Two and Three Pseudoscalar Production in $e^{+}e^{-}$ annihilation and their contributions to $(g-2)_{\mu}$

TL;DR

This paper analyzes two- and three-pseudoscalar meson production in electron-positron annihilation using resonance chiral theory, updating previous work with new data to evaluate their contributions to the muon's anomalous magnetic moment.

Contribution

It provides a revised analysis of pseudoscalar production processes and their impact on $(g-2)_{}$, incorporating latest experimental data and higher-order effects.

Findings

Contributions to muon  are estimated as $(21.6 \u00b1 7.4) imes 10^{-10}$.

Theoretical prediction still differs by 2.9 standard deviations from experimental value.

Updated analysis refines the understanding of hadronic vacuum polarization effects.

Abstract

A coherent study of $e^{+}e^{-}$ annihilation into two ($\pi^{+}\pi^{-}$,$K^{+}K^{-}$) and three ($\pi^{+}\pi^{-}\pi^{0},\pi^{+}\pi^{-}\eta$) pseudoscalar meson production is carried out within the framework of resonance chiral theory in energy region $E\lesssim 2 \, \mathrm{GeV}$. The work of {[}L. Y. Dai, J. Portol\'es, and O. Shekhovtsova, Phys. Rev. D 88,056001 (2013){]} is revisited with the latest experimental data and a joint analysis of two pseudoscalar meson production. Hence, we evaluate the lowest order hadronic vacuum polarization contributions of those two and three pseudoscalar processes to the anomalous magnetic moment of the muon. We also estimate some higher-order additions led by the same hadronic vacuum polarization. Combined with the other contributions from the standard model, the theoretical prediction differs still by $(21.6 \pm 7.4)\times 10^{-10}$ (2.9$\sigma$) from the experimental value.