## 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

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Eur.Phys.J.C 80 (2020) 113 arXiv: 1902.08191 [hep-lat] |
---|---|

[2] |
Lucius
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Isabel
Campos,
Marco
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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
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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] |