[Paper Review] Exploring the timelike region for the elastic form factors in a scalar field theory

Ho-Meoyng Choi, Chueng Ji|arXiv (Cornell University)|Jun 3, 1999

Gas Dynamics and Kinetic Theory2 citations

TL;DR

This study investigates elastic form factors of $q\bar{Q}$ bound states in both spacelike and timelike regions using an exactly solvable (3+1)-dimensional scalar field theory with gauge interactions. Employing light-front quantization in the Drell-Yan-West ($q^+=0$) and purely longitudinal momentum ($q^+ \neq 0$, $q_\perp=0$) frames, analytic continuation from the spacelike to timelike region yields results identical to direct timelike calculations, confirming exact equivalence and automatically incorporating nonvalence contributions, with meson peaks emerging at VMD-like positions.

ABSTRACT

We investigate the form factors of $q\\bar{Q}$ bound states both in spacelike and timelike region using an exactly solvable model of (3+1) dimensional scalar field theory interacting with gauge fields. Based on the light-front quantization, the Drell-Yan-West ($q^+=0$) frame as well as the purely longitudinal momentum ($q^+ \ eq 0$ and $q_{\\perp}=0$) frame were used for the calculations of the form factors of $M\ o\\gamma+M$ transitions. We then analytically continue the form factors in the spacelike region to the timelike region and compare those with the direct results of the timelike form factors of $\\gamma\ o M+\\bar{M}$ transitions. Our results verify the exact equivalence of the two results and exhibit that the method of analytic continuation automatically yields the effect of complicate nonvalence contributions. The meson peaks analogous to the vector meson dominance(VMD) phenomena are also generated at the usual VMD positions.

Motivation & Objective

• To investigate the behavior of elastic form factors in both spacelike and timelike regions for $q\bar{Q}$ bound states in a (3+1)-dimensional scalar field theory.
• To examine whether analytic continuation from the spacelike to timelike region reproduces the same results as direct computation in the timelike domain.
• To explore the role of nonvalence contributions in form factor calculations and assess whether they emerge naturally via analytic continuation.
• To determine if meson peaks analogous to vector meson dominance (VMD) phenomena appear at the expected positions in the timelike region.

Proposed method

• Utilization of light-front quantization in the Drell-Yan-West frame ($q^+=0$) for form factor calculations.
• Application of the purely longitudinal momentum frame ($q^+ \neq 0$, $q_\perp=0$) to compute form factors for $M \to \gamma + M$ transitions.
• Analytic continuation of form factors from the spacelike region to the timelike region to compare with directly computed timelike results.
• Use of an exactly solvable model of (3+1)-dimensional scalar field theory coupled to gauge fields to ensure analytical tractability.
• Comparison of the analytic continuation results with direct timelike calculations for $\gamma \to M + \bar{M}$ transitions.

Experimental results

Research questions

• RQ1 Does analytic continuation from the spacelike to timelike region reproduce the same form factor results as direct computation in the timelike domain?
• RQ2 Are nonvalence contributions to the form factors automatically captured through the analytic continuation procedure?
• RQ3 Do meson peaks analogous to vector meson dominance (VMD) phenomena emerge at the standard VMD positions in the timelike region?
• RQ4 How do the form factors behave in the purely longitudinal momentum frame compared to the Drell-Yan-West frame?

Key findings

• The form factors obtained via analytic continuation from the spacelike region exactly match the results from direct computation in the timelike region, confirming their equivalence.
• The analytic continuation method automatically incorporates complex nonvalence contributions without explicit construction.
• Meson peaks analogous to vector meson dominance (VMD) phenomena appear at the usual VMD positions in the timelike region.
• The results are consistent across both the Drell-Yan-West frame and the purely longitudinal momentum frame, validating the robustness of the approach.