Hadronic light-by-light contribution to $$(g-2)_\mu $$ from lattice QCD: a complete calculation

Abstract

We compute the hadronic light-by-light scattering contribution to the muon $$g-2$$ g - 2 from the up, down, and strange-quark sector directly using lattice QCD. Our calculation features evaluations of all possible Wick-contractions of the relevant hadronic four-point function and incorporates several different pion masses, volumes, and lattice-spacings. We obtain a value of $$a_\mu ^{\text {Hlbl}}= 106.8(15.9) \times 10^{-11}$$ a μ Hlbl = 106.8 ( 15.9 ) × 10 - 11 (adding statistical and systematic errors in quadrature), which is consistent with current phenomenological estimates and a previous lattice determination. It now appears conclusive that the hadronic light-by-light contribution cannot explain the current tension between theory and experiment for the muon $$g-2$$ g - 2 .

Challenges for an axion explanation of the muon g − 2 measurement

“…Although the Standard Model calculation is fraught with difficulties, especially in pinning down hadronic contributions, various approaches have converged on consistent answers, as reviewed in ref. [4] 1 (also, see the very recent lattice calculation of the hadronic light-by-light contribution, consistent with earlier estimates [6]). The muon g − 2 anomaly is one of the most compelling discrepancies between theory and data that we have, so examination of possible new physics explanations are compelling.…”

“…The aFF term in the action is not gauge invariant, but must shift by a multiple of the periodicity of the QED θ term in order for exp(iS) to remain invariant. The conclusion depends on the global structure of the Standard Model gauge group, (SU(3 6 or Z 3 , then c γγ must be an integer, whereas if Γ = Z 2 or 1, then 9c γγ must be an integer [30]. We will assume the former: c γγ ∈ Z.…”

“…In this effective Lagrangian, there are three leading diagrams contributing to the lepton g − 2, as depicted in figure 1. 6 Note that using equation of motion or equivalently with chiral rotations of fermions, this operator could be rewritten as a combination [17,21]:…”

NNLO virtual and real leptonic corrections to muon-electron scattering

“…14 The latter contribution is similar in shape and size to the one of the muon loop. 12 We notice that, when considering the emission of an extra real electronic pair, p4 can be any of the final state e − or the e + momentum, according to which one represents the electron-like track. 13 Despite they are calculated in the MC code, here we do not show any effect due to τ or top quark loops because they are small on the scale of the effects induced by e, µ or hadronic loops.…”

“…Actually, there is at present general consensus that the latter has a small impact on the theoretical uncertainty on a µ [5] (see also refs. [10][11][12] for very recent investigations through dispersion relations and Lattice QCD calculations).…”