15 February 2024 / Accepted: 14 April 2024 / Published online: 4 May 2024 | Emidio Gabrielli, Luca Marzola, Kristjan Müürsepp, Martti Raidal
The Belle II collaboration has observed an excess in the branching ratio (BR) of the rare decay $B^+ \rightarrow K^+ \nu \bar{\nu}$, which deviates from the Standard Model (SM) prediction by 2.7σ. This paper explores the possibility that this excess is explained by long-distance interactions induced by a massless dark photon, $\gamma_D$. The dark photon couples to an invisible dark sector and to the Standard Model via higher-dimensional operators, such as the chromomagnetic-dipole coupling. The process $B^+ \rightarrow K^+ \gamma_D$ is forbidden by angular momentum conservation, leading to a three-body final state with a pair of dark fermions, which appear as missing energy in the detector. The authors show that the Belle II data can be explained for perturbative values of the model parameters. This scenario predicts new contributions to the neutral $B$ meson decays $B^0 \rightarrow K^+ \gamma_D$, where the emission of a on-shell dark photon is allowed, resulting in a monochromatic missing energy signature. Additionally, an excess due to the emission of a dark photon is predicted for the $B^0_s \rightarrow \phi + E_{\text{miss}}$ decay, which could be observed at the LHCb experiments. The paper also discusses the Sommerfeld-Fermi and dark magnetic-dipole corrections, which enhance the differential BR for large values of the dark fine-structure constant $\alpha_D$. The authors conclude that the Belle II excess can be explained by dark fermion pair production through the process $B^+ \rightarrow K^+ Q_i \tilde{Q}_i$, mediated by an off-shell massless dark photon, with dark fermion masses of the order of 500 MeV.The Belle II collaboration has observed an excess in the branching ratio (BR) of the rare decay $B^+ \rightarrow K^+ \nu \bar{\nu}$, which deviates from the Standard Model (SM) prediction by 2.7σ. This paper explores the possibility that this excess is explained by long-distance interactions induced by a massless dark photon, $\gamma_D$. The dark photon couples to an invisible dark sector and to the Standard Model via higher-dimensional operators, such as the chromomagnetic-dipole coupling. The process $B^+ \rightarrow K^+ \gamma_D$ is forbidden by angular momentum conservation, leading to a three-body final state with a pair of dark fermions, which appear as missing energy in the detector. The authors show that the Belle II data can be explained for perturbative values of the model parameters. This scenario predicts new contributions to the neutral $B$ meson decays $B^0 \rightarrow K^+ \gamma_D$, where the emission of a on-shell dark photon is allowed, resulting in a monochromatic missing energy signature. Additionally, an excess due to the emission of a dark photon is predicted for the $B^0_s \rightarrow \phi + E_{\text{miss}}$ decay, which could be observed at the LHCb experiments. The paper also discusses the Sommerfeld-Fermi and dark magnetic-dipole corrections, which enhance the differential BR for large values of the dark fine-structure constant $\alpha_D$. The authors conclude that the Belle II excess can be explained by dark fermion pair production through the process $B^+ \rightarrow K^+ Q_i \tilde{Q}_i$, mediated by an off-shell massless dark photon, with dark fermion masses of the order of 500 MeV.