$B^+\to K^+ \nu \bar{\nu}$ Excess and DM semi-annihilation

TL;DR

This paper proposes a scalar dark matter model with local discrete symmetry to explain the observed excess in the $B^+ o K^+ u ar{ u}$ decay rate reported by Belle II, aligning with relic abundance constraints.

Contribution

It introduces a novel dark matter model with local $Z_3$ symmetry derived from $U(1)_{L_ - L_ au}$, explaining the decay excess and relic abundance simultaneously.

Findings

The model accounts for the $2.8\sigma$ excess in $B^+ \to K^+ \nu \bar{\nu}$ decay.

Dark Higgs mass of 2 GeV successfully explains the decay excess.

The model is consistent with dark matter relic abundance constraints.

Abstract

In 2023, Belle II collaboration announced the observarion of the $B^+ \to K^+ \nu\bar{\nu}$ decay channel for the first time. This decay channel provides a clean signal with high precision in theoretical calculation. However, we encounter $2.8\sigma$ 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 $U(1)_X \equiv U(1)_{L_\mu - L_\tau}$ symmetry, this $U(1)_{L_\mu - L_\tau}$ 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 ${\rm Br} (B^+ \to K^+ \nu\bar{\nu})$ excess reported from Belle II collaboration and relic abundance at the same time.