$b \to c$ semileptonic sum rule: exploring a sterile neutrino loophole

Abstract

We investigate the $b\to c$ semileptonic sum rule in the presence of a massive sterile neutrino. Recent measurements of charged-current semitauonic $B$-meson decays exhibit a $\sim4σ$ deviation from the Standard Model predictions, whereas no such tension has been reported for the lowest-lying baryonic counterpart, the $Λ_b$ decay. Since these decay rates are related through the sum rule, accommodating such a mismatch beyond the level of uncertainties is nontrivial. We revisit this issue by introducing new interactions involving a sterile neutrino. As the differential decay rates are modified by these new contributions, we evaluate the violation of the sum rule in the presence of a massive sterile neutrino. We find that the induced effect remains small compared with the current experimental uncertainties. Therefore, the sum rule provides a useful consistency check for the experimental data.

Figures (5)

• Figure 1: The $m_{N_R}$ dependence of the NP coefficients in $\Delta_{H_c,\,ij}^{N_R}$ defined in Eq. \ref{['eq:deltaNR']}. The left, middle, and right panels show $\Delta_{D,\,ij}^{N_R}$, $\Delta_{D^*,\,ij}^{N_R}$ and $\Delta_{\Lambda_c,\,ij}^{N_R}$, respectively. Different colors correspond to the different operator combinations, as indicated in the legend of the left panel. In the left panel, the $V'_RS'_R$ curve coincides with $V'_RS'_L$, and $V'_RV'_R$ lies close to $S'S'$. In the middle and right panels, the scalar curves are degenerate.
• Figure 2: The sum rule violation coefficients $\delta^{N_R}_{ij}$ in Eq. \ref{['eq:RSRHQw2']}. Different colors correspond to different operator combinations, as indicated in the legend of the left panel of Fig. \ref{['fig:delta_X_ij']}. Several curves overlap in the left panel, and the right panel shows a magnified view.
• Figure 3: $\delta^{N_R}$ and $\Delta_{H_c}^{N_R}$ in single operator scenarios as functions of the WCs. The sterile neutrino mass is fixed to $m_{N_R}=0.8$ GeV. The boundaries of the horizontal axis correspond to the maximally allowed values of the WCs under the relaxed LHC constraint.
• Figure 4: $\delta^{N_R}$ and $\Delta_{H_c}^{N_R}$ as functions of $C_{T^\prime}$ in the scenario in which both $C_{V_R^\prime}$ and $C_{T^\prime}$ are non-vanishing, while $C_{S_L^\prime}=C_{S_R^\prime}=0$. The boundaries of the horizontal axis correspond to the maximally allowed values under the relaxed LHC constraint.
• Figure 5: Normalized differential distributions for $B\to D\tau \bar{X}$, $B\to D^* \tau\bar{X}$ and $\Lambda_b\to\Lambda_c\tau \bar{X}$ (from left to right), where $X=\nu$ or $N_R$. The normalization is chosen such that the peak of the SM distribution is unity.