# The 39th International Symposium on Lattice Field Theory (Lattice 2022)

Aug 8 – 13, 2022
Hörsaalzentrum Poppelsdorf
Europe/Berlin timezone

## Finite-Size Effects of the Hadronic Vacuum Polarization Contribution to the Muon $(g-2)$ with C$^{\star}$ Boundary Conditions

Aug 11, 2022, 9:40 AM
20m
CP1-HSZ/Ground-0.001 - HS3 (CP1-HSZ)

### CP1-HSZ/Ground-0.001 - HS3

#### CP1-HSZ

50
Oral Presentation QCD in searches for physics beyond the Standard Model

### Speaker

Sofie Martins (University of Southern Denmark)

### Description

The muon $(g−2)$ is a compelling quantity due to the current standing tensions among the experimental average, data-driven theoretical results, and lattice results. Matching the final target accuracy of the experiments at Fermilab and J-PARC will constitute a major challenge for the lattice community in the coming years. For this reason, it is worthwhile to consider different options to keep the systematic errors under control. In this talk, we discuss finite-volume effects of the leading Hadron Vacuum Polarization (HVP) contribution to the muon $(g-2)$ in the presence of C$^{\star}$ boundary conditions. When considering isospin-breaking corrections to the HVP, C$^{\star}$ boundary conditions provide a possible consistent formulation of QCD+QED in finite volume. Even though these boundary conditions can be avoided in the calculation of the leading HVP contribution, we find the interesting result that they remove the leading exponential finite-volume correction. In practice, compared to the periodic case, C$^{\star}$ boundary conditions cut the finite-size effects in half on a lattice of physical size $M_{\pi}L=4$ and by a factor of almost ten for $M_{\pi}L=8$. The origin of this reduction will be the focus of this talk.

### Primary author

Sofie Martins (University of Southern Denmark)

### Co-author

Agostino Patella (Humboldt University Berlin)