23792 2402.19208 10.1007/JHEP06(2024)172 172 172 Deciphering the Belle II data on B → Kν ν ¯ $$ B\to K\nu \overline{\nu} $$ decay in the (dark) SMEFT with minimal flavour violation Regular Article - Theoretical Physics 1 48 2024 6 25 2024 3 15 2024 5 29 2024 6 25 The Author(s) 2024 Open Access. This article is distributed under the terms of the Creative Commons Attribution License ( CC-BY 4.0 ), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. 13130 2024 2024 6 6 Biao-Feng Hou resonhou@zknu.edu.cn Xin-Qiang Li xqli@ccnu.edu.cn Meng Shen shenmeng@mails.ccnu.edu.cn Ya-Dong Yang yangyd@ccnu.edu.cn Xing-Bo Yuan y@ccnu.edu.cn https://ror.org/03x1jna21 grid.411407.7 0000 0004 1760 2614 Institute of Particle Physics and Key Laboratory of Quark and Lepton Physics (MOE) Central China Normal University Wuhan 430079 Hubei China https://ror.org/02v51f717 grid.11135.37 0000 0001 2256 9319 Center for High Energy Physics Peking University Beijing 100871 China https://ror.org/00s13br28 grid.462338.8 0000 0004 0605 6769 Institute of Particle and Nuclear Physics Henan Normal University Xinxiang 453007 China Abstract Recently, the Belle II collaboration announced the first measurement of the branching ratio B B + → K + ν ν ¯ $$ \mathcal{B}\left({B}^{+}\to {K}^{+}\nu \overline{\nu}\right) $$ , which is found to be about 2.7σ higher than the Standard Model (SM) prediction. We decipher the data with two new physics scenarios: the underlying quark-level b → sν ν ¯ $$ b\to s\nu \overline{\nu} $$ transition is, besides the SM contribution, further affected by heavy new mediators that are much heavier than the electroweak scale, or amended by an additional decay channel with undetected light final states like dark matter or axion-like particles. These two scenarios can be most conveniently analyzed in the SM effective field theory (SMEFT) and the dark SMEFT (DSMEFT) framework, respectively. We consider the flavour structures of the resulting effective operators to be either generic or satisfy the minimal flavour violation (MFV) hypothesis, both for the quark and lepton sectors. In the first scenario, once the MFV assumption is made, only one SM-like low-energy effective operator induced by the SMEFT dimension-six operators can account for the Belle II excess, whose parameter space is, however, excluded by the Belle upper bound of the branching ratio B B 0 → K ∗ 0 ν ν ¯ $$ \mathcal{B}\left({B}^0\to {K}^{\ast 0}\nu \overline{\nu}\right) $$ . In the second scenario, it is found that the Belle II excess can be accommodated by 22 of the DSMEFT operators involving one or two scalar, fermionic, or vector dark matters as well as axion-like particles. These operators also receive dominant constraints from the B 0 → K *0 + inv and B s → inv decays. Once the MFV hypothesis is assumed, the number of viable operators is reduced to 14, and the B + → π + + inv and K + → π + + inv decays start to put further constraints on them. Within the parameter space allowed by all the current experimental data, the q 2 distributions of the B → K (*) + inv decays are then studied for each viable operator. We find that the resulting prediction of the operator Q qχ = q ¯ p γ μ q r χ ¯ γ μ χ $$ {\mathcal{Q}}_{q\chi}=\left({\overline{q}}_p{\gamma}_{\mu }{q}_r\right)\left(\overline{\chi}{\gamma}^{\mu}\chi \right) $$ with a fermionic dark matter mass m χ ≈ 700 MeV can closely match the Belle II event distribution in the bins 2 ≤ q 2 ≤ 7 GeV2. In addition, we, for the first time, calculate systematically the longitudinal polarization fraction F L of K * in the B → K * + inv decays within the DLEFT. By combining the decay spectra and F L , almost all the DSMEFT operators are found to be distinguishable from each other. Finally, the future prospects at Belle II, CEPC and FCC-ee are also discussed for some of these FCNC processes. Keywords New Light Particles Semi-Leptonic Decays Flavour Symmetries SMEFT ArXiv ePrint: 2402.19208