$Z \to \pi^+\pi^-, K^+K^-$: A touchstone of the PQCD approach

TL;DR

This paper calculates the rare decay rates of Z bosons into pion and kaon pairs using perturbative QCD up to next-to-leading order, providing predictions that can test the approach's validity at future colliders.

Contribution

It offers the first precise perturbative QCD predictions for Z decays into meson pairs, highlighting their potential as benchmarks for the approach's applicability.

Findings

Branching ratios are predicted as (0.83 ± 0.02 ± 0.02 ± 0.04)×10^{-12} for Z→π+π−.

Branching ratios are predicted as (1.74+0.03−0.05 ± 0.04 ± 0.02)×10^{-12} for Z→K+K−.

Subleading-power contributions are negligible, and leading contributions are parameter-free.

Abstract

We study two rare decays, $Z \to \pi^+\pi^-$ and $K^+K^-$, in the perturbative QCD approach up to the next-to-leading order of the strong coupling and the leading power of $1/m_Z$, $m_Z$ being the $Z$ boson mass. The branching ratios $\mathcal{B}(Z\to \pi^+\pi^-) = (0.83 \pm 0.02 \pm 0.02 \pm 0.04)\times 10^{-12}$ and $\mathcal{B}(Z\to K^+K^-) = (1.74^{+0.03}_{-0.05} \pm 0.04 \pm 0.02)\times 10^{-12}$ are obtained and can be measured at a tera-$Z$ factory. Because the subleading-power contributions to the branching ratios are negligible, and the leading one does not depend on any free parameter, the two channels can serve as a touchstone for the applicability of the perturbative QCD approach.