Charge asymmetry in the process $e^+e^-\to π^+π^-π^0γ$

TL;DR

This work analyzes charge asymmetry in the process $e^+e^-→ π^+π^-π^0γ$ in the photon-energy regime ν≪√s, incorporating longitudinal electron polarization. The authors model both one-photon (ω) and two-photon ($a_1^0(1260)$) production channels, employing a gauge-invariant amplitude decomposition and Sudakov logarithms to capture leading contributions. They find that the integral asymmetry $A_0^γ$ can reach several tens of percent, with a non-negligible role for the $a_1^0(1260)$ intermediate state, and a smaller helicity-dependent asymmetry $A_λ^γ$ that arises only when $a_1^0(1260)$ is included. These results offer a practical avenue to probe $ ext{γ}^* ext{γ}^*$-induced form factors and ISR-driven resonance variation in $e^+e^-$ annihilation.

Abstract

The charge asymmetry in the process $e^+e^-\to π^+π^-π^0γ$ is studied for photons with energies $ν\ll\sqrt{s}$. The longitudinal polarization of electrons (positrons) is taken into account. The asymmetry arises due to interference of the amplitudes for production of pion states with opposite $C$ parities. The contribution of $a_1^0(1260)$ meson in the intermediate state to the charge asymmetry is discussed. This contribution is not the leading one, however it is not negligible. It is shown that the charge asymmetry can reach several tens of percent.

Figures (6)

• Figure 1: Diagrams of the process $e^+e^-\to\pi^+\pi^-\pi^0\gamma$ with an intermediate $\omega$ meson.
• Figure 2: Diagrams of the process $e^+e^-\to\pi^+\pi^-\pi^0\gamma$ with the intermediate $a_1^0(1260)$ meson.
• Figure 3: Left plot: the energy dependence of $\sigma_{13}$ for $\nu=20\,\hbox{MeV}$ (solid curve), $\nu=40\,\hbox{MeV}$ (dotted curve), $\nu=60\,\hbox{MeV}$ (dashed curve), and $\nu=80\,\hbox{MeV}$ (dash-dotted curve). Right plot: the energy dependence of $\sigma_{24}$.
• Figure 4: Dependence of $A_0^{(12)}$ (left plot) and $A_0^{(13)}$ (right plot) on the energy $E$ for $\nu=20\,\hbox{MeV}$ (solid curve), $\nu=40\,\hbox{MeV}$ (dotted curve), $\nu=60\,\hbox{MeV}$ (dashed curve), and $\nu=80\,\hbox{MeV}$ (dash-dotted curve).
• Figure 5: Energy dependence of $A_0^\gamma$ (solid curve), $A_0^{(12)}$ (dashed curve), and $A_0^{(13)}$ (dotted curve) for $\nu=20\,\hbox{MeV}$ (left plot) and $\nu=80\,\hbox{MeV}$ (right plot).