Off-shell pion properties: Electromagnetic form factors and light-front wave functions

The off-shell pion electromagnetic form factors are explored with corresponding off-shell light-front wave functions modeled by constituent quark and antiquark. We apply the Mandelstam approach for the microscopic computation of the form factors relating the model parameters with the pion decay constant and charge radius. Analyzing the existing data on the cross sections for the Sullivan process, H1(e,e′,π+)n [H. P. Blok (Jefferson Lab Fπ Collaboration), Charged pion form factor between Q2=0.60, and 2.45 GeV2. I. Measurements of the cross section for the H1(e,e′π+)n reaction, Phys. Rev. C 78, 045202 (2008).PRVCAN0556-281310.1103/PhysRevC.78.045202], we extract the off-shell pion form factor using the relation derived from the generalized Ward-Takahashi identity for the pion electromagnetic current. They are compared with our previous results [H.-M. Choi, Pion off-shell electromagnetic form factors: Data extraction and model analysis, Phys. Rev. D 100, 116020 (2019).PRVDAQ2470-001010.1103/PhysRevD.100.116020] from exactly solvable manifestly covariant model of a (3+1)-dimensional fermion field theory. We find that the adopted constituent quark model reproduces the extracted off-shell form factor F1(Q2,t) from the experimental data within a few percent difference and matches well with our previous theoretical simulation which exhibits a variation of about 10% for the extracted off-shell pion form factor g(Q2,t). We also identify the pion valence parton distribution function (PDF) and transverse momentum distribution (TMD) in terms of the light-front wave function and discuss their off-shell properties.