Pion off-shell electromagnetic form factors: Data extraction and model analysis

We investigate the pion electromagnetic half-off-shell form factors, which parametrize the matrix element of the charged pion electromagnetic current with one leg off mass shell and the other leg on mass shell, using an exactly solvable manifestly covariant model of a (3+1)-dimensional fermion field theory. The model provides a three-dimensional imaging of the two off-shell pion form factors F1 and F2 as a function of (Q2,t), which are related to each other, satisfying the Ward-Takahashi identity. The normalization of the renormalized charge form factor F1 is fixed by F1(Q2=0,t=mπ2)=1, while the other form factor F2 vanishes; i.e., F2(Q2,t=mπ2)=0 for any value of Q2 due to the time-reversal invariance of the strong interaction. We define the new form factor g(Q2,t)=F2(Q2,t)/(t-mπ2) and find that g(Q2,t) can be measurable in the on-mass-shell limit. In particular, g(Q2=0,t=mπ2) is related with the pion charge radius. We also compare our form factors with the data extracted from the pion electroproduction reaction for both the off-shell region (t<0) and the on-shell limit (t→mπ2).