The leading disconnected contribution to the anomalous magnetic moment of the muon

Abstract

The hadronic vacuum polarization can be determined from the vector correlator in a mixed timemomentum representation. We explicitly calculate the disconnected contribution to the vector correlator, both in the N f = 2 theory and with an additional quenched strange quark, using non-perturbatively O(a)-improved Wilson fermions. All-to-all propagators are computed using stochastic sources and a generalized hopping parameter expansion. Combining the result with the dominant connected contribution, we are able to estimate an upper bound for the systematic error that arises from neglecting the disconnected contribution in the determination of (g − 2) µ .

The hadronic vacuum polarization contribution to the muon g − 2 from lattice QCD

“…This concerns both a hvp µ , studied in [28][29][30][31][32][33][34][35][36][37][38][39][40], as well as a hlbl µ [41][42][43][44][45][46][47][48][49]. Lattice calculations of a hvp µ proceed by evaluating a convolution integral over Euclidean momenta Q 2 [28,50].…”

“…Statistically accurate results for quantities such as ∆ f require "all-to-all" propagators which are commonly computed using stochastic noise sources. In [35] it was shown that the statistical accuracy of G disc (x 0 ) can be significantly enhanced when ∆ ud and ∆ s are computed using the same random noise vectors, since the correlations between the light and strange quark contributions largely cancel the stochastic noise.…”

Lattice calculation of the leading strange quark-connected contribution to the muon g − 2

“…Recently, for example, the full set of quark-disconnected contributions, so far believed to be the main obstacle in obtaining a lattice determination of a (2)had µ at the percent level, has been computed with much improved precision in lattice QCD with physical light quark masses [17]. The crucial step in this computation was identifying the dynamics mainly responsible for the disconnected contribution and tailoring corresponding lattice techniques [17,22].…”

Estimate of the hadronic vacuum polarization disconnected contribution to the anomalous magnetic moment of the muon from lattice QCD

“…The fit, using a time range from 3 to 40 is stable from 6 exponentials upwards with a χ 2 /dof = 1.1 (Q=0.2). It gives am ω = 0.1537 (10) and am φ = 0.1775 (7). am ω is somewhat lower than the value (0.1568(4)) obtained by the Hadron Spectum collaboration which included mixing between light and strange bilinears using more operators and the generalised eigenvalue fit method [24].…”

“…Calculations of the disconnected contribution to a μ;HVP have concentrated on stochastic determinations using various noise-reduction methods and several calculations are underway, see, for example Ref. [10].…”