Scalar and Pseudo-Scalar Form Factors in Electro- and Weak-Production of Pion Near Threshold

We investigated pion production near threshold by the weak current in terms of multipole amplitudes. By exploiting the chiral Ward identity based on the QCD Lagrangian, we derived relevant multipole amplitudes in closed forms and presented their numerical results. In the amplitudes, scalar and pseudo scalar (PS) form factors, which represent the scalar and the PS quark density distributions, manifest by themselves. We applied these amplitudes to the cross sections for the weak- and electro-production near threshold. Both pion and PS form factor contributions are shown to account for the t-channel contribution in the charged pion electro-production near threshold. The asymmetry on the pion production by the neutrino and anti-neutrino is also discussed with their longitudinal and transverse cross sections.