The Mellin-Barnes Approach to Hadronic Vacuum Polarization and $g_{\mu }-2$

Abstract

It is shown that with a precise determination of a few derivatives of the hadronic vacuum polarization (HVP) self-energy function $\Pi (Q^2)$ at $Q^2=0$, from lattice QCD (LQCD) or from a dedicated low-energy experiment, one can obtain an evaluation of the lowest order HVP contribution to the anomalous magnetic moment of the muon $a_{\mu }^{\mathrm{HVP}}$ with an accuracy comparable to the one reached using the $e^{+}{e}^{-}$ annihilation cross-section into hadrons. The technique of Mellin-Barnes approximants (MBa) that we propose is illustrated in detail with the example of the two loop vacuum polarization function in QED. We then apply it to the first few moments of the hadronic spectral function obtained from experiment and show that the resulting MBa evaluations of $a_{\mu }^{\mathrm{HVP}}$ converge very quickly to the full experimental determination.

arXiv comment37 pages, many figures. V2: Numerical results updated according to arXiv:1802.02995v1. V3: Published version with improvements suggested by the referee, conclusions unchanged

References in corpus (22)

• Final Report of the Muon E821 Anomalous Magnetic Moment Measurement at BNL
• Reevaluation of the Hadronic Contributions to the Muon g-2 and to alpha(MZ)
• The muon $g-2$ and $\alpha (M_Z^2)$: a new data-based analysis
• (g-2)_mu and alpha(M_Z^2) re-evaluated using new precise data
• 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
• Lattice calculation of the lowest order hadronic contribution to the muon anomalous magnetic moment
• Measuring the leading hadronic contribution to the muon g-2 via $\mu e$ scattering
• Hadronic vacuum polarization contribution to the anomalous magnetic moments of leptons from first principles
• Hadronic Contributions to the Muon $g-2$ and Low-Energy QCD
• Strong-isospin-breaking correction to the muon anomalous magnetic moment from lattice QCD at the physical point
• The hadronic vacuum polarization contribution to $a_{\mu }$ from full lattice QCD
• Towards a precise lattice determination of the leading hadronic contribution to (g-2)_mu
• The Muon (g-2) Theory Value: Present and Future
• Four-Flavour Leading-Order Hadronic Contribution To The Muon Anomalous Magnetic Moment
• Isospin breaking corrections to meson masses and the hadronic vacuum polarization: a comparative study
• 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
• Slope and curvature of the hadron vacuum polarization at vanishing virtuality from lattice QCD
• Multiple Mellin-Barnes Integrals as Periods of Calabi-Yau Manifolds With Several Moduli
• Moment Analysis of Hadronic Vacuum Polarization - Proposal for a lattice QCD evaluation of $g_{\mu }-2$
• Hadronic Vacuum Polarization in QCD and its Evaluation in the Euclidean
• Anomalous magnetic moment of the muon, a hybrid approach

Cited by in corpus (12)

• The anomalous magnetic moment of the muon in the Standard Model
• Leading hadronic contribution to the muon magnetic moment from lattice QCD
• Calculation of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment
• Scalar Meson Contributions to a_μfrom Hadronic Light-by-Light Scattering
• Lattice QCD and 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
• Hadronic corrections to $\mu$-$e$ scattering at NNLO with space-like data
• Multiple Series Representations of $N$-fold Mellin-Barnes Integrals
• On Constraints Between $\Delta {\alpha }_{\mathrm{had}}(M_Z^2)$ and $(g_{\mu }-2{)}_{\mathrm{HVP}}$
• Higher-order hadronic-vacuum-polarization contribution to the muon g-2 from lattice QCD
• Hadronic Vacuum Polarization and the MUonE proposal
• On the Time Momentum Representation of Hadronic Vacuum Polarization and ${\mathbf{g}}_{\mathbf{\mu }}-2$