# Electromagnetic finite-size effects to the hadronic vacuum polarization

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**Electromagnetic finite-size effects to the hadronic vacuum polarization.** / Bijnens, Johan; Harrison, James; Hermansson Truedsson, Nils; Janowski, Tadeusz; Juettner, Andreas; Portelli, Antonin.

Research output: Contribution to journal › Article

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*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 100, no. 1, 014508. https://doi.org/10.1103/PhysRevD.100.014508

### APA

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*100*(1), [014508]. https://doi.org/10.1103/PhysRevD.100.014508

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### MLA

*Physical Review D - Particles, Fields, Gravitation and Cosmology*. 2019. 100(1). https://doi.org/10.1103/PhysRevD.100.014508

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### RIS

TY - JOUR

T1 - Electromagnetic finite-size effects to the hadronic vacuum polarization

AU - Bijnens, Johan

AU - Harrison, James

AU - Hermansson Truedsson, Nils

AU - Janowski, Tadeusz

AU - Juettner, Andreas

AU - Portelli, Antonin

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

U2 - 10.1103/PhysRevD.100.014508

DO - 10.1103/PhysRevD.100.014508

M3 - Article

VL - 100

JO - Physical Review D

JF - Physical Review D

SN - 2470-0010

IS - 1

M1 - 014508

ER -