[Paper Review] Electromagnetic Corrections to Meson Masses and the HVP

Peter Boyle, Vera Gülpers+4 more|arXiv (Cornell University)|Dec 18, 2016

Particle physics theoretical and experimental studies23 references4 citations

TL;DR

This study computes electromagnetic corrections to meson masses and the hadronic vacuum polarization (HVP) using two methods: a stochastic approach with dynamical U(1) photon fields and a perturbative QED expansion in the path integral. Both methods agree within errors, with the stochastic method yielding ~2× lower statistical errors for the same computational cost, and QED corrections to the anomalous magnetic moment are consistent with zero at ≤1% for the up quark.

ABSTRACT

We present an exploratory study of the electromagnetic corrections to meson masses and the hadronic vacuum polarization using $N_f=2+1$ Domain Wall fermions. These corrections are estimated with two different approaches, a stochastic approach using $U(1)$ gauge configurations for the photon fields, and a perturbative approach through a QED perturbative expansion of the QCD+QED path integral. We compare results and statistical errors from both methods.

Motivation & Objective

• To compute electromagnetic corrections to meson masses and the hadronic vacuum polarization (HVP) in lattice QCD with full QED inclusion.
• To compare two distinct approaches—stochastic generation of U(1) photon fields and perturbative QED expansion—for handling QED effects.
• To assess the statistical efficiency and consistency of both methods in estimating QED corrections at the 1% precision level.
• To evaluate the impact of QED corrections on the anomalous magnetic moment and HVP form factors.
• To identify key open issues, such as disconnected diagrams and finite-volume effects, for future work.

Proposed method

• Uses Nf=2+1 Domain Wall fermions on a 64×24³ lattice with a⁻¹ = 1.78 GeV and mπ ≈ 340 MeV.
• Employs a stochastic method by generating U(1) photon fields independently on SU(3) gauge configurations, using the QEDL formulation to remove zero modes.
• Applies a perturbative approach by expanding the QCD+QED path integral in the fine-structure constant α, computing corrections at O(α) to meson masses and HVP.
• Implements Feynman and Coulomb gauge fixing in the photon action to ensure gauge invariance and reflection positivity.
• Uses the same bare quark masses for both QCD and QCD+QED calculations, with valence up/down quark masses tuned to approximate physical isospin splitting.
• Scales statistical errors by computational cost (number of inversions) to compare efficiency between methods.

Experimental results

Research questions

• RQ1 How do the stochastic and perturbative methods for QED corrections compare in terms of statistical precision and consistency for meson masses and HVP?
• RQ2 What is the magnitude of QED corrections to the anomalous magnetic moment of the muon, and are they consistent with zero within errors?
• RQ3 Does the stochastic method yield lower statistical errors than the perturbative approach for the same computational cost in HVP and meson mass corrections?
• RQ4 What is the impact of QED corrections on the multiplicative renormalization ZV of the vector current in the HVP?
• RQ5 How significant are finite-volume effects and quark-disconnected diagrams for QED corrections to the HVP?

Key findings

• The stochastic and perturbative methods yield consistent results for QED corrections to meson masses and the HVP, validating both approaches.
• The stochastic method achieves approximately 2 times lower statistical error per inversion for the HVP form factor and 2–2.5 times lower for the renormalized HVP compared to the perturbative method.
• QED corrections to the anomalous magnetic moment are consistent with zero within statistical errors, with an upper limit of ≤1% for the up quark and smaller for down and strange quarks due to charge suppression.
• The QED correction to the HVP is dominated by the additive renormalization of the vector current, and future work will include the multiplicative correction ZV¹Π⁰(Q²).
• Disconnected diagrams, such as the one with a photon coupling two quark loops, are expected to contribute significantly and are not SU(3) flavor suppressed, necessitating inclusion in future studies.
• Finite-volume effects for QED corrections to the HVP are expected to be significant and will be addressed in future work.