Abstract
We investigate the electromagnetic form factor $F(q^2)$ of the meson by using the solvable $\phi^{3}$ 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 to get the analytic result for the one-loop triangle diagram which covers not only the spacelike ($q^{2}<0$) but also timelike region ($q^{2}>0$). 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 $\tilde z = p^+ x^-$ in LFD.
Highlights
The formulation of light-front dynamics (LFD) based on the equal light-front time xþ 1⁄4 x0 þ x3 quantization has shown remarkable advantages for calculations in elementary particle physics, nuclear physics, and hadron physics
Taking advantage of the LFD, one of the new experiments planned at JLab is to measure the transverse charge densities of hadrons [1], which are defined by the twodimensional Fourier transforms of the electromagnetic (EM) form factors describing the distribution of charge
While the valence contribution dominates for small Q2 region, the nonvalence contribution takes over the valence one for Q2 ≥ 0.1 GeV2 and most of the contribution to the form factor for high Q2 comes from the nonvalence diagram, indicating significant contributions from the higher-Fock components
Summary
The formulation of light-front dynamics (LFD) based on the equal light-front time xþ 1⁄4 x0 þ x3 quantization has shown remarkable advantages for calculations in elementary particle physics, nuclear physics, and hadron physics. The same level of significant progresses as in the case of the transverse charge density is yet to be expected in the analysis of the longitudinal charge density, it may be worthwhile to facilitate the scalar φ3 model in the (1 þ 1)-dimensional LFD extending the previous LFD analyses in (1 þ 1) dimensions [33,34,35] restricted only for the spacelike momentum transfer region to the entire kinematic regions including the timelike momentum transfers as well. We present the (1 þ 1)-dimensional analysis of the form factor in the solvable model both for the spacelike region and the timelike region, obtaining the analytic results both for the valence and nonvalence contributions.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
