Finite-volume and thermal effects in the leading-HVP contribution to muonic $(g-2)$

Abstract

The leading finite-volume and thermal effects, arising in numerical lattice QCD calculations of $a_{\mu }^{\text{HVP,LO}}\equiv (g-2{)}_{\mu }^{\text{HVP,LO}}/2$, are determined to all orders with respect to the interactions of a generic, relativistic effective field theory of pions. In contrast to earlier work based in the finite-volume Hamiltonian, the results presented here are derived by formally summing all Feynman diagrams contributing to the Euclidean electromagnetic-current two-point function, with any number of internal pion loops and interaction vertices. As was already found in our previous publication, the leading finite-volume corrections to $a_{\mu }^{\text{HVP,LO}}$ scale as $\exp [-mL]$ where $m$ is the pion mass and $L$ is the length of the three periodic spatial directions. In this work we additionally control the two sub-leading exponentials, scaling as $\exp [-\sqrt{2}mL]$ and $\exp [-\sqrt{3}mL]$. As with the leading term, the coefficient of these is given by the forward Compton amplitude of the pion, meaning that all details of the effective theory drop out of the final result. Thermal effects are additionally considered, and found to be sub-percent-level for typical lattice calculations. All finite-volume corrections are presented both for $a_{\mu }^{\text{HVP,LO}}$ and for each time slice of the two-point function, with the latter expected to be particularly useful in correcting small to intermediate current separations, for which the series of exponentials exhibits good convergence.

arXiv comment74 pages, 7 figures, 3 tables, CERN-TH-2020-053, HU-EP-20/08; v2: added missing references and included more detailed numerical comparison, corrected factor of (-1/3) in finite-T results, leading to a change in table 3

References in corpus (35)

• Final Report of the Muon E821 Anomalous Magnetic Moment Measurement at BNL
• The Muon g-2
• Measurement of the Negative Muon Anomalous Magnetic Moment to 0.7 ppm
• The muon $g-2$ and $\alpha (M_Z^2)$: a new data-based analysis
• Reevaluation of the hadronic vacuum polarisation contributions to the Standard Model predictions of the muon g-2 and alpha(mZ) using newest hadronic cross-section data
• The $g-2$ of charged leptons, $\alpha (M_Z^2)$ and the hyperfine splitting of muonium
• A new evaluation of the hadronic vacuum polarisation contributions to the muon anomalous magnetic moment and to $\mathbf{\alpha }({\mathbf{m}}_{\mathbf{Z}}^2)$
• Calculation of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment
• Weak transition matrix elements from finite-volume correlation functions
• Vector Correlators in Lattice QCD: methods and applications
• Lattice calculation of the lowest order hadronic contribution to the muon anomalous magnetic moment
• Hadronic vacuum polarization contribution to the anomalous magnetic moments of leptons from first principles
• Muon g-2 Theory: the Hadronic Part
• The leading hadronic contribution to $(g-2{)}_{\mu }$ from lattice QCD with $N_{\mathrm{f}}=2+1$ flavours of O($a$) improved Wilson quarks
• Lattice QCD and the Timelike Pion Form Factor
• Hadronic-vacuum-polarization contribution to the muon's anomalous magnetic moment from four-flavor lattice QCD
• Light quark vacuum polarization at the physical point and contribution to the muon $g-2$
• The hadronic vacuum polarization contribution to the muon $g-2$ from lattice QCD
• Connected and leading disconnected hadronic light-by-light contribution to the muon anomalous magnetic moment with physical pion mass
• The pion form factor from lattice QCD with two dynamical flavours
• The hadronic vacuum polarization contribution to $a_{\mu }$ from full lattice QCD
• Calculation of the hadronic vacuum polarization disconnected contribution to the muon anomalous magnetic moment
• Charged hadrons in local finite-volume QED+QCD with C* boundary conditions
• Strange and charm quark contributions to the anomalous magnetic moment of the muon
• The light-quark contribution to the leading HVP term of the muon $g-2$ from twisted-mass fermions
• Four-Flavour Leading-Order Hadronic Contribution To The Muon Anomalous Magnetic Moment
• Strange and charm HVP contributions to the muon ($g-2)$ including QED corrections with twisted-mass fermions
• Finite-volume effects in the muon anomalous magnetic moment on the lattice
• Finite-volume effects in $(g-2{)}_{\mu }^{\text{HVP,LO}}$
• An estimate of the hadronic vacuum polarization disconnected contribution to the anomalous magnetic moment of the muon from lattice QCD
• Lattice calculation of the leading strange quark-connected contribution to the muon $g-2$
• Vector two-point functions in finite volume using partially quenched chiral perturbation theory
• Hadronic light-by-light scattering contribution to the muon g-2 on the lattice
• Recent Developments of Muon g-2 from Lattice QCD
• Experiences from the Commissioning and First Physics Run of the Fermilab Muon g-2 Experiment

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• Leading hadronic contribution to the muon magnetic moment from lattice QCD
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• The anomalous magnetic moment of the muon in the Standard Model: an update
• Light-quark connected intermediate-window contributions to the muon $g-2$ hadronic vacuum polarization from lattice QCD
• The hadronic running of the electromagnetic coupling and the electroweak mixing angle from lattice QCD
• The role of boundary conditions in quantum computations of scattering observables
• The anomalous magnetic moment of the muon: status of Lattice QCD calculations
• Study muon g-2 at two-loop level in the $U(1{)}_X$SSM
• Variations on the Maiani-Testa approach and the inverse problem
• On the application of Effective Field Theory to finite-volume effects in $a_{\mu }^{\mathrm{HVP}}$
• 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
• Running of the Electroweak Gauge Couplings from First Principles
• Hadronic vacuum polarization to three loops in chiral perturbation theory
• A model-independent framework for determining finite-volume effects of spatially nonlocal operators
• Precision lattice calculation of the hadronic contribution to the running of the electroweak gauge couplings