$(g-2)_{\mu}$ Versus $K \to \pi+E_{miss}$ Induced by the $(B-L)_{23}$ Boson

To address the long-standing $(g-2)_{\mu}$ anomaly via a light boson, in Ref. [1] we proposed to extend the standard model (SM) by the local $(B-L)_{23}$, under which only the second and third generations of fermions are charged. It predicts an invisible $Z'$ with mass ${\cal O}(100)$ MeV, and moreover it has flavor-changing neutral current (FCNC) couplings to the up-type quarks at tree level. Such a $Z'$, via $K_L \to \pi^0 + Z'(\to \nu \bar{\nu})$ at loop level, may be a natural candidate to account for the recent KOTO anomaly. In this article, we investigate this possibility, to find that $Z'$ can readily do this job if it is no longer responsible for the $(g-2)_{\mu}$ anomaly. We further find that both anomalies can be explained with moderate tuning of the CP violation, but may contradict the $B$ meson decays.