Constraints on the [Formula: see text] form factor from analyticity and unitarity

Area of Science:

• High Energy Physics
• Quantum Chromodynamics (QCD)
• Particle Physics

Background:

• Recent theoretical calculations of the electromagnetic pion form factor show discrepancies with experimental data.
• Understanding the pion form factor is crucial for testing fundamental physics theories.

Purpose of the Study:

• To investigate the electromagnetic pion form factor using analyticity and unitarity.
• To derive bounds on the pion form factor and check against experimental results.

Main Methods:

• Employed the method of unitarity bounds, utilizing analyticity and unitarity principles.
• Used a QCD correlator computed via operator product expansion and perturbative QCD.
• Incorporated the two-pion contribution using high-precision pion form factor data.

Main Results:

• Derived upper and lower bounds for the modulus of the pion form factor in the elastic region.
• The results serve as a significant check on standard dispersion relation calculations.
• Confirmed a disagreement between theoretical predictions and experimental data around 1 GeV.

Conclusions:

• The method of unitarity bounds provides a robust framework for constraining the pion form factor.
• The confirmed discrepancy suggests potential issues with either theoretical models or experimental measurements.
• Further investigation is warranted to resolve the observed tension in the electromagnetic pion form factor.