Hunting Down Massless Dark Photons in Kaon Physics

If dark photons are massless, they couple to standard-model particles only via higher dimensional operators, while direct (renormalizable) interactions induced by kinetic mixing, which motivates most of the current experimental searches, are absent. We consider the effect of possible flavor-changing magnetic-dipole couplings of massless dark photons in kaon physics. In particular, we study the branching ratio for the process $K^{+}\to {\pi }^{+}{\pi }^0\overline{\gamma }$ with a simplified-model approach, assuming the chiral quark model to evaluate the hadronic matrix element. Possible effects in the $K^0\text{−}{\overline{K}}^0$ mixing are taken into account. We find that branching ratios up to $O({10}^{-7})$ are allowed—depending on the dark-sector masses and couplings. Such large branching ratios for $K^{+}\to {\pi }^{+}{\pi }^0\overline{\gamma }$ could be of interest for experiments dedicated to rare $K^{+}$ decays like NA62 at CERN, where $\overline{\gamma }$ can be detected as a massless invisible system.

Figure 1

Vertex diagrams for the generation of the dipole operator in the simplified model of the dark sector (same for the specific model in Refs. [10, 11, 12]).

Figure 2

$\chi \mathrm{QM}$ diagrams for the process $K^{+}\to {\pi }^{+}{\pi }^0\tilde{\gamma }$. The crossed circle stands for the insertion of the magnetic dipole operator $\widehat{Q}$ in Eq. (6).

Figure 3

$\mathrm{BR}(K^{+}\to {\pi }^{+}{\pi }^0\overline{\gamma })$) as a function of the effective scale $\mathrm{\Lambda }$ and coupling $\xi =g_L{g}_R/2$, for a representative choice of the coupling strength ${\alpha }_D=0.1$.