Hunting down massless dark photons in kaon physics

If dark photons are massless, they couple to standard-model particles only via higher dimensional operators, while the kinetic mixing with photons, which motivates most of the current experimental searches, is absent. We consider the effect of possible flavor-changing magnetic-dipole couplings of massless dark photons in kaon physics. In particular, we study the branching ratio for the process $K^+\rightarrow \pi^+\pi^0 \bar \gamma$ with a simplified-model approach, assuming the chiral quark model to evaluate the hadronic matrix element. Possible effects in the $K^0$-$\bar K^0$ mixing are taken into account. We find that branching ratios up to $O(10^{-7})$ are allowed---depending on the dark-sector masses and couplings. Such large branching ratios for $K^+\rightarrow \pi^+\pi^0 \bar \gamma$ could be of interest for experiments dedicated to rare $K^+$ decays like NA62 at CERN, where $\bar \gamma$ can be detected as a massless invisible system.