the initial and final baryons to get the wave function, which is then used to calculate the form factors, including corrections up to order $1/m_Q$ within the framework of Heavy Quark Effective Theory (HQET). The obtained form factors are implemented in the helicity formalism to evaluate the differential decay rates, total decay width and branching ratio. We compare our results for the form factors at both the maximum and minimum recoil points with previous theoretical studies, finding good agreement. We observe that the form factors depend on the transferred momentum $q^2$ and their magnitude gradually increases with increasing $q^2$. The dominant form factors are $f_1$ and $g_1$, and they also exhibit similar $q^2$ dependencies. Additionally, we calculate the lepton flavour universality (LFU) ratio $R(\Xi_c) \approx 0.3$, which is in agreement with existing theoretical predictions.