Constraining secret gauge interactions of neutrinos by meson decays

Secret coupling of neutrinos to a new light vector boson, $Z^{\prime }$, with a mass smaller than 100 MeV is motivated within a myriad of scenarios which are designed to explain various anomalies in particle physics and cosmology. Due to the longitudinal component of the massive vector boson, the rates of three-body decay of charged mesons ($M$) such as the pion and the kaon to the light lepton plus neutrino and $Z^{\prime }$ ($M\to l\nu Z^{\prime }$) are enhanced by a factor of $(m_M/m_{Z^{\prime }}{)}^2$. On the other hand, the standard two body decay $M\to l\nu$ is suppressed by a factor of $(m_l/m_M{)}^2$ due to chirality. We show that in the case of ($M\to e\nu Z^{\prime }$), the enhancement of $m_M^4/m_e^2{m}_{Z^{\prime }}^2\sim 10^8–10^{10}$ relative to two-body decay ($M\to e\nu$) enables us to probe very small values of gauge coupling for ${\nu }_e$. The strongest bound comes from the $R_K\equiv \mathrm{Br}(K\to e+\nu )/\mathrm{Br}(K\to \mu +\nu )$ measurement in the NA62 experiment. The bound can be significantly improved by customized searches for signals of three-body charged meson decay into the positron plus missing energy in the NA62 and/or PIENU data.

Figure 1

Feynman diagram for charged meson decay to a charged lepton, $l_{\alpha }$, neutrino, and the new light vector boson, $Z^{\prime }$.

Figure 2

The 90% C.L. constraints on $\sqrt{\sum _i{g}_{ei}^2}$ versus $m_{Z^{\prime }}$ from constraints on $\pi \to e\nu Z^{\prime }$ [9] and $K^{+}\to e^{+}\nu \nu \nu$ [19] branching ratios, from current and projected $R_{\pi }$ measurement by PIENU [20], and from the $R_K$ measurement by NA62 [22].

Figure 3

The 90% C.L. constraints on $\sqrt{\sum _i{g}_{\mu i}^2}$ versus $m_{Z^{\prime }}$ from the $K^{+}\to {\mu }^{+}\nu \nu \nu$ branching ratio [23]. The band shows the parameter space within the $L_{\mu }$ gauge models (giving rise to equal couplings to $\mu$ and ${\nu }_{\mu }$) that can explain the $(g-2{)}_{\mu }$ anomaly [38].