$B^+\to K^+ ν\barν$ Excess and DM semi-annihilation

TL;DR

This work targets the Belle II B^+ → K^+ νν̄ excess by embedding a scalar DM sector into a dark U(1)_{L_μ-L_τ} that is spontaneously broken to a local Z3. The neutral DM X interacts via a light Z' mediator (m_{Z'} ~ 10 MeV) and a dark Higgs H1 (m_{H1} ~ 2 GeV), enabling DM semi-annihilation channels XX → X̄Z' and XX → X̄H1 to set the relic density while also generating a missing-energy signal in B decays through B^+ → K^+ H1 (or K^+ Z' Z' in three-body decays). With small mixing sinθ and modest g_X, the model can explain both the Belle II excess and the Planck relic abundance, while evading stringent CMB, direct-detection, and Higgs invisible-width constraints; potential IceCube and GC neutrino signals from semi-annihilation offer avenues for future tests. The viability of the Belle II region depends on Higgs invisible width limits, but portions of parameter space remain accessible to future e^+e^- colliders and neutrino observatories.

Abstract

In 2023, Belle II collaboration announced the observarion of the $B^+ \to K^+ ν\barν$ decay channel for the first time. This decay channel provides a clean signal with high precision in theoretical calculation. However, we encounter $2.8σ$ deviation from the Standard Model (SM) prediction. To resolve this excess, we study scalar dark matter (DM) model with local discrete $Z_3$ symmetry. Assuming dark $U(1)_X \equiv U(1)_{L_μ- L_τ}$ symmetry, this $U(1)_{L_μ- L_τ}$ symmetry is spontaneously broken into local discrete $Z_3$ by non-zero vacuum expectation value of dark Higgs boson. Considering dark Higgs mass is $2$GeV, we can explain the recent ${\rm Br} (B^+ \to K^+ ν\barν)$ excess reported from Belle II collaboration and relic abundance at the same time.

Figures (4)

• Figure 1: Feynman diagrams for dark matter semi-annihilation.
• Figure 2: The relic density in the $(m_X,\, \lambda_3)$ plane is shown. We fix $m_{Z'} = 10~\mathrm{MeV}$, $m_{H_1} = 2~\mathrm{GeV}$, and $\sin\theta = 3 \times 10^{-3}$ to account for the Belle II excess. The impact of varying $\sin\theta$ is negligible due to its small value. The red solid line corresponds to the observed dark matter relic density measured by Planck Planck:2018vyg. To the left (right) of the dashed vertical line, the relic abundance is dominantly determined by the process $XX \to \bar{X}Z'$ ($XX \to \bar{X}Z',\, \bar{X}H_1$), respectively.
• Figure 3: Allowed $(m_X,~g_X)$ space when $m_{Z'} = 10~\mathrm{MeV}$. The blue-shaded region is excluded by the DAMIC-M result DAMIC-M:2025luv, while the green area is ruled out by the bound $\Delta N_{\rm eff}$. The purple region is excluded by the NA64 NA64:2024klw. The light-cyan band is disfavored by the latest muon $(g-2)$ measurement at $\Delta a_\mu > 10^{-10}$. Finally, the gray-shaded area is constrained by the current dark matter direct detection limits.
• Figure 4: The regions allowed at the $1\sigma$ and $2\sigma$ CL by the Belle II excess correspond to the areas enclosed within the green (inner) and yellow (outer) shaded bands, respectively. We adopt $g_X = 10^{-4}$ for the left panel and $g_X = 10^{-5}$ for the right panel. The red-shaded region is excluded by the constraint from the invisible decay width of the SM Higgs boson ATLAS:2023tktCMS:2023sdw. For 3-body decay case, the preferred region is already ruled out by the Higgs invisible decay bound. However, the parameter space can be partially reopened when the couplings $\lambda_{X\Phi}$ and/or $\lambda_{H\Phi}$ are nonzero. The gray-shaded area denotes the parameter region excluded by $K^+ \to \pi^+ + {\rm inv.}$, $K^0_L \to \pi^0 \nu\bar{\nu}$, and $B^0 \to K^{*0} \nu\bar{\nu}$NA62:2021zjwKOTO:2020prkBelle:2017oht.