Semileptonic decay and form factors of $Ω_b^- \rightarrow Ω_c^0\,e\,\bar{ν_e}$

TL;DR

This work studies the semileptonic decay $\Omega_b^- \rightarrow \Omega_c^0 e \bar{\nu}_e$ within the Hypercentral Constituent Quark Model (HCQM). The authors solve the six-dimensional hyperradial Schrödinger equation with a hyper-Coulomb plus linear potential, including spin-dependent perturbations, to obtain ground-state masses and the hyperradial wavefunctions. Using HQET up to subleading order, they compute the six form factors $F_i$ and $G_i$ (and their $f_i,g_i$ relations) from the Isgur-Wise function $\xi(\omega)$, with slope $\rho^2$ and curvature $c$ determined from the HCQM wavefunctions; subleading $1/m_Q$ corrections are incorporated via $B_1(\omega)$ and $B_2(\omega)$. Helicity amplitudes are then constructed, enabling the calculation of the differential and total semileptonic decay rate via the helicity formalism, yielding a predicted width $\Gamma = 4.01 \times 10^{10}\ \mathrm{s}^{-1}$ and branching ratio $\mathcal{B} = 6.57\%$, in reasonable agreement with several other theoretical approaches and providing a concrete testbed for HQET and three-body heavy-baryon dynamics in future experiments.

Abstract

We investigate the heavy-to-heavy semileptonic decay $Ω_b^- \rightarrow Ω_c^0\,e\,\bar{ν_e}$ within the framework of the Hypercentral Constituent Quark Model (HCQM). The ground state masses of the involved baryons are evaluated by numerically solving the six-dimensional hyperradial Schrödinger equation, incorporating both hyper-Coulomb and linear confinement potentials along with spin-dependent interactions. The Heavy Quark Effective Field Theory (HQET) form factors are computed up to the subleading order, incorporating $1/m_Q$ corrections that account for finite mass effects beyond the heavy quark symmetry limit. These form factors are then employed to analyse the heavy-to-heavy semileptonic decay rate via helicity formalism. Our results for the decay width and branching ratio are compared with those from various theoretical approaches.

Figures (2)

• Figure 1: The form factors $f_1$, $f_2$, $f_3$, $g_1$, $g_2$ and $g_3$ as a function of $q^2$.
• Figure 2: The semileptonic decay of the $\Omega_b^- \rightarrow \Omega_c^0\,e\,\bar{\nu_e}$ in $q^2$ kinetic region.