2021 journal article
Light-front dynamic analysis of the longitudinal charge density using the solvable scalar field model in (1+1) dimensions
PHYSICAL REVIEW D, 103(7).
open access via link.aps.org (publisher PDF)
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We investigate the electromagnetic form factor $F({q}^{2})$ of the meson by using the solvable ${\ensuremath{\phi}}^{3}$ scalar field model 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 ${x}^{+}={x}^{0}+{x}^{3}$ as the evolution parameter is maximized in contrast to the usual instant form dynamics (IFD) with the ordinary time ${x}^{0}$ as the evolution parameter. In LFD, the individual ${x}^{+}$-ordered amplitudes contributing to $F({q}^{2})$ are invariant under the boost, i.e., frame independent, while the individual ${x}^{0}$-ordered amplitudes in IFD are not invariant under the boost but dependent on the reference frame. The LFD allows us to get the analytic result for the one-loop triangle diagram which covers not only the spacelike (${q}^{2}<0$) but also timelike (${q}^{2}>0$) region. Using the analytic results, we verify that the real and imaginary parts of the form factor satisfy the dispersion relations in the entire ${q}^{2}$ space. Comparing with the results in ($3+1$) dimensions, we discuss the transverse momentum effects on $F({q}^{2})$. We also discuss the longitudinal charge density in terms of the boost-invariant variable $\stackrel{\texttildelow{}}{z}={p}^{+}{x}^{\ensuremath{-}}$ in LFD.