
Nils HermanssonTruedsson, Johan Bijnens, James Harrison, Tadeusz Janowski, Andreas Jüttner, Antonin Portelli
Electromagnetic finitesize effects to the hadronic vacuum polarisation
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 finitesize effects are potentially large due to the absence of a mass gap. This means that the finitesize effects scale as an inverse polynomial in L rather than being exponentially suppressed. Considering the O(α) corrected hadronic vacuum polarisation in QEDL 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 finitesize 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.
LU TP 1947
