Electromagnetic finitesize effects to the hadronic vacuum polarization
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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 hadronicvacuumpolarization contribution. This requires the inclusion of O(α) electromagnetic corrections. The inclusion of electromagnetic interactions in lattice simulations is known to generate potentially large finitesize effects suppressed only by powers of the inverse spatial extent. In this paper we derive an analytic expression for the QEDL finitevolume corrections to the twopion contribution to the hadronic vacuum polarization at nexttoleading 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 finitevolume effects. For completeness we also calculate the hadronic vacuum polarization in infinite volume using a basis of 2loop master integrals.
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Research areas and keywords  Subject classification (UKÄ) – MANDATORY

Original language  English 

Article number  014508 
Journal  Physical Review D  Particles, Fields, Gravitation and Cosmology 
Volume  100 
Issue number  1 
Publication status  Published  2019 
Publication category  Research 
Peerreviewed  Yes 