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

Abstract

We investigate the electromagnetic form factor $F(q^2)$ of the meson by using the solvable ${\varphi }^3$ 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.

arXiv comment15 pages, 12 figures; Slight changes have been made in the title and abstract. Version to appear in Phys. Rev. D

References in corpus (25)

• Impact Parameter Dependent Parton Distributions and Off-Forward Parton Distributions for $\zeta \to 0$
• Impact Parameter Space Interpretation for Generalized Parton Distributions
• Generalized parton distributions in impact parameter space
• Charge Density of the Neutron
• Empirical transverse charge densities in the nucleon and the nucleon-to-$\Delta$ transition
• Defining the Proton Radius: a Unified Treatment
• Exact Light-Cone Wavefunction Representation of Matrix Elements of Electroweak Current
• Realistic Transverse Images of the Proton Charge and Magnetic Densities
• Charge Distributions of Moving Nucleons
• Regularizing the Divergent Structure of the Light-Front Currents
• Pairs in the light-front and covariance
• Nonvanishing zero modes in the light-front current
• Pion Eletromagnetic Current in the Ligth-Cone Formalism
• Electromagnetic Form Factors and Charge Densities From Hadrons to Nuclei
• Singular Charge Density at the Center of the Pion?
• Solving the Bars-Green equation for moving mesons in two-dimensional QCD
• The Frame-Independent Spatial Coordinate $\tilde{z}$: Implications for Light-Front Wave Functions, Deep Inelastic Scattering, Light-Front Holography, and Lattice QCD Calculations
• Equivalence of renormalized covariant and light-front perturbation theory: I. Longitudinal divergences in the Yukawa model
• Quantifying the nucleon's pion cloud with transverse charge densities
• Pion transverse charge density from timelike form factor data
• Disentangling Intertwined Embedded States and Spin Effects in Light-Front Quantization
• Equivalence of renormalized covariant and light-front perturbation theory: II. Transverse divergences in the Yukawa model
• Spacelike and timelike form factors for the $({\pi }^0,\eta ,{\eta }^{\prime })\to {\gamma }^{\ast }\gamma$ transitions in the light-front quark model
• Pion transverse charge density and the edge of hadrons
• Exploring the timelike region for the elastic form factor in the light-front quantization

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