Study of electron-positron annihilation into four pions within chiral effective field theory in the low energy region

TL;DR

This study uses chiral effective field theory to analyze electron-positron annihilation into four pions at low energies, comparing theoretical predictions with experimental data and calculating contributions to muon g-2.

Contribution

It applies both chiral perturbation theory and resonance chiral theory to model the process, including resonance effects and calculating muon g-2 contributions.

Findings

Chiral perturbation theory underestimates experimental cross sections.

Resonance contributions are larger but still smaller than experimental data.

Calculated muon g-2 contributions are provided for specific channels.

Abstract

In this paper, we employ chiral effective field theory to study the process of electron-positron annihilation into four pions in the low energy region within $E_{c.m.}\leq 0.6$ GeV. The prediction of the cross section is obtained through $SU(3)$ chiral perturbation theory up to the next-to-leading order, which is smaller than the experimental data in the energy region [0.6-0.65] GeV, though the data has only a few points and poor statistics. Then, the resonance chiral theory is applied to include the resonance contribution, with the lightest scalars and vectors written in the effective Lagrangians. A series of relevant decay widths and the masses of the vectors are studied to fix the unknown couplings. The resonance contribution should be one order larger than that of the chiral perturbation theory but still one to two orders smaller than the data. The significant discrepancy urged the new experimental measurements to give more guidance. We also compute the leading order hadronic vacuum polarization contribution from the four pion channels to the anomalous magnetic moment of the muon, $(g-2)_\mu$. In the energy range from threshold up to 0.6 GeV within resonance chiral theory, the contributions are $a_\mu=(0.680\pm0.062)\times10^{-16}$ and $a_\mu=(0.597\pm0.058)\times10^{-16}$ for the processes of $e^+e^-\to\pi^+\pi^+\pi^-\pi^-$, $\pi^0\pi^0\pi^+\pi^-$, respectively.