Pion pair production in e + e − annihilation

We present an analysis of the process ee → γ orZ → ππγ, in the kinematical region where √ s, the c.m. energy of the ee pair, is large but much below the Z-pole. The subprocess γ orZ → ππγ can be described by the convolution of the hard scattering coefficient γ orZ → qq̄γ and the general distribution amplitude of two pions qq̄ → ππ. In the case of neutral pion, the production through γ is the dominant process, which can therefore be used to access the generalized distribution amplitudes (GDAs) of the pion, especially their C-even parts. The γZ interference term provides an alternative approach to extract the weak mixing angle sin θW through measuring the helicity asymmetry in the process ee → ππγ. In the case of charged pion pair production, the Bremsstrahlung process dominates and its interference with ee → γ → ππγ can be applied to study the process γ → ππγ at the amplitude level.