Two body final states production in electron-positron annihilation and their contributions to $(g-2)_{\mu}$

TL;DR

This study calculates hadronic contributions to the muon's anomalous magnetic moment using resonance chiral theory for electron-positron annihilation into two-body final states, providing insights into the existing discrepancy with experimental data.

Contribution

It offers a detailed theoretical analysis of hadronic vacuum polarization effects in $e^{+}e^{-}$ annihilation processes, improving the understanding of their impact on $(g-2)_{m}$ within the resonance chiral theory framework.

Findings

Calculated contributions to $(g-2)_{m}$ from specific two-body final states.

Identified a 4.5$7$ discrepancy between theory and experiment.

Provided a refined estimate of hadronic vacuum polarization effects.

Abstract

In this paper, we study the processes of $e^{+}e^{-}$ annihilation into two body final states, either two pseudoscalar mesons or one meson with a photon. The hadronic vacuum polarization form factors are calculated within the framework of resonance chiral theory in the energy region of $E \lesssim 2$ GeV, with final state interactions taken into account. A joint analysis on the processes of $e^{+}e^{-} \rightarrow \pi^{+}\pi^{-}$, $K^{+}K^{-}$, $K_{L}^{0}K_{S}^{0}$, $\pi^{0}\gamma$, and $\eta\gamma$ has been performed, and the latest experimental data are included. Based on the vacuum polarization form factors of these processes, we estimate their contributions to the lowest order of anomalous magnetic moment of the muon, $(g-2)_\mu$. Combined with other contributions from hadronic vacuum polarization and other interactions from the standard model, the discrepancy between theoretical prediction and experimental measurement is $\Delta a_{\mu}=(24.1\pm5.4)\times 10^{-10}$, i.e., 4.5$\sigma$.