Finite-volume effects in $(g-2{)}_{\mu }^{\text{HVP,LO}}$

Abstract

An analytic expression is derived for the leading finite-volume effects arising in lattice QCD calculations of the hadronic-vacuum-polarization contribution to the muon's magnetic moment, $a_{\mu }^{\text{HVP,LO}}\equiv (g-2{)}_{\mu }^{\text{HVP,LO}}/2$. For calculations in a finite spatial volume with periodicity $L$, $a_{\mu }^{\text{HVP,LO}}(L)$ admits a transseries expansion with exponentially suppressed $L$ scaling. Using a Hamiltonian approach, we show that the leading finite-volume correction scales as $\exp [-M_{\pi }L]$ with a prefactor given by the (infinite-volume) Compton amplitude of the pion, integrated with the muon-mass-dependent kernel. To give a complete quantitative expression, we decompose the Compton amplitude into the space-like pion form factor, $F_{\pi }(Q^2)$, and a multi-particle piece. We determine the latter through NLO in chiral perturbation theory and find that it contributes negligibly and through a universal term that depends only on the pion decay constant, with all additional low-energy constants dropping out of the integral.

5 pages, 2 tables, 1 figure, CERN-TH-2019-051, v2: Matches the published version. Fixed a sign mistake in a numerically suppressed contribution

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Cited by in corpus (20)

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• The hadronic running of the electromagnetic coupling and the electroweak mixing angle from lattice QCD
• The anomalous magnetic moment of the muon: status of Lattice QCD calculations
• Finite-volume and thermal effects in the leading-HVP contribution to muonic $(g-2)$
• Variations on the Maiani-Testa approach and the inverse problem
• On the application of Effective Field Theory to finite-volume effects in $a_{\mu }^{\mathrm{HVP}}$
• Muon $g-2$: Lattice calculations of the hadronic vacuum polarization
• Coordinate-space calculation of the window observable for the hadronic vacuum polarization contribution to $(g-2{)}_{\mu }$
• Hybrid calculation of hadronic vacuum polarization in muon g-2 to 0.48\%
• Analytic expansions of multi-hadron finite-volume energies: I. Two-particle states
• Recent Developments of Muon g-2 from Lattice QCD
• A model-independent framework for determining finite-volume effects of spatially nonlocal operators
• Running of the Electroweak Gauge Couplings from First Principles
• Round table on Standard Model Anomalies
• Precision lattice calculation of the hadronic contribution to the running of the electroweak gauge couplings
• Hadronic vacuum polarization to three loops in chiral perturbation theory