  Weakly interacting K --> pi X^0 emission with m_{X^0} \simeq m_{pi^0} is out
of sight of the current K^+ --> pi^+ nu nubar study, but it can be sensed by
the K_L --> pi^0 nu nubar search. This evades the usual Grossman-Nir bound of
B(K_L --> pi^0 nu nubar) < 1.4 x 10^-9, thus the KOTO experiment is already
starting to probe New Physics. An intriguing possibility is the Z' gauge boson
of a weak leptonic force that couples to L_mu - L_tau (the difference between
the muon and tauon numbers), which may explain the long-standing "muon g-2"
anomaly, but is constrained by nu_mu N --> nu_mu N mu^+ mu^- scattering to
m_{Z'} \lesssim 400 MeV. An explicit model for K --> pi Z' is given, which
illustrates the link between rare kaon and B --> K mu^+ mu^-, K^{(*)} nu nubar
decays. Complementary to these searches and future lepton experiments, the LHC
might discover the scalar boson phi responsible for light m_{Z'} generation via
phi --> Z' Z' --> 2(mu^+ mu^-).

High Energy Physics - Phenomenology