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Electromagnetic finite-size effects to the hadronic vacuum polarization

Electromagnetic finite-size effects to the hadronic vacuum polarization
Electromagnetic finite-size effects to the hadronic vacuum polarization

In order to reduce the current hadronic uncertainties in the theory prediction for the anomalous magnetic moment of the muon, lattice calculations need to reach subpercent accuracy on the hadronic-vacuum-polarization contribution. This requires the inclusion of O(α) electromagnetic corrections. The inclusion of electromagnetic interactions in lattice simulations is known to generate potentially large finite-size effects suppressed only by powers of the inverse spatial extent. In this paper we derive an analytic expression for the QEDL finite-volume corrections to the two-pion contribution to the hadronic vacuum polarization at next-to-leading order in the electromagnetic coupling in scalar QED. The leading term is found to be of order 1/L3 where L is the spatial extent. A 1/L2 term is absent since the current is neutral and a photon far away thus sees no charge and we show that this result is universal. Our analytical results agree with results from the numerical evaluation of loop integrals as well as simulations of lattice scalar U(1) gauge theory with stochastically generated photon fields. In the latter case the agreement is up to exponentially suppressed finite-volume effects. For completeness we also calculate the hadronic vacuum polarization in infinite volume using a basis of 2-loop master integrals.

2470-0010
1-22
Bijnens, J.
da3af796-8096-43d0-bf11-163fe0945c53
Harrison, J.
fdf514a9-bd98-4fbc-9431-56b053cbd2fc
Hermansson-Truedsson, N.
949c6b3d-7b1c-4a1a-a5fd-fbe09b9e8053
Janowski, T.
775172a7-cf5f-4ea5-b92e-ed718faf7485
Jüttner, A.
a90ff7c5-ae8f-4c8e-9679-b5a95b2a6247
Portelli, A.
a2526d4a-144e-4095-802a-229cddb10f0f
Bijnens, J.
da3af796-8096-43d0-bf11-163fe0945c53
Harrison, J.
fdf514a9-bd98-4fbc-9431-56b053cbd2fc
Hermansson-Truedsson, N.
949c6b3d-7b1c-4a1a-a5fd-fbe09b9e8053
Janowski, T.
775172a7-cf5f-4ea5-b92e-ed718faf7485
Jüttner, A.
a90ff7c5-ae8f-4c8e-9679-b5a95b2a6247
Portelli, A.
a2526d4a-144e-4095-802a-229cddb10f0f

Bijnens, J., Harrison, J., Hermansson-Truedsson, N., Janowski, T., Jüttner, A. and Portelli, A. (2019) Electromagnetic finite-size effects to the hadronic vacuum polarization. Physical Review D, 100 (1), 1-22. (doi:10.1103/PhysRevD.100.014508).

Record type: Article

Abstract

In order to reduce the current hadronic uncertainties in the theory prediction for the anomalous magnetic moment of the muon, lattice calculations need to reach subpercent accuracy on the hadronic-vacuum-polarization contribution. This requires the inclusion of O(α) electromagnetic corrections. The inclusion of electromagnetic interactions in lattice simulations is known to generate potentially large finite-size effects suppressed only by powers of the inverse spatial extent. In this paper we derive an analytic expression for the QEDL finite-volume corrections to the two-pion contribution to the hadronic vacuum polarization at next-to-leading order in the electromagnetic coupling in scalar QED. The leading term is found to be of order 1/L3 where L is the spatial extent. A 1/L2 term is absent since the current is neutral and a photon far away thus sees no charge and we show that this result is universal. Our analytical results agree with results from the numerical evaluation of loop integrals as well as simulations of lattice scalar U(1) gauge theory with stochastically generated photon fields. In the latter case the agreement is up to exponentially suppressed finite-volume effects. For completeness we also calculate the hadronic vacuum polarization in infinite volume using a basis of 2-loop master integrals.

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e-pub ahead of print date: 24 July 2019
Published date: July 2019

Identifiers

Local EPrints ID: 433427
URI: https://eprints.soton.ac.uk/id/eprint/433427
ISSN: 2470-0010
PURE UUID: 65c42f36-d49b-41a7-8386-4a575a4e4bbb
ORCID for A. Portelli: ORCID iD orcid.org/0000-0002-6059-917X

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Date deposited: 22 Aug 2019 16:30
Last modified: 17 Sep 2019 00:43

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Contributors

Author: J. Bijnens
Author: J. Harrison
Author: N. Hermansson-Truedsson
Author: T. Janowski
Author: A. Jüttner
Author: A. Portelli ORCID iD

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