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

We study two rare decays, $Z \to π^{+} π^{-}$ 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 $ $B$ (Z\to \pi^+\pi^-) = (0.83 \pm 0.02 \pm 0.02 \pm 0.04)\times 10^{-12} $a n d$ $B$ (Z\to K^+K^-) = (1.74^{+0.03}_{-0.05} \pm 0.04 \pm 0.02)\times 10^{-12} $a r e o b t a i n e d a n d c a n b e m e a s u r e d a t a t e r a -$ 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.

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

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

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Z→π+π−,K+K−Z→π+π−,K+K−: A touchstone of the PQCD approach

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Z→π+π−,K+K−Z→π+π−,K+K−: A touchstone of the PQCD approach

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

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

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