Discriminating Tauphilic Leptoquark Explanations of the $B$ Anomalies via $K\to πν\barν$ and $B\to Kν\barν$

TL;DR

This work compares two tauphilic leptoquark explanations for the B-physics anomalies, focusing on neutrino-rich decays as discriminants. By analyzing the scalar S1+S3 and vector U1 models with tau-dominated couplings and TeV-scale masses, the authors map how neutrino final states constrain the parameter space while attempting to accommodate R(D) and b → s ll anomalies. A key result is that large effects in kaon decays to neutrinos are achievable in the S1+S3 scenario when alignment is slightly broken, whereas the U1 model tends to produce smaller neutrino-nu effects, predominantly at loop level. The study demonstrates that neutrino channels, together with kaon decays, provide a powerful avenue to distinguish between these tauphilic leptoquark explanations, with clear predictions testable at Belle II and NA62.

Abstract

Leptoquark models are prime candidates for new physics (NP) explanations of the long-standing anomalies in semi-leptonic $B$ decays; $b\to c τ\barν$ (encoded in $R(D^{(\ast)})$) and $b\to s\ell\bar\ell (\ell=e,μ)$ transitions. Furthermore, Belle II and NA62 reported weaker-than-expected limits on $B^+ \to K^+ ν\barν$ and $K^+ \to π^+ ν\barν$, respectively. While the $R(D^{(\ast)})$ and $b\to s\ell \bar\ell$ measurements can be explained with NP contributions at the $O(10\%)$ level, the neutrino channels suggest that the NP effect could be comparable in size to the Standard Model one. In this context, we consider the two types of leptoquark models with minimal sets of the couplings that can best describe the semi-leptonic $B$ anomalies and lead at the same time to effects in the neutrino modes, the singlet-triplet scalar leptoquark model ($S_1+S_3$) and the singlet vector leptoquark model ($U_1$). More specifically, the neutrino channels pose non-trivial constraints on the parameter space, and we find that large effects (i.e., accounting for the current central value) in $B\to K^{(*)}ν\barν$ are only possible in the $S_1+S_3$ setup, while both models can account for the central value of $K^+\to π^+ν\barν$.

Figures (3)

• Figure 1: The preferred and excluded region in the $\epsilon$--$\delta$ plane for $m_{S_1} = m_{S_3} = 2\,\text{TeV}$ and $\lambda^L =1, r = 0.2, \lambda^R_{23}= -0.5$ of the $S_1+S_3$ LQ model, such that entire shown plane can accommodate $R(D^{(\ast)})$ at the 1$\sigma$ level, i.e., $R(D)\approx 0.35$ and $R(D^\ast)\approx 0.28$. The blue and green contours represent $C_9^{\text{U}}$ and Br$(B\to K\tau\overline\tau)\times 10^{-5}$, respectively. The red region is preferred by $K^+\to \pi^+ \nu\overline\nu$ ($1\sigma$), the yellow region is the global fit to $K^+\to \pi^+ \nu\overline\nu$ and $\mu(B^+ \to K^{+} \nu\overline\nu)$. $B_s-\bar{B}_s$ and $B\to K^*\nu\overline\nu$ exclude the black and red hatched regions, respectively. Note that the NP effect in $B^-\to \tau \overline\nu$ is small with our CKM-like coupling structure.
• Figure 2: For the $U_1$ LQ model we take $m_{U_1} = 2\,\text{TeV}$ and $\kappa_L^{33}=1.5$. Then, the blue region can accommodate the $R(D^{(\ast)})$ (at 1$\sigma$, 2$\sigma$), while the red and green regions are consistent with $K^+ \to \pi^+ \nu \overline\nu$ and $B^- \to \tau\overline\nu$. The yellow area represents the global fit for these observables, including $B^+ \to K^+ \nu \overline\nu$. The contours are the predictions for $\mu(B^+ \to K^+ \nu\overline\nu)$, $C_9^{\text{U}}$, $\mathcal{B}(B \to \tau\overline\tau)$, and $\mathcal{B}(B \to K \tau\overline\tau)$ and the dashed lines show the Belle II sensitivity at $50\,\text{ab}^{-1}$ of data Belle-II:2018jsg.
• Figure 3: Preferred and excluded regions for the $S_1+S_3$ LQ model for the flavor structure given in Eq. \ref{['eq:S1S3_coupling_structure']}. We take a common mass $m_{S_1} = m_{S_3} = 2\,\text{TeV}$ and $\lambda^R_{23}= -0.5$. In the left panel, we assume the alignment limit $\epsilon=\delta=0$, while on the right panel, we take $\epsilon=0.2$ but keep $\delta=0$. The blue region can accommodate the $R(D^{(\ast)})$ anomaly at the 1, 2$\sigma$ levels, while the red and green regions are consistent with the data of $K^+ \to \pi^+ \nu \overline\nu$ and $B^- \to \tau\overline\nu$. The yellow region represents the global fit for these observables (including $B^+ \to K^+ \nu \overline\nu$). The blue contours are the predictions of $C_9^{\text{U}}$. The hatched region is excluded by the $B_s\!-\!\overline{ B}{}\xspace{}_s\,$ mixing bound at the $95\%$ CL, and the dashed lines represent the bound from the kaon mixing. Furthermore, the upper-right regions of the magenta lines are excluded by the high-$p_{\text{T}}$ search Allwicher:2022mcg.