Abstract
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 3D imaging of the two off-shell pion form factors $F_1$ and $F_2$ as a function of $(Q^2,t)$, which are related to each other satisfying the Ward-Takahashi identity. The normalization of the renormalized charge form factor $F_1$ is fixed by $F_1(Q^2=0, t=m^2_\pi)=1$ while the other form factor $F_2$ vanishes, i.e. $F_2(Q^2, t=m^2_\pi)=0$ for any value of $Q^2$ due to the time-reversal invariance of the strong interaction. We define the new form factor $g(Q^2,t)=F_2(Q^2,t)/(t-m^2_\pi)$ and find that $g(Q^2,t)$ can be measurable in the on-mass-shell limit. In particular, $g(Q^2=0, t=m^2_\pi)$ 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 ($t \rightarrow m_\pi^2$).
Highlights
Electromagnetic (EM) form factors of hadrons are the important physical observables providing the EM information on the bound-state properties of hadrons and their internal structures of quarks and gluons
We explore the electromagnetic off-shell effects for the pion using an exactly solvable manifestly covariant model of (3 þ 1)-dimensional fermion field theory and compare the two off-shell form factors F1ðQ2; tÞ and F2ðQ2; tÞ with the data extracted from the pion electroproduction reaction[7,8]
As the loop correction to the charge form factor F1ðQ2; t 1⁄4 m2πÞ must vanish at Q2 1⁄4 0, the charge at Q2 1⁄4 0 is given by a subtraction to the contribution by the loop integral
Summary
Electromagnetic (EM) form factors of hadrons are the important physical observables providing the EM information on the bound-state properties of hadrons and their internal structures of quarks and gluons. We explore the electromagnetic off-shell effects for the pion using an exactly solvable manifestly covariant model of (3 þ 1)-dimensional fermion field theory and compare the two off-shell form factors F1ðQ2; tÞ and F2ðQ2; tÞ with the data extracted from the pion electroproduction reaction[7,8]. The aimof this paperis toprovideat least a clear example of demonstration discussing the validity of the extrapolation of the off-shell results (t ≠ m2π) to the onshell limit (t 1⁄4 m2π) for the pion.
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