Sigma terms in Pion Weak-production near Threshold by Charged Current

We investigated pion production by charged weak current, which comprises vector and axial vector current. In particular, the contribution by the axial vector current is detailed at the pion threshold in terms of multipole amplitudes, which are useful tools for understanding the pion weak-production by combining the multipole amplitudes deduced from other probes. By exploiting the chiralWard identities based on the QCD Lagrangian, we derived relevant multipole amplitudes in closed forms and showed their numerical results. In the amplitudes, scalar and pseudo scalar form factor generating sigma terms manifest by themselves. Physical implications and roles of the scalar and the pseudo scalar form factor in pion weak-production are also discussed