Light gauge boson interpretation for (g - 2)(mu) and the K-L -> pi(0) + (invisible) anomaly at the J-PARC KOTO experiment

We discuss a list of possible light gauge boson interpretations for the long- standing experimental anomaly in (g - 2)(mu) and also recent anomalous excess in K-L -> pi (0) + (invisible) events at the J-PARC KOTO experiment. We consider two models: i) L-mu- L-tau gauge boson with heavy vector-like quarks and ii) (L-mu- L-tau) + (B-3- L-tau ) gauge boson in the presence of right-handed neutrinos. When the light gauge boson has mass close to the neutral pion in order to satisfy the Grossman-Nir bound, the models successfully explain the anomalies simultaneously while satisfying all known experimental constraints. We extensively provide the future prospect of suggested models.