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

TL;DR

This paper investigates how rare $B$ and $K$ meson decays with missing energy can reveal new light dark matter particles, constraining their interactions and mass scales up to $10^{11}$ GeV.

Contribution

It develops a general effective Lagrangian for FCNC decays involving pairs of light dark sector particles with various spins and provides numerical bounds on new physics scales from experimental data.

Findings

Constraints on new physics scale range from 10 to 10^11 GeV.

Effective interactions depend on the spin and mass of dark particles.

Experimental bounds can probe very high energy scales, sensitive to interaction details.

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 ${\cal O}(10)$-${\cal O}(10^{11})$ GeV can be probed, with the exact value strongly depending on the interaction structure as well as the mass of the invisible particle. For $K^+\to \pi^+ \displaystyle{\not} E$ we incorporate into our constraints the effect of using only the signal regions of NA62, and for $B^+\to K^+ \displaystyle{\not} E$ the $q^2$-dependent efficiency of Belle II.