White Paper Summary: Lattice QCD calculations of the HVP Aida X. El-Khadra University of Illinois Hadronic contributions to (g-2) μ Third Plenary Workshop of the Muon g-2 Theory Initiative Institute for Nuclear Theory, University of Washington 9-13 September 2019
Hadronic vacuum polarization ˆ Π ( q 2 ) = Π ( q 2 ) − Π (0) Z d 4 xe iqx h j µ ( x ) j ν (0) i = ( q µ q ν � q 2 g µ ν ) Π ( q 2 ) Π µ ν = ⌘ 2 Z ⇣ α Leading order HVP correction: dq 2 ω ( q 2 ) ˆ a HVP , LO Π ( q 2 ) = µ π • Use optical theorem and dispersion relation to rewrite the integral in terms of the hadronic e+e- cross section: ˆ = m 2 K ( s ) Z a HVP , LO µ σ exp ( s ) ds 12 π 3 µ s • This talk: discuss � calculated in lattice QCD a HVP,LO μ A. El-Khadra INT g-2 workshop, 9-13 Sep 2019 2 �
Lattice HVP WP authors Tom Blum, Mattia Bruno, Christine Davies, Michele Della Morte, Davide Giusti, Steven Gottlieb, Vera Gülpers, Gregorio Herdoíza, Taku Izubuchi, Christoph Lehner, Laurent Lellouch, Marina Marinkovic, Aaron S. Meyer, Kohtaroh Miura, Antonin Portelli, Silvano Simula, Ruth Van de Water, Georg von Hippel, Hartmut Wittig A. El-Khadra INT g-2 workshop, 9-13 Sep 2019 � 3
Lattice HVP WP organization III. Comparisons I. Introduction A. Comparison of total LO-HVP contribution A. The hadronic vacuum polarization B. Flavor-by-flavor comparison B. Calculating and integrating � to Π ( q 2 ) C. Toward lattice QCD consensus and permil- obtain � a μ level precision C.Time moments IV. Connections D. Coordinate-space representation A. HVP from lattice QCD and the MUonE E. Common issues experiment II. Strategies B. HVP from tau decays A. Connected light-quark contribution C. Hadronic corrections to the running of � α � a HLO ( ud ) μ sin 2 θ W and � 1. Statistical errors V.Summary and conclusions 2. Finite volume effects and long- A. Current status distance two-pion contributions B. Lessons learned 3. Discretization and scale setting C. Expected progress in the next (2?) years 4. Chiral extrapolation/interpolation B. Connected strange and charm contributions � a HLO ( s ), a HLO ( c ), a HLO ( b ) μ μ μ C. Disconnected term [ � ] a HLO discussion μ D. Strong and em IB contributions � δ a HLO μ A. El-Khadra INT g-2 workshop, 9-13 Sep 2019 � 4
Outline Introduction Methods for � with lattice QCD a HLO μ Charm and Strange contributions Noise reduction methods for light quark contributions Finite Volume corrections Lattice scale Continuum extrapolation Light quark connected � ( � ) a HVP m u = m d μ QED and Strong Isospin Breaking corrections Disconnected � a HVP μ Comparisons Summary and outlook A. El-Khadra INT g-2 workshop, 9-13 Sep 2019 � 5
Outline Introduction Methods for � with lattice QCD a HLO μ Charm and Strange contributions Noise reduction methods for light quark contributions Reviews by: Finite Volume corrections K. Miura @ Lattice 2018 Lattice scale V. Gülpers @ Lattice 2019 Continuum extrapolation Light quark connected � ( � ) a HVP m u = m d μ QED and Strong Isospin Breaking corrections Disconnected � a HVP μ Comparisons Summary and outlook A. El-Khadra INT g-2 workshop, 9-13 Sep 2019 � 5
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