Pion pair production in $e^{+}{e}^{-}$ annihilation

Abstract

We present an analysis of the process $e^{+}{e}^{-}\to V^{\ast }\to \pi \pi \gamma$, where $V=\gamma$ or $V=Z$ boson, in the kinematical region where $\sqrt{s}$, the c.m. energy of the $e^{+}{e}^{-}$ pair, is large but much below the $Z$-pole. The subprocess $V^{\ast }\to \pi \pi \gamma$ can be described by the convolution of the hard scattering coefficient $V\to q\bar{q}\gamma$ and the general distribution amplitude of two pions $q\bar{q}\to \pi \pi$. In the case of neutral pion production, $V=\gamma$ is the dominant process, which can therefore be used to access the GPAs of the pion, especially their $C$-even parts. The $\gamma Z$ interference term provides an alternative approach to extract the weak mixing angle $\sin {\theta }_W$ through measuring the helicity asymmetry in the process $e^{+}{e}^{-}\to {\pi }^0{\pi }^0\gamma$. In the case of charged pion pair production, the Bremsstrahlung process dominates and its interference with $e^{+}{e}^{-}\to {\gamma }^{\star }\to {\pi }^{+}{\pi }^{-}\gamma$ can be applied to study the process ${\gamma }^{\star }\to \pi \pi \gamma$ at the amplitude level.

Comments: Figure added, version to appear in Physical Review D