Semileptonic decay form factors of $Ξ_b^0 \rightarrow Ξ_c^+\ell\barν$ in HQET

TL;DR

The paper addresses the semileptonic decay of a singly heavy baryon, Ξ_b^0 → Ξ_c^+ ℓ ν, within HQET using a Hypercentral Constituent Quark Model to obtain ground-state wavefunctions and the Isgur–Wise function. HQET corrections up to order $1/m_Q$ are incorporated, yielding the six form factors $F_1,F_2,F_3,G_1,G_2,G_3$ (and corresponding $f_i,g_i$) that feed a helicity-based decay-rate calculation. The authors determine the Isgur–Wise slope and curvature from the wavefunctions, confirm the dominance of $F_1$ and $G_1$, and predict a LFU ratio $R_{Ξ_c} ≈ 0.325$ along with total widths and branching ratios that agree reasonably with other theoretical approaches. The work provides a coherent HCQM+HQET framework for heavy baryon semileptonic transitions and offers concrete predictions for upcoming measurements and lattice QCD studies.

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 $Ξ_b^0 \rightarrow Ξ_c^+\ell\barν$ (where $\ell = e$, $τ$) 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 $R(Ξ_c) \approx 0.3$, which is in agreement with existing theoretical predictions.

Figures (1)

• Figure 1: $q^2$ dependency of six-form factors (left) and the variation of differential decay rate for $\Xi_b^0 \rightarrow \Xi_c^+e\bar{\nu}_e$ (right).