Semileptonic and nonleptonic weak decays of bottom baryons $Ω^{(*)}_{b}$

TL;DR

The paper develops a three-point QCD sum rule framework to study semileptonic and nonleptonic weak decays of bottom baryons $\Omega_b$ and $\Omega_b^{*}$, focusing on $\Omega_b^{*}\to\Omega_c$ and $\Omega_b\to\Omega_c^{*}$ transitions. By performing an operator product expansion up to dimension six and employing double Borel transforms, the authors extract the full set of transition form factors $F_i(q^2)$ and $G_i(q^2)$ and fit them over the entire physical $q^2$ range. These form factors feed the calculation of helicity amplitudes to obtain semileptonic decay widths across $e$, $\mu$, and $\tau$ channels and, under factorization, nonleptonic two-body widths for emissions of pseudoscalar and vector mesons. The results include branching ratios and ratios of leptonic channels, providing SM-consistent predictions and a rich set of benchmarks for future experimental tests and potential probes of new physics in heavy-baryon decays.

Abstract

We present an investigation into the semileptonic and nonleptonic weak decays of bottom baryons $Ω^{*}_{b}$ and $Ω_{b}$ within the framework of three-point QCD sum rules. In the semileptonic sector, the $Ω^{*}_b\rightarrowΩ_c\ell\barν_{\ell}$ and $Ω_b\rightarrowΩ^*_c\ell\barν_{\ell}$ transitions are specifically considered. Utilizing the operator product expansion up to dimension six, the responsible form factors of these decays are obtained. The acquired form factors enable us to determine the decay widths in three leptonic channels. Branching ratios related to the $Ω_{b}$ baryon semileptonic decays are also presented. These invariant form factors are subsequently employed as inputs to determine the nonleptonic weak decay widths in various modes with emitting a pseudoscalar or vector meson. An extensive investigation into all possible decay channels of bottom baryons provides valuable information for future experiments to examine the SM predictions, explores the new physics effects in heavy baryonic decays, and advances the understanding of the internal structure of heavy baryons.

Figures (5)

• Figure 1: Behavior of the form factors in relation to the Borel parameter $M^2$ for different values of the parameter $s_0$, $q^{2}=0$, and the central values of the other helping parameters. The graphs are associated with the structures $g_{\mu\nu}\slashed{p}^{\prime}\gamma_5, p^{\prime}_{\nu}\gamma_{\mu}\slashed{p}\slashed{p}^{\prime}\gamma_{5}, p_{\mu}p^{\prime}_{\nu}\slashed{p}^{\prime}\gamma_{5}, p^{\prime}_{\mu}p^{\prime}_{\nu}\slashed{p}\slashed{p}^{\prime}\gamma_{5}, g_{\mu\nu}\slashed{p}, p^{\prime}_{\nu}\gamma_{\mu}\slashed{p}^{\prime}, p_{\mu}p^{\prime}_{\nu}\slashed{p},$ and $p^{\prime}_{\mu}p^{\prime}_{\nu}\slashed{p}\slashed{p}^{\prime}$ matching to the form factors $F_{1}, F_{2}, F_{3}, F_{4}, G_{1}, G_{2}, G_{3}$, and $G_{4}$, respectively, of the $\Omega_{b}^{*}\rightarrow \Omega_{c}\ell\bar{\nu}_{\ell}$ transition, (see Table \ref{['fitparameters1']}).
• Figure 2: Behavior of the form factors in relation to the Borel parameter $M^2$ for different values of the parameter $s'_0$, $q^{2}=0$, and the central values of the other helping parameters. The graphs are associated with the structures $g_{\mu\nu}\slashed{p}^{\prime}\gamma_5, p^{\prime}_{\nu}\gamma_{\mu}\slashed{p}\slashed{p}^{\prime}\gamma_{5}, p_{\mu}p^{\prime}_{\nu}\slashed{p}^{\prime}\gamma_{5}, p^{\prime}_{\mu}p^{\prime}_{\nu}\slashed{p}\slashed{p}^{\prime}\gamma_{5}, g_{\mu\nu}\slashed{p}, p^{\prime}_{\nu}\gamma_{\mu}\slashed{p}^{\prime}, p_{\mu}p^{\prime}_{\nu}\slashed{p},$ and $p^{\prime}_{\mu}p^{\prime}_{\nu}\slashed{p}\slashed{p}^{\prime}$ matching to the form factors $F_{1}, F_{2}, F_{3}, F_{4}, G_{1}, G_{2}, G_{3}$, and $G_{4}$, respectively, of the $\Omega_{b}^{*}\rightarrow \Omega_{c}\ell\bar{\nu}_{\ell}$ transition, (see Table \ref{['fitparameters1']}).
• Figure 3: Behavior of the form factors in relation to the Borel parameter $M'^2$ for different values of the parameter $s_0$, $q^{2}=0$, and the central values of the other helping parameters. The graphs are associated with the structures $g_{\mu\nu}\slashed{p}^{\prime}\gamma_5, p^{\prime}_{\nu}\gamma_{\mu}\slashed{p}\slashed{p}^{\prime}\gamma_{5}, p_{\mu}p^{\prime}_{\nu}\slashed{p}^{\prime}\gamma_{5}, p^{\prime}_{\mu}p^{\prime}_{\nu}\slashed{p}\slashed{p}^{\prime}\gamma_{5}, g_{\mu\nu}\slashed{p}, p^{\prime}_{\nu}\gamma_{\mu}\slashed{p}^{\prime}, p_{\mu}p^{\prime}_{\nu}\slashed{p},$ and $p^{\prime}_{\mu}p^{\prime}_{\nu}\slashed{p}\slashed{p}^{\prime}$ matching to the form factors $F_{1}, F_{2}, F_{3}, F_{4}, G_{1}, G_{2}, G_{3}$, and $G_{4}$, respectively, of the $\Omega_{b}^{*}\rightarrow \Omega_{c}\ell\bar{\nu}_{\ell}$ transition, (see Table \ref{['fitparameters1']}) .
• Figure 4: Behavior of the form factors in relation to the Borel parameter $M'^2$ for different values of the parameter $s'_0$, $q^{2}=0$, and the central values of the other helping parameters. The graphs are associated with the structures $g_{\mu\nu}\slashed{p}^{\prime}\gamma_5, p^{\prime}_{\nu}\gamma_{\mu}\slashed{p}\slashed{p}^{\prime}\gamma_{5}, p_{\mu}p^{\prime}_{\nu}\slashed{p}^{\prime}\gamma_{5}, p^{\prime}_{\mu}p^{\prime}_{\nu}\slashed{p}\slashed{p}^{\prime}\gamma_{5}, g_{\mu\nu}\slashed{p}, p^{\prime}_{\nu}\gamma_{\mu}\slashed{p}^{\prime}, p_{\mu}p^{\prime}_{\nu}\slashed{p},$ and $p^{\prime}_{\mu}p^{\prime}_{\nu}\slashed{p}\slashed{p}^{\prime}$ matching to the form factors $F_{1}, F_{2}, F_{3}, F_{4}, G_{1}, G_{2}, G_{3}$, and $G_{4}$, respectively of the $\Omega_{b}^{*}\rightarrow \Omega_{c}\ell\bar{\nu}_{\ell}$ transition, (see Table \ref{['fitparameters1']}).
• Figure 5: Behavior of the form factors $F_{1}, F_{2}, F_{3}, F_{4}, G_{1}, G_{2}, G_{3}$, and $G_{4}$ of the $\Omega_{b}^{*}\rightarrow \Omega_{c}\ell\bar{\nu}_{\ell}$ transition, in relation to $q^2$ for central values of the helping parameters, considering the error bands, presented in Table \ref{['fitparameters1']}.