Pion electromagnetic form factor at spacelike momenta.

Area of Science:

• Quantum Chromodynamics (QCD)
• Particle Physics
• Theoretical Nuclear Physics

Background:

• The pion electromagnetic form factor is crucial for understanding hadron structure.
• Previous calculations often relied on approximations that limited their domain of validity.
• Dynamical chiral symmetry breaking is a fundamental phenomenon in QCD.

Purpose of the Study:

• To develop a novel method for computing the pion electromagnetic form factor across its entire spacelike domain.
• To unify the calculation of the form factor with the pion's valence-quark parton distribution amplitude.
• To investigate the role of hard contributions and dynamical chiral symmetry breaking.

Main Methods:

• Utilizing the Dyson-Schwinger equation (DSE) framework within Quantum Chromodynamics (QCD).
• Integrating the computation of the pion electromagnetic form factor with its valence-quark parton distribution amplitude (PDA).
• Comparing leading-order perturbative QCD results with the full DSE computation.

Main Results:

• The DSE framework successfully computes the pion electromagnetic form factor over the entire spacelike momentum transfer domain.
• The unified PDA, derived from the DSE, leads to a leading-order perturbative QCD result that underestimates the full computation by only 15% for Q²≳8 GeV².
• Hard contributions are shown to dominate the pion form factor at high momentum transfer (Q²≳8 GeV²).

Conclusions:

• The DSE approach provides a consistent framework for understanding the pion's electromagnetic form factor and its PDA.
• The results highlight the importance of non-perturbative effects, such as dynamical chiral symmetry breaking, in shaping the pion's properties.
• The study offers a more accurate description of the pion electromagnetic form factor compared to methods using asymptotic PDAs.