3D imaging of the pion off-shell electromagnetic form factors

We study the pion electromagnetic half-off-shell form factors F₁ and F₂ using an exactly solvable manifestly covariant model of a (3 + 1) dimensional fermion field theory. The model provides a three-dimensional imaging of F₁ and F₂ as a function of (Q²,t), which are constrained by the Ward-Takahashi identity. The normalization of the charge form factor F₁ is fixed by F₁(Q² = 0,t = m²_π) = 1 while the other form factor F₂ vanishes, i.e. F₂(Q²,t = m²_π) = 0 for any value of Q² due to the time-reversal invariance of the strong interaction. The new form factor defined by g(Q²,t) = F₂(Q²,t)/(t − m²_π) is however measurable in the on-mass-shell limit. We note that g(Q² = 0,t = m²_π) is related with the pion charge radius.