Resonant ALP-Portal Dark Matter Annihilation as a Solution to the $B^{\pm} \to K^{\pm} ν\barν$ Excess

TL;DR

The paper demonstrates that an axion-like particle (ALP) portal to dark matter can simultaneously address the Belle II $B^all(K^all u\bar{\nu})$ excess and the DM relic density via resonant annihilation with $m_a \sim 2 m_\chi$. It shows that the displaced-diphoton ALP scenario is excluded by flavor and beam-dump constraints, while the missing-energy channel—where $a$ decays invisibly to $\chi\bar{\chi}$—remains viable for $m_a$ in the $0.6$–$4.8$ GeV range and couplings $g_{aWW}$ and $g_{a\chi\chi}$ in the specified bands. A central methodological advance is the use of coupled Boltzmann equations that incorporate early kinetic decoupling, revealing up to a factor of about 20 difference in the predicted relic density in the resonance region compared with conventional treatments. The results define a testable parameter space that can be probed by Belle II and future experiments, linking collider anomalies to the thermal history of DM through precision resonance dynamics.

Abstract

The Belle II collaboration recently reported a $2.7σ$ excess in the rare decay $B^\pm \to K^\pm ν\barν$, potentially signaling new physics. We propose an axion-like particle (ALP)-portal dark matter (DM) framework to explain this anomaly while satisfying the observed DM relic abundance. By invoking a resonant annihilation mechanism ($m_a \sim 2m_χ$), we demonstrate that the ALP-mediated interactions between the Standard Model and DM sectors simultaneously account for the $B^\pm \to K^\pm ν\barν$ anomaly and thermal freeze-out dynamics. Two distinct scenarios-long-lived ALPs decaying outside detectors (displaced diphotons) and ALPs decaying invisibly to DM pairs (missing energy)-are examined. While the displaced diphotons scenario is excluded by kaon decay bounds ($K^\pm \to π^\pm + \text{inv.}$), the invisible decay channel remains unconstrained and aligns with Belle II's missing energy signature. Using the coupled Boltzmann equation formalism, we rigorously incorporate early kinetic decoupling effects, revealing deviations up to a factor of 20 from traditional relic density predictions in resonance regions. For the missing energy scenario, the viable parameter space features ALP-SM and ALP-DM couplings: $g_{aWW}(g_{aγγ}) \in (7.13 \times 10^{-5} - 9.60 \times 10^{-5})\, \text{GeV}^{-1}$ (from $B^\pm \to K^\pm a$) and $g_{aχχ} \in (7.12\times10^{-5} - 7.73\times 10^{-3})\, \text{GeV}^{-1}$ (for resonant annihilation), accommodating ALP masses $m_a \in (0.6, 4.8)\, \text{GeV}$. Therefore, this work establishes the ALP portal as a viable bridge between the $B^\pm \to K^\pm ν\barν$ anomaly and thermal DM production, emphasizing precision calculations of thermal decoupling in resonance regimes.

Figures (7)

• Figure 1: Branching ratios for two ALP decay channels, $a \to \gamma\gamma$ and $a \to \chi\bar{\chi}$. Here we take $m_a=1$ GeV, $m_\chi=0.475 m_a$, $g_{a\gamma\gamma}= 10^{-4}$ GeV$^{-1}$ as a benchmark point and vary the value of $g_{a\chi\chi}$.
• Figure 2: The required value of the coupling $g_{a\gamma\gamma}$ to achieve the correct relic density is shown in the figure. The red dashed line represents the results using the NBE method, which relies on the assumption of kinetic equilibrium throughout the entire freeze-out epoch. The blue line corresponds to the results derived from the CBE method. For illustration, we adopt $m_a=1~\rm GeV$ and $g_{a\chi\chi}=10^{-2}~\rm GeV^{-1}$.
• Figure 3: The relic density ratio between CBE and NBE methods, where we require the parameters to match the observed abundance in the NBE approach, i.e. $\Omega_{\rm NBE} h^2=0.12$. Here we set $m_a=1$ GeV.
• Figure 4: The evolution of the DM 'temperature' $y_{\chi}$ with respective to $x=m_{\chi}/T$. The gray line represents the temperature of the thermal bath. The blue, orange, and green curves correspond to $r\equiv m_{\chi}/m_a=0.45,~0.49$, and $0.5$, respectively. Here we take $m_a=1 \rm GeV$ for illustration.
• Figure 5: The evolution of DM abundance $Y_\chi$ with respect to $x=m_{\chi}/T$. Left panel: The blue line depicts the DM yields in the CBE approach, with benchmark parameters labeled in the plot. The gray dashed line represents the NBE approach. Right panel: The red line shows the DM yields in the CBE approach for a different set of benchmark parameters. The gray dashed line corresponds to the yield in the NBE approach. We observe significantly different evolutionary trajectories for varying mass ratios $r\equiv m_{\chi}/m_a$.