Revisiting models that enhance $B^{+}\to K^{+}\nu \overline{\nu }$ in light of the new Belle II measurement

Belle II recently reported the new measurement $\mathcal{B}(B^{+}\to K^{+}\nu \overline{\nu })=(2.3\pm 0.7)\times {10}^{-5}$ [I. Adachi et al. (Belle-II Collaboration), arXiv:2311.14647] which is two times larger than their previous result (although consistent within errors) and about $2.7\sigma$ higher than the SM prediction. We reexamine new physics scenarios we discussed previously, which can enhance this rate to determine if they can accommodate the higher value reported in the new measurement. We use consistency with existing bounds on $B\to K^{*}\nu \overline{\nu }$, $b\to s{\ell }^{+}{\ell }^{-}$, $B\to D^{(*)}\ell \overline{\nu }$, and $B_s$ mixing to limit possible explanations for the excess. For the case of lepton flavor violating neutrino couplings, we find that only two leptoquarks remain viable requiring a large $C_{9^{\prime }}^{\tau \tau }=-C_{{10}^{\prime }}^{\tau \tau }$. For models with different types of light dark matter particle pairs (scalar, fermion, or vector), the preliminary $q^2$ distribution from Belle II, which shows that the excess appears mostly for bins with $3\le q^2\le 7{\mathrm{GeV}}^2$ [I. Adachi et al. (Belle-II Collaboration), arXiv:2311.14647], implies only the vector current operators with scalar or vector dark matter particles with masses in the hundreds of MeV can match the anomaly.

Figure 1

The correlation between $R_K^{\nu \nu }$ and $R_{K^{*}}^{\nu \nu }$ scanning the 12 parameters $C_L^{ij},C_R^{ij}$ is shown in the left panel as the shaded light gray region. The corresponding 12 parameter scan in $C_L^{\prime ij},C_R^{\prime ij}$ is shown as the shaded dark gray region. The figure highlights in green the $3\sigma$ SM prediction. The right panel shows the corresponding scan including only the six parameters $C_R^{ij}$. The points highlighted in blue or red fall within the new $1\sigma$ range of $R_K^{\nu \nu }$ (also marked by the vertical solid black lines). Additionally, the blue (red) points satisfy $R_{K^{*}}^{\nu \nu }\le 2.7(1.9)$, respectively (values marked by the horizontal dashed red lines). The diagonal black line marks $R_K=R_{K^{*}}$.

Figure 2

Left panel: Scan of parameters $C_R^{ij}$ where the only nonzero diagonal term is $C_R^{\tau \tau }$ with the same color code as in Fig. 1. Center panel: A selected slice of a projection in parameter space illustrating the location of the red and blue clusters in the six-parameter space of $C_R^{ij}$. As this figure suggests, these clusters concentrate in regions where at least one of the diagonal entries $|C_R^{ii}|$ is near 10. Right panel: Parameter region allowed when only $C_R^{\tau \tau }$ and $C_R^{\mu \tau }$ are nonzero, we have added in this panel the hashed regions showing the corresponding solutions when the average value of $R_K^{\nu \nu }$ is used.

Figure 3

Mapping of the parameter space selected in Fig. 2 into predictions for other $B$ meson decay modes. The solid black line for the lepton flavor conserving processes marks the SM prediction.

Figure 4

The pink [purple] region is the parameter space that could explain the recent Belle II excess [new average] with scalar DM for scalar (vector) quark current operators ${\mathcal{O}}_{q\varphi }^{S,sb}({\mathcal{O}}_{q\varphi }^{V,sb})$. The gray region is excluded by other $B$ meson decay modes that are indicated in the plots by color lines.

Figure 5

The pink [purple] region shows the parameter space that could explain the recent Belle II excess [new average] with fermion DM for the operators in Eq. (19). The gray region is excluded by other $B$ meson decay modes that are indicated in the plots by colored lines.

Figure 6

The pink (purple) region shows the parameter space that could explain the recent Belle II excess (new average) with vector DM for the operators in Eq. (20). The gray region is excluded by other $B$ meson decay modes that are indicated in the plots by colored lines.

Figure 7

The $q^2$ distribution of normalized differential decay widths from all three cases: scalar DM (left panel), fermion DM (middle panel), vector DM (right panel) for selected masses.

Figure 8

The $q^2$ distribution of normalized differential decay widths after taking into account the experimental efficiency. The left panel for scalar DM and right panel for fermion DM.