Dispersive analysis of the pion transition form factor

Area of Science:

• High Energy Physics
• Quantum Field Theory
• Hadron Physics

Background:

• The pion transition form factor is crucial for understanding hadron structure and interactions.
• Previous studies have explored specific aspects of the pion transition form factor, but a comprehensive analysis is needed.
• Accurate calculations are essential for interpreting experimental data and theoretical predictions.

Purpose of the Study:

• To analyze the pion transition form factor using dispersion theory.
• To calculate the singly-virtual form factor in the time-like region and extend the analysis to the space-like region.
• To provide predictions for poorly-constrained regions and extract key parameters like the form factor slope.

Main Methods:

• Utilizing dispersion theory to analyze the pion transition form factor.
• Calculating the singly-virtual form factor in the time-like region using data for the e+e- cross section.
• Performing analytic continuation to the space-like region and deriving the necessary dispersive formalism for the doubly-virtual case.

Main Results:

• The singly-virtual pion transition form factor in the time-like region was calculated and verified against experimental data.
• The space-like transition form factor was predicted for the region below Q^2 = 1 GeV^2.
• The slope of the form factor at vanishing momentum transfer (Q^2 = 0) was extracted.

Conclusions:

• The study provides a robust framework for analyzing the pion transition form factor across different kinematic regimes.
• The results offer valuable predictions for the space-like form factor and its slope, aiding future experimental and theoretical investigations.
• The derived formalism is essential for calculating the pion-pole contribution to hadronic light-by-light scattering, impacting the anomalous magnetic moment of the muon.