Lattice Field Theory

Institut für Physik
Mathematisch-Naturwissen­schaft­liche Fakultät
Humboldt-Universität zu Berlin

QCD+QED simulations

Isospin is an approximate symmetry of Quantum Chromodynamics. Under an isospin transformation, the up and down quarks are rotated one into another. In reality this symmetry is broken by the fact that the up and down quark have different masses and electric charges. Isospin-breaking effects on hadronic observables are of order of 1%. Just to give an example, in an isospin-symmetric universe the proton and neutron would be completely indentical. Because of isospin-symmetric effects the proton is slightly lighter than the neutron.

Since isospin-breaking effects are generally small, traditionally lattice QCD simulations are performed in the isospin-symmetric limit. This approximation is no longer justified when observables are calculated with a subpercent precision, as in the case of leptonic and semileptonic decay rates of π and K mesons [1]. At this level of precision, the up and down mass difference and the coupling to QED can not be neglected.

In practice we simulate QCD+QED on a four-dimensional lattice at various values of the fine-structure constant α in such a way that physical observables can be interpolated at the physical value of α ≃ 1/137 [2]. The signature of this project is the use of C* (aka C-parity) boundary conditions [3][4][5][6] which allow for a local and gauge-invariant formulation of QED in finite volume and in the charged sector of the theory [7][8][9].

The generated configurations will be used to explore a variety of observables, primarily meson and baryon correlators and masses, leptonic and (in a more distant future) semileptonic decay rates of mesons, the hadronic contributions to the anomalous magnetic moment of the muon.

The open-source openQ*D-1.1 code [10] is used to generate gauge configurations and measure observables.


This work is done with the RC* collaboration, which includes researcher from several international institutions. The active members of the RC* collaboration are:

Computing grants and resources


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arXiv: 1902.08191 [hep-lat]
Jens Luecke, Lucius Bushnaq, Isabel Campos, Marco Catillo, Alessandro Cotellucci, Madeleine Evie Beth Dale, Patrick Fritzsch, Marina Krstić Marinković, Agostino Patella, Nazario Tantalo
An update on QCD+QED simulations with C* boundary conditions
PoS LATTICE2021 (2022) 293
arXiv: 2108.11989 [hep-lat]
Andreas S. Kronfeld, U.J. Wiese
SU(N) gauge theories with C periodic boundary conditions. 1. Topological structure
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Andreas S. Kronfeld, U.J. Wiese
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arXiv: hep-lat/9210008 [hep-lat]
U.J. Wiese
C periodic and G periodic QCD at finite temperature
Nucl.Phys.B 375 (1992) 45
L. Polley
Boundaries for SU(3)(C) x U(1)-el lattice gauge theory with a chemical potential
Z.Phys.C 59 (1993) 105
Biagio Lucini, Agostino Patella, Alberto Ramos, Nazario Tantalo
Charged hadrons in local finite-volume QED+QCD with C$^{⋆}$ boundary conditions
JHEP 02 (2016) 076
arXiv: 1509.01636 [hep-th]
Agostino Patella
QED Corrections to Hadronic Observables
PoS LATTICE2016 (2017) 020
arXiv: 1702.03857 [hep-lat]
Martin Hansen, Biagio Lucini, Agostino Patella, Nazario Tantalo
Gauge invariant determination of charged hadron masses
JHEP 05 (2018) 146
arXiv: 1802.05474 [hep-lat]
Isabel Campos, Patrick Fritzsch, Martin Hansen, Marina Krstic Marinkovic, Agostino Patella, Alberto Ramos, Nazario Tantalo
openQ*D code: a versatile tool for QCD+QED simulations
Eur.Phys.J.C 80 (2020) 195
arXiv: 1908.11673 [hep-lat]