Hadronic vacuum polarization and vector-meson resonance parameters from .

Area of Science:

• Particle Physics
• Quantum Chromodynamics

Background:

• The anomalous magnetic moment of the muon ($$) is a key observable in particle physics.
• Hadronic vacuum polarization (HVP) contributions to $$ are sensitive to $$ and $$ resonance parameters.

Purpose of the Study:

• To evaluate the $$ channel's contribution to the HVP correction of the muon's anomalous magnetic moment.
• To determine the resonance parameters of $$ and $$ using a dispersive representation.

Main Methods:

• Dispersive representation of the $$ transition form factor.
• Analysis of the $$ and $$ channels within the $$ reaction.

Main Results:

• The $$ contribution to $$ was found to be $$.
• Resonance parameters for $$ and $$ were determined, resolving previous mass discrepancies.
• The $$ mass agrees with the Particle Data Group (PDG) average, while the $$ mass shows increased precision, highlighting tensions with isospin-breaking extractions.

Conclusions:

• The dispersive approach provides a consistent framework for analyzing $$ and $$ data.
• Precise determination of $$ and $$ masses is crucial for understanding $$ and potential new physics.