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Understanding the internal structures of hadrons in terms of quarks and glu- ons (partons) is one of the most critical tasks in hadron physics. Three types of electron-hadron scattering provide incomplete information about the parton’s posi- tion, momentum, and angular momentum inside the hadron. Electromagnetic form factors (EM FFs), parton distribution functions (PDFs), and generalized parton dis- tributions (GPDs) can be obtained from elastic scattering, inclusive inelastic scattering, and exclusive inelastic scattering. A comprehensive understanding of these processes is crucial in studying hadron structure. In perturbative quantum chromodynamics, light-front dynamics is an essential theoretical framework for describing high-energy scattering processes, as it offers relatively simple vacuum states and has advantages of simple formulations in a Bjorken limit. In particular, the advantages of light-front dynamics are maximized in (1+1) dimensions, as each of light-front time-ordered amplitudes for light-front time ($x^+$) evolution is Lorentz invariant. Using $\phi^3$-scalar field theory, electromagnetic form factors of various mesons (pion, kaon, and D-meson) are described by a one-loop approximation, triangle diagrams, and fully analytical results of a local electromagnetic current allow us to analyze the EM FFs not only in a spacelike region ($q^2 < 0$) but also in a timelike region ($q^2 > 0$). In addition, the EM FFs of these two regions satisfy a dispersion relation induced by the analyticity of a scattering matrix. Singularity structures of a photon-loop correction in the timelike region are identified for several mesons, and various physical interpretations of charge and magnetic moment densities are con- sidered in the spacelike region. Since the existing perspective of spatial densities using a Breit frame exclude relativistic corrections, we newly defined the charge and magnetic moment densities with relativistic length contractions. It can be seen that the smaller the mass of the target, such as the pion meson, the greater the length contraction. In addition, a frame-independent variable $\tilde{z} = x^−P^+$ in the light- front coordinate was recently introduced. Using the variable, a longitudinal density is calculated in this work. The electromagnetic form factors of hadrons can be expressed in the longitudinal density through a Fourier transform, which can be seen to exist even in very large $\tilde{z}$ and to oscillate. Using the same theoretical model, exclusive inelastic scattering of $γ^∗(q)+ {}^4 \mbox{He}(P) → f_0(980)(q′)+ {}^4 \mbox{He}(P′)$ is evaluated through box and cat’s ears diagrams in the one-loop approximation, providing general Compton form factors (CFFs) in allowed kinematic regions ($q^2 = −Q^2 < 0$, $t < 0$). This is referred to as a VMP model in this study. For the same scattering process, a perturbative part and a non-perturbative part (GPDs) can be separated using a factorization method in perturbative quantum chromodynamics, which can be derived through an operator product expansion. If Q2 is much larger than mass squares of the target and produced meson, the cat’s ears diagram and some of the light-front time-order amplitudes are ignored, which is called leading-twist GPDs assuming handbag dominance. We discussed the importance of the cat’s ears contributions and validity of the handbag dominance from the perspective of a Ward identity and confirmed that the Ward identity is not restored even at points beyond large kinematic regions of $Q^2 > 20$ GeV$^2$. The main interest in the kinematic re- gion of deeply virtual Compton scattering at Jefferson Laboratory is $−t/Q^2 \sim 0.5$, and the CFFs obtained from VMP and GPDs models show a big difference in this kinematic region. Therefore, it is emphasized in this study that using the leading- twist GPDs for experimental observations requires careful attention. Additionally, the longitudinal density of the light-front wave function is evaluated in the PDFs, which shows sensitivity to binding energies of hadron targets and has a longer tail and faster oscillation behavior as the binding energy decreases.
Supervisor: Prof. Yongseok Oh