Lattice Field Theory

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.

People

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

• Lucius Bushnaq (Trinity College Dublin)
• Dr. Isabel Campos (Instituto de Física de Cantabria & IFCA-CSIC)
• Dr. Marco Catillo (ETH Zürich)
• Alessandro Cotellucci (Humboldt-Universität zu Berlin)
• Madeleine Dale (Università di Roma Tor Vergata & INFN)
• Dr. Patrick Fritzsch (Trinity College Dublin)
• Jens Lücke (Humboldt-Universität zu Berlin & IRIS Adlershof & DESY Zeuthen)
• Prof. Dr. Marina Krstić Marinković (ETH Zürich)
• Prof. Dr. Agostino Patella (Humboldt-Universität zu Berlin & IRIS Adlershof & DESY Zeuthen)
• Prof. Dr. Nazario Tantalo (Università di Roma Tor Vergata & INFN)

Computing grants and resources

• North-German Supercomputing Alliance (HLRN), Germany; projects bep00085 and bep00102; machine: Lise; principal investigator: Agostino Patella.
• Poznan Supercomputing and Networking Center (PSNC), Poland; projects 450 and 466; machine: Eagle; principal investigator: Isabel Campos.
• Swiss National Supercomputing Centre (CSCS), Switzerland; projects go22 and go24 (ETHZ’s share); machine: Piz Daint; principal investigator: Marina Krstic Marinkovic.
• CINECA, Italy; LQCD123 INFN theoretical initiative’s share; machine: Marconi; subproject leader: Nazario Tantalo.

Documents and links

• Initial application for bep00085 project at HLRN here.
• Initial application for bep00102 project at HLRN here.
• Jens Lücke’s presentation at Lattice2021 here.
• Madelaine Dale’s presentation at Lattice2021 here.

Bibliography

[1]	S. Aoki, Y. Aoki, D. Bečirević, T. Blum, G. Colangelo, S. Collins, M. Della Morte, P. Dimopoulos, S. Dürr, H. Fukaya, et al. FLAG Review 2019: Flavour Lattice Averaging Group (FLAG) Eur.Phys.J.C 80 (2020) 113 arXiv: 1902.08191 [hep-lat]
[2]	Lucius Bushnaq, Isabel Campos, Marco Catillo, Alessandro Cotellucci, Madeleine Dale, Patrick Fritzsch, Jens Lücke, Marina Krstić Marinković, Agostino Patella, Nazario Tantalo An update on QCD+QED simulations with C* boundary conditions arXiv: 2108.11989 [hep-lat]
[3]	Andreas S. Kronfeld, U.J. Wiese SU(N) gauge theories with C periodic boundary conditions. 1. Topological structure Nucl.Phys.B 357 (1991) 521
[4]	Andreas S. Kronfeld, U.J. Wiese SU(N) gauge theories with C periodic boundary conditions. 2. Small volume dynamics Nucl.Phys.B 401 (1993) 190 arXiv: hep-lat/9210008 [hep-lat]
[5]	U.J. Wiese C periodic and G periodic QCD at finite temperature Nucl.Phys.B 375 (1992) 45
[6]	L. Polley Boundaries for SU(3)(C) x U(1)-el lattice gauge theory with a chemical potential Z.Phys.C 59 (1993) 105
[7]	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]
[8]	Agostino Patella QED Corrections to Hadronic Observables PoS LATTICE2016 (2017) 020 arXiv: 1702.03857 [hep-lat]
[9]	Martin Hansen, Biagio Lucini, Agostino Patella, Nazario Tantalo Gauge invariant determination of charged hadron masses JHEP 05 (2018) 146 arXiv: 1802.05474 [hep-lat]
[10]	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]