Dark light shining on $B\to K^{(*)} E_{\rm miss}$

TL;DR

The paper addresses the Belle II excess in $B^+ \to K^+ E_{\rm miss}$ by constructing a UV-complete Higgsed $U(1)'$ model with a light $Z'$ and a vector-like top partner to generate $b \to s Z'$. The minimal model is ruled out by LHCb due to $Z' \to \mu^+\mu^-$, motivating a minimal extension that introduces a light SM-singlet fermion $\psi$ so that $Z'$ decays dominantly invisibly and can also serve as a DM candidate. The analysis connects flavor observables, collider searches, electroweak precision data, Higgs measurements, and DM phenomenology, identifying a resonant $\psi$ window around $m_\psi \sim 0.9$–$1.0$ GeV where the relic abundance matches Planck while satisfying current constraints. The framework offers a tightly constrained, testable link between a missing-energy signature in rare $B$ decays and a broader dark sector, with implications for future Belle II, LHCb, and DM experiments.

Abstract

Recent Belle II data on $B^+ \to K^+ E_{\rm miss}$ show an excess consistent with a two-body decay involving a light invisible particle with mass around $2.1\,\mathrm{GeV}$. We present a UV-complete explanation based on a Higgsed $U(1)'$ gauge symmetry with a light vector boson $Z'$ and a vector-like top partner, which naturally enhances $b \to s$ transitions. While the minimal model can reproduce the required $B \to K^{(*)} Z'$ rate, it is excluded by LHCb searches for resonant dimuon decays due to unavoidable loop-induced couplings of $Z'$ to charged leptons. We show that a minimal extension with an additional light $U(1)'$-charged singlet fermion allows $Z'$ to decay dominantly invisibly, evades existing constraints coming also from dark photon and collider searches as well as Higgs measurements, and can simultaneously account for the Belle II excess and the observed dark matter abundance through resonant thermal freeze-out.

Figures (12)

• Figure 1: One-loop contributions of $t/T$ to the kinetic and mass mixing between $Z'$ and $\gamma/Z$.
• Figure 2: Two-body decay contributing to $B^+ \to K^{+}E_{\text{miss}}$, with a single light $Z'$ in the final state.
• Figure 3: (Left and centre) One-loop induced decays of the light $Z'$ in the minimal model. (Right) Tree-level decay of $Z'$ to a vector-like dark fermion $\psi$, considered in Sec. \ref{['sec:minimal_DM']}.
• Figure 4: Favoured branching fractions for $B^+\to K^+Z'$ and $B^0\to K^{*0}Z'$ from the Belle II Belle-II:2023esi and BaBar BaBar:2013npw data, as a function of the ratio $|C_{bs}^{V}/C_{bs}^{T}|$ for $M_{Z'} = 2.1$ GeV. Solid (dashed) lines show positive (negative) values of $C_{bs}^{V}/C_{bs}^{T}$.
• Figure 5: (Above) Branching fractions of $Z'$ in the minimal model accommodating the Belle II measurement in Eq. \ref{['eq:BelleII_constraint']} as a function of $m_T$, for $y_T^t = 1$. Solid (faint dashed) lines are shown for $\epsilon_{B}(\Lambda) = 0$ ($10^{-4}$). Also shown are $y_t$ perturbativity limits (vertical dashed lines) for both cases. (Below) Proper lifetime of $Z'$ as a function of $m_T$ for $\epsilon_{B}(\Lambda) = 0$ and different values of $y_T^t$. Envelopes of possible $c\tau_{Z'}$ values are shown for $\epsilon_{B}(\Lambda) = 0$ and $10^{-4}$.