[Paper Review] Electromagnetic corrections to light hadron masses

Antonin Portelli, Stephan Dürr+10 more|arXiv (Cornell University)|Nov 18, 2010

Quantum Chromodynamics and Particle Interactions8 references4 citations

TL;DR

This paper presents a lattice QCD+QED framework to compute electromagnetic corrections to light hadron masses, incorporating U(1) QED fields on Nf=2+1 QCD ensembles. Preliminary results yield ΔₐD = 830 ± 180 MeV² and ΔᵣD = 0.60 ± 0.14, indicating significant violations to Dashen’s theorem, with strong consistency in isospin symmetry restoration via quark mass tuning.

ABSTRACT

At the precision reached in current lattice QCD calculations, electromagnetic effects are becoming numerically relevant. We will present preliminary results for electromagnetic corrections to light hadron masses, based on simulations in which a $\mathrm{U}(1)$ degree of freedom is superimposed on $N_f=2+1$ QCD configurations from the BMW collaboration.

Motivation & Objective

• To compute electromagnetic corrections to light hadron masses with high precision using lattice QCD+QED simulations.
• To investigate violations of Dashen’s theorem, particularly the absolute (ΔₐD) and relative (ΔᵣD) corrections.
• To validate a method for handling electromagnetic effects in finite-volume lattice QCD with global charge neutrality constraints.
• To restore isospin symmetry by tuning bare quark masses to cancel additive O(α/a) divergences from QED self-energy corrections.
• To provide a foundation for future high-precision studies of hadronic observables beyond the current preliminary results.

Proposed method

• Formalism of non-compact QED on a 4-torus with a constant background current to enforce global charge neutrality.
• Use of forward finite differences in the lattice action to avoid photon self-interactions, requiring explicit gauge fixing.
• Implementation of gauge conditions: A₀(0,0) = 0 and ∑ₖ p̃ₖÂₖ(p) = 0 in momentum space to ensure unique field configurations.
• Generation of QED gauge fields via multi-dimensional Gaussian random number drawing in momentum space, followed by inverse FFT to obtain position-space fields.
• Construction of U(1) compact links via U^QED_μ = exp(iqA_μ), embedding electromagnetic interactions into the QCD action.
• Subtraction of O(Q_q² α/a) additive divergences by retuning u and d quark masses to restore isospin symmetry in simulations.

Experimental results

Research questions

• RQ1 What is the magnitude of electromagnetic corrections to the pion and kaon squared masses in the isospin limit?
• RQ2 To what extent do electromagnetic effects violate Dashen’s theorem, as quantified by ΔₐD and ΔᵣD?
• RQ3 How do additive O(α/a) divergences from QED affect light quark masses, and can they be effectively subtracted?
• RQ4 Does the isospin symmetry restoration via quark mass tuning eliminate spurious electromagnetic splittings in the simulation?
• RQ5 Can a consistent QCD+QED framework be established on existing Nf=2+1 lattice ensembles for precision hadronic physics?

Key findings

• The electromagnetic mass splitting for the pion is Δ_EM M_π = 5.1 ± 1.1 MeV, yielding Δ_EM M_π² = 1380 ± 50 MeV².
• The kaon electromagnetic splitting is Δ_EM M_K = 2.2 ± 0.2 MeV, with Δ_EM M_K² = 2200 ± 180 MeV².
• The absolute violation to Dashen’s theorem is ΔₐD = 830 ± 180 MeV², indicating a significant deviation from the chiral limit prediction.
• The relative violation ΔᵣD = 0.60 ± 0.14 is consistent with non-perturbative QCD+QED effects and lies within the range of previous lattice and phenomenological estimates.
• Isospin symmetry is restored with high precision via quark mass tuning, as confirmed by linear dependence of PCAC masses on the subtraction parameter δ.
• The preliminary results validate the QCD+QED framework and support further high-precision studies with finer lattices, lighter quarks, and larger volumes.