Light-front dynamic analysis of the longitudinal charge density using the exactly solvable scalar field theory in (1+1) dimensions

Yongwoo Choi,1 Ho-Meoyng Choi,2, ∗ Chueng-Ryong Ji,3, † and Yongseok Oh1, 4, ‡ 1Department of Physics, Kyungpook National University, Daegu 41566, Korea 2Department of Physics, Teachers College, Kyungpook National University, Daegu 41566, Korea 3Department of Physics, North Carolina State University, Raleigh, NC 27695-8202 4Asia Pacific Center for Theoretical Physics, Pohang, Gyeongbuk 37673, Korea We investigate the electromagnetic form factor F(q2) of the meson by using exactly solvable φ 3 scalar field theory in (1+ 1) dimensions. As the transverse rotations are absent in (1+ 1) dimensions, the advantage of the light-front dynamics (LFD) with the light-front time x+ = x0 + x3 as the evolution parameter is maximized in contrast to the usual instant form dynamics (IFD) with the ordinary time x0 as the evolution parameter. In LFD, the individual x+-ordered amplitudes contributing to F(q2) are invariant under the boost, i.e., frameindependent, while the individual x0-ordered amplitudes in IFD are not invariant under the boost but dependent on the reference frame. The LFD allows to get the exact analytic result which covers not only the spacelike (q2 < 0) but also timelike region (q2 > 0). Using the analytic results, we verify that the real and imaginary parts of the form factor satisfy the dispersion relations in the entire q2 space. Comparing with the results in (3+ 1) dimensions, we discuss the transverse momentum effects on F(q2) . We also discuss the longitudinal charge density in terms of the boost invariant variable z̃ = p+x− in LFD.