Dark photon effect on the rare kaon decay $K_L \rightarrow \pi^0 \nu {\bar \nu}$

TL;DR

This paper investigates how a dark photon could influence the rare kaon decay $K_L ightarrow \pi^0 u ar{ u}$, finding it causes only minor corrections within the studied parameter space.

Contribution

The study explicitly derives dark photon couplings to Standard Model particles and assesses their impact on the rare kaon decay process.

Findings

Dark photon causes less than a 5% correction to the decay rate.

Couplings depend explicitly on dark photon mass and mixing parameter.

Standard Model predictions remain robust against dark photon effects.

Abstract

We present an analysis of the effect of a dark photon on the rare kaon decay $K_L \rightarrow \pi^0 \nu {\bar \nu}$. All relevant couplings of the dark photon to the Standard Model particles are derived explicitly in terms of the dark photon mass and the mixing parameter. We find that the dark photon yields no more than a few percent correction to the Standard Model branching ratio ${\rm Br}(K_L \rightarrow \pi^0 \nu {\bar \nu})$ in the region of interest.