Constraint on Parity-Violating Muonic Forces

Using the nonobservance of missing mass events in the leptonic kaon decay $K\to \mu X$, we place a strong constraint on exotic parity-violating gauge interactions of the right-handed muon. By way of illustration, we apply it to an explanation of the proton size anomaly that invokes such a new force; scenarios in which the gauge boson decays invisibly or is long lived are constrained.

Figure 1

$V$ bremsstrahlung in $K^{-}\to {\mu }^{-}{\overline{\nu }}_{\mu }$ decay.

Figure 2

Differential decay rate of muonic kaon decay with $V$ bremsstrahlung as a function of the missing mass, normalized to the standard two-body muonic kaon decay. The 90% C.L. upper limit in the mass range $227.6\le m_X\le 302.2\mathrm{MeV}$ is marked by a short horizontal line. The distributions for the three benchmark points shown violate the upper limit. We remind the reader that the bound is evaded by the minimal model of Ref. 1, since $V$ decays promptly to $e^{+}{e}^{-}$; model extensions in which $V$ decays invisibly or is long lived are strongly constrained.

Figure 3

The $(m_V,g_R)$ parameter space above the solid curve is excluded at the 90% C.L. The three red dots are the benchmark points in Fig. 2 and are disallowed if $V$ decays invisibly or is long lived.