Long vs. short distance dispersive two-photon K_L \to \mu^+ \mu^- amplitude

TL;DR

This paper calculates the short-distance dispersive amplitude for the decay K_L to mu+ mu- via two-loop electroweak and two-photon processes, showing QCD corrections significantly impact the amplitude and help constrain long-distance effects.

Contribution

It provides a detailed two-loop electroweak calculation of the decay amplitude, including QCD corrections that alter previous estimates and enable better constraints on long-distance contributions.

Findings

QCD corrections reverse the sign of the amplitude

QCD corrections reduce the amplitude by an order of magnitude

The results help constrain long-distance dispersive effects

Abstract

We report on the calculation of the two-loop electroweak, two-photon mediated short-distance dispersive K_L \to \mu^+\mu^- decay amplitude. QCD corrections change the sign of this contribution and reduce it by an order of magnitude. The resulting amplitude enables us to provide a constraint on the otherwise uncertain long-distance dispersive amplitude.