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Electromagnetic finite-size effects to the hadronic vacuum polarization

Bijnens, Johan LU orcid ; Harrison, James ; Hermansson Truedsson, Nils LU orcid ; Janowski, Tadeusz ; Juettner, Andreas and Portelli, Antonin (2019) In Physical Review D - Particles, Fields, Gravitation and Cosmology 100(1).
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... (More)
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. (Less)
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author
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organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Physical Review D - Particles, Fields, Gravitation and Cosmology
volume
100
issue
1
article number
014508
publisher
American Physical Society
external identifiers
  • scopus:85070282662
ISSN
2470-0010
DOI
10.1103/PhysRevD.100.014508
project
Higher Order Calculations for Low Energy Precision Physics
language
English
LU publication?
yes
id
90b063d8-b53a-45f1-8626-a212e5653426
date added to LUP
2019-08-12 14:33:37
date last changed
2024-04-16 17:42:14
@article{90b063d8-b53a-45f1-8626-a212e5653426,
  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.}},
  author       = {{Bijnens, Johan and Harrison, James and Hermansson Truedsson, Nils and Janowski, Tadeusz and Juettner, Andreas and Portelli, Antonin}},
  issn         = {{2470-0010}},
  language     = {{eng}},
  number       = {{1}},
  publisher    = {{American Physical Society}},
  series       = {{Physical Review D - Particles, Fields, Gravitation and Cosmology}},
  title        = {{Electromagnetic finite-size effects to the hadronic vacuum polarization}},
  url          = {{http://dx.doi.org/10.1103/PhysRevD.100.014508}},
  doi          = {{10.1103/PhysRevD.100.014508}},
  volume       = {{100}},
  year         = {{2019}},
}