Is Dark Matter the origin of the $B\to K ν\barν$ excess at Belle II?

TL;DR

This work investigates whether dark matter can account for the Belle II excess in B^+ → K^+ + invisible by proposing two mediator-based scenarios. An axion-like particle (ALP) portal achieves the signal via B^+ → K^+ a with m_a ≈ 2 GeV, followed by a → χχ, with χ as a light DM candidate produced through freeze-in; the mechanism yields the observed relic density for MeV-scale DM and ultra-weak couplings, while evading current direct/indirect searches. A dark photon portal explains the excess through B^+ → K^+ X, with X decaying invisibly to a Majorana DM ψ and freeze-out setting the relic abundance via ψψ → φφ, subject to BBN and flavor-constraint bounds; this scenario tends to be viable at 2σ, with distinct predictions for DM mass, mediator lifetimes, and future measurements. Overall, both models illustrate how light DM with GeV-scale mediators can reconcile the Belle II anomaly with cosmological DM, yielding complementary experimental consequences for Belle II, LHCb, NA62, and future direct-detection probes.

Abstract

We present two models of dark matter (DM) that can provide a natural explanation of the excess of $B^+\to K^+ +\,\text{invisible}$ events with respect to the Standard Model (SM) prediction for $B^+\to K^+ ν\barν$, which has been reported by the Belle II collaboration. Interactions between the dark and the visible sector are mediated by an axion-like particle (ALP) in one case, by the kinetic mixing between a dark photon and the SM photon in the second case. Both models encompass a light fermion singlet as the DM candidate and can account for the observed DM relic abundance through, respectively, the freeze-in and the freeze-out production mechanism, while simultaneously explaining the Belle II excess.

Figures (4)

• Figure 1: Illustration of the parameter space of the ALP model that is able to explain the observed Belle II excess in $B\to K+ \mathrm{inv}$ at the $1\sigma$ (dark red band) and $2\sigma$ level (light red band) for $m_a = 2~\mathrm{GeV}$. The gray region is excluded at $95\%$ CL by searches for $B\to K^{*} + {\rm inv}$. See the main text for details.
• Figure 2: Left: The shaded area shows the region where $b$ decays (purple) or scattering processes (orange) keep a 2 GeV ALP in equilibrium with the thermal bath. The gray region shows the region where the number density of $b$-quarks is too suppressed to keep the ALP in thermal equilibrium. The dashed blue line indicates the central value of the axion coupling $C_q/f_a$ required to explain the excess observed by Belle II in $B^+\to K^+ +\mathrm{inv}$. Right: Evolution of different particle yields as a function of $x = m_b/T$ for universal ALP couplings $C_{q}/f_a = C_{\chi\chi}^A/f_a = 6\times 10^{-9}~\rm{GeV}^{-1}$, and ALP mass of $m_a = 2~\mathrm{GeV}$ and DM mass of $m_\chi = 3~\mathrm{MeV}$ and a vanishing UV coupling to gluons $C_G^\text{UV}=0$. The dot-dashed cyan curve represents the ALP yield while the solid purple curve shows the dark matter yield. The dashed orange curve shows the equilibrium yield of the $b$ quark.
• Figure 3: Contours of the DM mass $m_\chi$ corresponding to the observed relic abundance $\Omega_\chi h^2 = 0.12$ on the ($C^{V,A}_{bs}/f_a = C_{qq}^A/f_a \equiv C_q/f_a$, $C^A_{\chi\chi}/f_a$) plane. The $1\sigma$ ($2\sigma$) range of $C_q/f_a$ preferred by $B^+\to K^++{\rm inv}$ data is shown as a dark (light) red band. In the upper gray region, a DM abundance not exceeding the observed amount can only be obtained for values of the DM mass $m_\chi \lesssim 15~\mathrm{keV}$, which are in conflict with structure formation bounds on warm DM (WDM) Ballesteros:2020adhDEramo:2020gprDecant:2021mhj. In the lower region DM production through the decay $a\to \chi\bar{\chi}$ is kinematically forbidden.
• Figure 4: Dark photon parameter space for $m_{\rm DM}=0.1~\mathrm{GeV}$ (left) and $m_{\rm DM}=0.8~\mathrm{GeV}$ (right). The yellow and gray regions are excluded by searches for $B^+\to K^+\mu\bar{\mu}$LHCb:2014cxeDatta:2022zng and $B^0\to K^{*0} +\mathrm{inv}$Belle:2017oht, respectively. The kinetic mixing has been fixed at the maximum allowed value of $\varepsilon =8.3\times 10^{-4}$BaBar:2017tiz. Smaller values weaken the LHCb constraint. The Belle II $B^+\to K^++\mathrm{inv}$ excess is accounted for at the $1\sigma$ and $2\sigma$ level in the red regions. The blue bands show the region of parameter space where the DM relic abundance is explained by the Majorana singlet $\psi$. The solid blue line corresponds to a dark Higgs with mass $m_\varphi=4~\mathrm{MeV}$ and the blue shaded region displays the range $m_{\varphi} \in [4\,\mathrm{MeV},0.99\,m_{\rm DM}]$.