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

TL;DR

This paper explores a light $Z'$ boson from a $(B-L)_{23}$ extension of the Standard Model as a common explanation for the muon $(g-2)$ anomaly and the KOTO $K o \pi + E_{miss}$ anomaly, analyzing its implications and potential conflicts.

Contribution

It demonstrates that a $Z'$ boson can potentially explain both anomalies with moderate CP violation tuning, highlighting the model's phenomenological viability and challenges.

Findings

$Z'$ can explain the KOTO anomaly via $K_L o \pi^0 + Z'$ decay.

The same $Z'$ can account for the $(g-2)_{\mu}$ anomaly if not responsible for it.

Possible tension with $B$ meson decay constraints.

Abstract

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.