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Register a new userElectromagnetic finite-size effects to the hadronic vacuum polarisation
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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 finite-size effects are potentially large due to the absence of a mass gap. This means that the finite-size effects scale as an inverse polynomial in $L$ rather than being exponentially suppressed. Considering the $mathcal{O}(alpha)$ corrected hadronic vacuum polarisation in QED$_{mathrm{L}}$ 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 finite-size 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.
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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 sub-percent accuracy on the hadronic-vacuum-polarization contribution. This requires the inclusion of $mathcal{O}(alpha)$ 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 $mathrm{QED}_{mathrm{L}}$ 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 $1/L^{3}$ where $L$ is the spatial extent. A $1/L^{2}$ 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.
We present steps towards the computation of the leading-order hadronic contribution to the muon anomalous magnetic moment on RBC/UKQCD physical point DWF ensembles. We discuss several methods for controlling and reducing uncertainties associated to the determination of the HVP form factor.
We compute the vacuum polarisation on the lattice in quenched QCD using non-perturbatively improved Wilson fermions. Above Q^2 of about 2 GeV^2 the results are very close to the predictions of perturbative QCD. Below this scale we see signs of non-perturbative effects which we can describe by the use of dispersion relations. We use our results to estimate the light quark contribution to the muons anomalous magnetic moment. We find the result 446(23) x 10^{-10}, where the error only includes statistical uncertainties. Finally we make some comments on the applicability of the Operator Product Expansion to our data.
We present a relativistic and model-independent method to derive structure-dependent electromagnetic finite-size effects. This is a systematic procedure, particularly well-suited for automatization, which works at arbitrarily high orders in the large-volume expansion. Structure-dependent coefficients appear as zero-momentum derivatives of physical form factors which can be obtained through experimental measurements or auxiliary lattice calculations. As an application we derive the electromagnetic finite-size effects on the pseudoscalar meson mass and leptonic decay amplitude, through orders $mathcal{O}(1/L^3)$ and $mathcal{O}(1/L^2)$, respectively. The structure dependence appears at this order through the meson charge radius and the real radiative leptonic amplitude, which are known experimentally.
We report on the MILC Collaboration calculation of electromagnetic effects on light pseudoscalar mesons. The simulations employ asqtad staggered dynamical quarks in QCD plus quenched photons, with lattice spacings varying from 0.12 to 0.06 fm. Finite volume corrections for the MILC realization of lattice electrodynamics have been calculated in chiral perturbation theory and applied to the lattice data. These corrections differ from those calculated by Hayakawa and Uno because our treatment of zero modes differs from theirs. Updated results for the corrections to Dashens theorem are presented.
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