Hadronic light-by-light scattering contribution to the muon g – 2 on the lattice

Abstract

We briefly review several activities at Mainz related to hadronic light-by-light scattering (HLbL) using lattice QCD. First we present a position-space approach to the HLbL contribution in the muon g−2, where we focus on exploratory studies of the pion-pole contribution in a simple model and the lepton loop in QED in the continuum and in infinite volume. The second part describes a lattice calculation of the double-virtual pion transition form factor F π 0 γ * γ * (q 2 1 , q 2 2 ) in the spacelike region with photon virtualities up to 1.5 GeV 2 which paves the way for a lattice calculation of the pion-pole contribution to HLbL. The third topic involves HLbL forward scattering amplitudes calculated in lattice QCD which can be described, using dispersion relations (HLbL sum rules), by γ * γ * → hadrons fusion cross sections and then compared with phenomenological models.

Hadronic-vacuum-polarization contribution to the muon’s anomalous magnetic moment from four-flavor lattice QCD

“…1, a HVP,LO µ requires knowledge of the quark vacuum-polarization function that couples to 1 Another key uncertainty in the Standard Model result comes from a higher-order hadronic piece known as the hadronic-lightby-light contribution. This is also being calculated in lattice QCD [8,9]. a photon [10,11].…”

Pion distribution amplitude from Euclidean correlation functions: Exploring universality and higher-twist effects

“…Hadronic contributions to the muon anomalous magnetic moment, which is on the verge of becoming a sensitive probe of physics beyond the Standard Model, constitute one such prominent example. In particular lattice calculations of the hadronic "light-by-light" scattering contribution [1,2] are set to become more precise than inferring this quantity from experimental measurements; see, e.g., Refs. [3,4] and references therein.…”

“…Taking into account contributions of the lowest and the next-to-lowest conformal spin, one obtains [57] Φ 4;π (α) = 120α 1 α 2 α 3 φ 1,π (α 1 − α 2 ) , Φ 4;π (α) = 120α 1 α 2 α 3 φ 0,π +φ 2,π (3α 3 − 1) , Ψ 4;π (α) = −30α 2 3 ψ 0,π (1−α 3…”

Elastic light-by-light scattering in a nonminimal Lorentz violation scenario

“…Elastic LbyL scattering is used to constrain nonlinear corrections to Maxwell electrodynamics [47] and it can also provide contribution to the anomalous magnetic moment of the muon [48,49], including chiral theories [50] and quantum chromodynamics (QCD) calculations, both for holographic models [51] and lattice QCD [52]. Furthermore, the signal of the vacuum processes are affected if new particles are coupled to photons.…”