Finite-Volume Effects in (g-2)_{μ}^{HVP,LO}

Area of Science:

• Quantum Chromodynamics (QCD)
• Particle Physics
• Computational Physics

Background:

• The muon's magnetic moment anomaly is a key observable in particle physics.
• Lattice QCD calculations are crucial for theoretical predictions.
• Finite-volume effects can impact the accuracy of these calculations.

Purpose of the Study:

• To derive an analytic expression for leading-order finite-volume effects in lattice QCD.
• To analyze the hadronic-vacuum-polarization contribution to the muon's magnetic moment.
• To provide a quantitative understanding of volume dependence in lattice calculations.

Main Methods:

• Development of an analytic expression for finite-volume effects.
• Utilizing a Hamiltonian approach to study volume scaling.
• Decomposition of the Compton amplitude into pion form factor and multiparticle contributions.
• Employing chiral perturbation theory to determine multiparticle contributions.

Main Results:

• The leading finite-volume correction scales as exp[-MπL].
• The prefactor is related to the pion Compton amplitude and a muon-mass-dependent kernel.
• The multiparticle contribution is found to be negligible and universal, depending only on the pion decay constant.

Conclusions:

• An accurate analytic expression for leading-order finite-volume effects in lattice QCD is established.
• The derived formula provides insights into the volume dependence of the muon's magnetic moment calculation.
• The results simplify the analysis by showing the independence of low-energy constants in the multiparticle contribution.