Implication of $R_{D^{(*)}}$ anomalies on semileptonic decays of ${\mathrm{\Sigma }}_b$ and ${\mathrm{\Omega }}_b$ baryons

The flavor changing decays of heavy bottom quarks to the corresponding lighter quarks ($u$, $c$, and $s$) in various $B$-meson decays via charged current and neutral current semileptonic transitions have emerged as promising candidates to explore physics beyond the standard model. Experimentally the lepton flavor universality violation in $b\to (c,u)l\nu$ and $b\to s{l}^{+}{l}^{-}$ transitions have been reported to a higher precision. The measurements of the lepton flavor violating ratios such as $R_{D^{(*)}}$, $R_{J/\mathrm{\Psi }}$, and $R_{K^{(*)}}$ are observed to deviate from the standard model expectations at the level of $1.4\sigma$, $2.5\sigma$, $1.5\sigma$, $2.4\sigma$, and $2.2\sigma$ respectively. Motivated by these anomalies, we investigate the lepton flavor universality violation in ${\mathrm{\Sigma }}_b\to {\mathrm{\Sigma }}_{c}l\nu$ and ${\mathrm{\Omega }}_b\to {\mathrm{\Omega }}_{c}l\nu$ decays. We follow a model independent effective field theory formalism and study the implications of $R_{D^{(*)}}$ anomalies on ${\mathrm{\Sigma }}_b\to {\mathrm{\Sigma }}_c\tau \nu$ and ${\mathrm{\Omega }}_b\to {\mathrm{\Omega }}_c\tau \nu$ decay modes. We give predictions of various physical observables such as the ratio of branching ratios, total differential decay rate, forward-backward asymmetry, lepton side polarization fraction, and convexity parameter within the standard model and within various new physics scenarios.

Figure 1

Tree level Feynman diagram representing the transitions of ${\mathrm{\Sigma }}_b^{-}(ddb)\to {\mathrm{\Sigma }}_c^0(ddc)l^{-}{\overline{\nu }}_l$ and ${\mathrm{\Omega }}_b^{-}(ssb)\to {\mathrm{\Omega }}_c^0(ssc)l^{-}{\overline{\nu }}_l$.

Figure 2

${\mathrm{\Sigma }}_b\to {\mathrm{\Sigma }}_c$ (left) and ${\mathrm{\Omega }}_b\to {\mathrm{\Omega }}_c$ (right) transition form factors as a function of $q^2$.

Figure 3

Ratio of branching ratio $R_{{\mathrm{\Sigma }}_c}(q^2)$, the total differential decay rate $d\mathrm{\Gamma }/d{q}^2$, the lepton polarization fraction $P^l(q^2)$, the forward-backward asymmetry $A_{FB}^l(q^2)$, and the convexity parameter $C_F^l(q^2)$ for the ${\mathrm{\Sigma }}_b\to {\mathrm{\Sigma }}_{c}l\nu$ decays in the SM. The purple color represents the $e$ mode and the green color represents the $\tau$ mode.

Figure 4

Ratio of branching ratio $R_{{\mathrm{\Omega }}_c}(q^2)$, the total differential decay rate $d\mathrm{\Gamma }/d{q}^2$, the lepton polarization fraction $P^l(q^2)$, the forward-backward asymmetry $A_{FB}^l(q^2)$, and the convexity parameter $C_F^l(q^2)$ as a function of $q^2$ for the ${\mathrm{\Omega }}_b\to {\mathrm{\Omega }}_{c}l\nu$ decays in the SM. Purple represents the $e$ mode and green represents the $\tau$ mode.

Figure 5

The $q^2$ dependency of the ratio of branching ratio $R_{{\mathrm{\Sigma }}_c}(q^2)$, the total differential decay rate $d\mathrm{\Gamma }/d{q}^2$, the lepton polarization fraction $P^{\tau }(q^2)$, the forward-backward asymmetry $A_{FB}^{\tau }(q^2)$, and the convexity factor $C_F^{\tau }(q^2)$ in SM (red) and in the presence of $V_L$ (purple), $V_R$ (green), $S_L$ (black), and $S_R$ (pink) NP couplings for the ${\mathrm{\Sigma }}_b\to {\mathrm{\Sigma }}_c\tau \nu$ decay mode.

Figure 6

The $q^2$ dependency of the ratio of branching ratio $R_{{\mathrm{\Omega }}_c}(q^2)$, the total differential decay rate $d\mathrm{\Gamma }/d{q}^2$, the lepton polarization fraction $P^{\tau }(q^2)$, the forward-backward asymmetry $A_{FB}^{\tau }(q^2)$, and the convexity factor $C_F^{\tau }(q^2)$ in SM (red) and in the presence of $V_L$ (purple), $V_R$ (green), $S_L$ (black), and $S_R$ (pink) NP couplings for the ${\mathrm{\Omega }}_b\to {\mathrm{\Omega }}_c\tau \nu$ decay mode.

Figure 7

The allowed regions of $V_L$, $V_R$, $S_L$, and $S_R$ NP couplings once the $3\sigma$ constraint coming from the measured values of the ratio of branching ratios $R_D$ and $R_{D^{*}}$ are applied. Red represents $R_D$ and purple represents $R_{D^{*}}$. The $3\sigma$ range for $R_D$ is [0.2503, 0.4297] and $R_{D^{*}}$ is [0.2542, 0.3358].

Figure 8

The $q^2$ dependency of various observables such as the ratio of branching ratio $R_{{\mathrm{\Sigma }}_c}(q^2)$, the total differential decay rate $d\mathrm{\Gamma }/d{q}^2$, the tau polarization fraction $P^{\tau }(q^2)$, the forward-backward asymmetry $A_{FB}^{\tau }(q^2)$, and the convexity parameter $C_F^{\tau }(q^2)$ for the ${\mathrm{\Sigma }}_b\to {\mathrm{\Sigma }}_c\tau \nu$ decay mode in the presence of $V_L$ (first column), $V_R$ (second column), $S_L$ (third column), and $S_R$ (fourth column). NP couplings are shown with the purple band, whereas the SM prediction is shown with the red band. The red solid line represents the SM prediction with the central values of each input parameter and the purple solid line represents the prediction once the best fit values of the NP couplings are used.

Figure 9

The $q^2$ dependency of various observables such as the ratio of branching ratio $R_{{\mathrm{\Sigma }}_c}(q^2)$, the total differential decay rate $d\mathrm{\Gamma }/d{q}^2$, the tau polarization fraction $P^{\tau }(q^2)$, the forward-backward asymmetry $A_{FB}^{\tau }(q^2)$, and the convexity parameter $C_F^{\tau }(q^2)$ for the ${\mathrm{\Omega }}_b\to {\mathrm{\Omega }}_c\tau \nu$ decay mode in the presence of $V_L$ (first column), $V_R$ (second column), $S_L$ (third column), and $S_R$ (fourth column). NP couplings are shown with the purple band, whereas the SM prediction is shown with the red band. The red solid line represents the SM prediction with the central values of each input parameter and the purple solid line represents the prediction once the best fit values of the NP couplings are used.