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

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 $\mathcal{B}(Z\to K^{+}{K}^{-})=(1.74_{-0.05}^{+0.03}\pm 0.04\pm 0.02)\times 10^{-12}$ 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.

Comments: matches published version