Kaon decay constraints on vector bosons coupled to nonconserved currents

We study rare three- and four-body kaon decays as a probe of light vector and axial-vector bosons coupled to nonconserved currents. We find that searches for K L → π 0 π 0 ( X → e + e − ) decays constrain the couplings of light X bosons to light quarks to be as small as O ( 10 − 5 ) . The charged-pion modes K + → π + π 0 ( X → e + e − ) and K L → π + π − ( X → e + e − ) provide weaker limits, but constrain complementary combinations of couplings to the u , d , and s quarks at the level of O ( 10 − 4 ) . Finally, we also find that double emission of X in K → π X X decays can provide yet additional constraints on the parameter space of light X bosons due to a double ( m K / m X ) 2 enhancement to the rate. For a 17 MeV boson, these limits add to the known tension between spin-1 bosons coupled to vector and axial-vector currents interpretations of the results of the ATOMKI experiment with meson decay data. Finally, we also comment on negative pion capture on hydrogen and deuterium as a source of light particles and discuss the prospects for testing the 17 MeV boson hypothesis.