FCNC $B$ and $K$ Meson Decays with Light Bosonic Dark Matter

Abstract

We consider decays of $B$ and $K$ mesons into a pseudo-scalar or vector meson plus missing energy. Within the SM, these modes originate from flavor changing neutral current (FCNC) processes with two neutrinos in the final state. In this paper we consider the experimental upper bounds on these modes and interpret the difference between these bounds and the SM prediction as a window into new light invisible particles. In particular we consider the case where some new symmetry requires the new particles to be produced in pairs. We first construct the general low energy effective Lagrangian coupling an FCNC with two dark sector particles of spin zero, one-half and one. We then present numerical estimates for the constraints that can be placed on these interactions, finding that an effective new physics scale from $\mathcal{O}(10)$-$\mathcal{O}(10^{11})$ GeV can be probed, with the exact value strongly depending on the interaction structure as well as the mass of the invisible particle. For $K^{+}\to {\pi }^{+}/E$ we incorporate into our constraints the effect of using only the signal regions of NA62, and for $B^{+}\to K^{+}/E$ the $q^2$-dependent efficiency of Belle II.

40 pages, 42 figures, the consideration of Belle II efficiency is clarified and corrected, several new references are added, to appear in JHEP

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• $B\to K\nu \bar{\nu }$, MiniBooNE and muon $g-2$ anomalies from a dark sector
• The decay $B\to K+\nu +\bar{\nu }$ at Belle II and a massless bino in R-parity-violating supersymmetry
• The first limit on invisible decays of $B_s$ mesons comes from LEP
• $B\to K+$invisible, dark matter, and $CP$ violation in hyperon decays
• Invisible Higgs decay from dark matter freeze-in at stronger coupling
• Searching for heavy neutral leptons coupled to axion-like particles at the LHC far detectors and SHiP
• FCNC charmed-hadron decays with invisible singlet particles in light of recent data
• Light dark-matter window constrained by \boldmath$K^{+}\to {\pi }^{+}$$+$$/E$
• Workshop summary -- Kaons@CERN 2023
• The dark Stodolsky effect: constraining effective dark matter operators with spin-dependent interactions
• Charged lepton flavor violating decays with a pair of light dark matter and muonium invisible decay
• ${\Sigma }^{+}\to p{\ell }^{+}{\ell }^{-}$ decays within the standard model and beyond
• Can a Nonstandard Invisible Pair Mimic the Michel Distribution?