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Pion electromagnetic form factor at spacelike momenta.

L Chang1, I C Cloët, C D Roberts

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This study computes the pion electromagnetic form factor using Dyson-Schwinger equations. The novel method unifies predictions and shows hard contributions dominate at high momentum transfer.

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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.