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Electromagnetic finite-size effects to the hadronic vacuum polarisation

Electromagnetic finite-size effects to the hadronic vacuum polarisation
Electromagnetic finite-size effects to the hadronic vacuum polarisation
In order to reach (sub-)per cent level precision in lattice calculations of the hadronic vacuum polarisation, isospin breaking corrections must be included. This requires introducing QED on the lattice, and the associated finite-size effects are potentially large due to the absence of a mass gap. This means that the finite-size effects scale as an inverse polynomial in $L$ rather than being exponentially suppressed. Considering the $\mathcal{O}(\alpha)$ corrected hadronic vacuum polarisation in QED$_{\mathrm{L}}$ with scalar QED as an effective theory, we show that the first possible term, which is of order $1/L^{2}$, vanishes identically so that the finite-size effects start at order $1/L^{3}$. This cancellation is understood from the neutrality of the currents involved, and we show that this cancellation is universal by also including form factors for the pions. We find good numerical agreement with lattice perturbation theory calculations, as well as, up to exponentially suppressed terms, scalar QED lattice simulations.
hep-lat, hep-ph
1824-8039
Hermansson-Truedsson, Nils
9d43bb05-729d-4f80-88e8-e578cf30e6d9
Bijnens, Johan
f1bad498-910e-4411-9918-9fae78c70e2d
Harrison, James
3bf4b4aa-9186-45bb-9888-87bf46284172
Janowski, Tadeusz
775172a7-cf5f-4ea5-b92e-ed718faf7485
Jüttner, Andreas
a90ff7c5-ae8f-4c8e-9679-b5a95b2a6247
Portelli, Antonin
a2526d4a-144e-4095-802a-229cddb10f0f
Hermansson-Truedsson, Nils
9d43bb05-729d-4f80-88e8-e578cf30e6d9
Bijnens, Johan
f1bad498-910e-4411-9918-9fae78c70e2d
Harrison, James
3bf4b4aa-9186-45bb-9888-87bf46284172
Janowski, Tadeusz
775172a7-cf5f-4ea5-b92e-ed718faf7485
Jüttner, Andreas
a90ff7c5-ae8f-4c8e-9679-b5a95b2a6247
Portelli, Antonin
a2526d4a-144e-4095-802a-229cddb10f0f

Hermansson-Truedsson, Nils, Bijnens, Johan, Harrison, James, Janowski, Tadeusz, Jüttner, Andreas and Portelli, Antonin (2020) Electromagnetic finite-size effects to the hadronic vacuum polarisation. Proceedings of Science, 363. (doi:10.22323/1.363.0018).

Record type: Article

Abstract

In order to reach (sub-)per cent level precision in lattice calculations of the hadronic vacuum polarisation, isospin breaking corrections must be included. This requires introducing QED on the lattice, and the associated finite-size effects are potentially large due to the absence of a mass gap. This means that the finite-size effects scale as an inverse polynomial in $L$ rather than being exponentially suppressed. Considering the $\mathcal{O}(\alpha)$ corrected hadronic vacuum polarisation in QED$_{\mathrm{L}}$ with scalar QED as an effective theory, we show that the first possible term, which is of order $1/L^{2}$, vanishes identically so that the finite-size effects start at order $1/L^{3}$. This cancellation is understood from the neutrality of the currents involved, and we show that this cancellation is universal by also including form factors for the pions. We find good numerical agreement with lattice perturbation theory calculations, as well as, up to exponentially suppressed terms, scalar QED lattice simulations.

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1910.03250v1
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e-pub ahead of print date: 5 November 2019
Published date: 27 August 2020
Venue - Dates: International Symposium on Lattice Field Theory, , Wuhan, China, 2019-06-16 - 2019-06-22
Keywords: hep-lat, hep-ph

Identifiers

Local EPrints ID: 448057
URI: http://eprints.soton.ac.uk/id/eprint/448057
ISSN: 1824-8039
PURE UUID: 2e517aa1-caf4-472b-a583-84a790aabea1
ORCID for James Harrison: ORCID iD orcid.org/0000-0002-3643-0489
ORCID for Andreas Jüttner: ORCID iD orcid.org/0000-0002-3978-0927
ORCID for Antonin Portelli: ORCID iD orcid.org/0000-0002-6059-917X

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Date deposited: 01 Apr 2021 15:40
Last modified: 13 Apr 2021 01:46

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Contributors

Author: Nils Hermansson-Truedsson
Author: Johan Bijnens
Author: James Harrison ORCID iD
Author: Tadeusz Janowski
Author: Antonin Portelli ORCID iD

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