Frequency-splitting estimators of single-propagator traces

Giusti, Leonardo; Harris, Tim; Nada, Alessandro; Schaefer, Stefan

doi:10.1140/epjc/s10052-019-7049-0

Cited by 34 publications

(37 citation statements)

References 45 publications

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“…To compute this difference, the "one-end trick", which has been applied extensively in twisted-mass fermion calculations [51,52], is used as proposed in Ref. [53]. The one-end trick yields an efficient estimator for the required difference of Wilson-quark loops based on the identity…”

Section: Higher-order Contributionsmentioning

confidence: 99%

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

et al. 2021

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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 .

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Section: Higher-order Contributionsmentioning

confidence: 99%

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

et al. 2021

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“…The results of the Mainz group was obtained on a reduced set of ensembles that includes 3 lattice spacings but no ensemble directly at the physical pion mass such that a chiral extrapolation was required and turned out to be the main source of uncertainty (since the isoscalar contribution is not singular in the chiral limit, the disconnected piece has to compensate the singularity present in the light quark contribution [ 72 ]). The Mainz group has recently presented a preliminary update [ 77 ] that includes more ensembles, including one at the physical pion mass and the new noise reduction technique proposed in [ 78 ]. Their preliminary results reduces the tension.…”

Section: Hadronic Vacuum Polarizationmentioning

confidence: 99%

The anomalous magnetic moment of the muon: status of lattice QCD calculations

Gérardin

2021

Eur. Phys. J. A

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In recent years, the anomalous magnetic moment of the muon has triggered a lot of activity in the lattice QCD community because a persistent tension of about is observed between the phenomenological estimate and the Brookhaven measurement. The current best phenomenological estimate has an uncertainty comparable to the experimental one and the error is completely dominated by hadronic effects: the leading order hadronic vacuum polarization (HVP) contribution and the hadronic light-by-light (HLbL) scattering contribution. Both are accessible via lattice simulations and a reduction of the error by a factor 4 is required in view of the forthcoming experiments at Fermilab and J-PARC whose results, expected in the next few years, should reduce the experimental precision down to the level of 0.14 ppm. In this article, I review the status of lattice calculations of those quantities, starting with the HVP. This contribution has now reached sub-percent precision and requires a careful understanding of all sources of systematic errors. The HLbL contribution, that is much smaller, still contributes significantly to the error. This contribution is more challenging to compute, but rapid progress has been made on the lattice in the last few years.

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“…We compute the light-connected contraction by averaging over 216 local sources put on the time-slice y 0 /a = 32 of Λ 0 which is at a distance of 8 lattice spacings from its right boundary and, as usual, by summing over the sink space-position. We determine the disconnected contraction by averaging each single-propagator trace over a large number of Gaussian random sources, namely 768, so to have a negligible random-noise contribution to the variance [4,7].…”

Section: Lattice Computationmentioning

confidence: 99%

“…A novel computational paradigm for the hadronic contribution to (g µ − 2) Leonardo Giusti = 3.0 fm, its statistical uncertainty is 2.1 which is still 3 times smaller with respect to the light-connected one. Clearly the disconnected contribution must be taken into account to attain a per-mille precision on the HVP, but the combined usage of split-even estimators [7] and two-level integration solves the problem of its computation. By combining the connected contributions at x max 0 = 3.0 fm with the disconnected part at x max 0 = 2.0 fm, the best total value that we obtain is a HVP µ = 522.4(6.2) • 10 −10 .…”

Section: Pos(ichep2020)378mentioning

confidence: 99%

A novel computational paradigm for a precise determination of the hadronic contribution to $(g-2)_\mu$ from lattice QCD

Giusti¹,

Brida²,

Harris³

2021

Proceedings of 40th International Conference on High Energy Physics — PoS(ICHEP2020)

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The hadronic contribution to the muon anomalous magnetic moment a µ = (g µ − 2)/2 has to be determined at the per-mille level for the Standard Model prediction to match the expected final uncertainty of the ongoing E989 experiment. That is 3 times better than the current precision from the dispersive approach, and 5-15 times smaller than the uncertainty based on the purely theoretical determinations from lattice QCD. So far the stumbling-block is the large statistical error in the Monte Carlo evaluation of the required correlation functions which can hardly be tamed by brute force. In this talk we present our proposal to solve this problem by multi-level Monte Carlo integration, a technique which reduces the variance of correlators exponentially in the distance of the fields. We report the results of our feasibility tests for the computation of the Hadronic Vacuum Polarization on a lattice with a linear extension of 3 fm, a spacing of 0.065 fm, and a pion mass of 270 MeV. Indeed the two-level integration makes the contribution to the statistical error from long-distances de-facto negligible by accelerating its inverse scaling with the cost of the simulation. These findings establish multi-level Monte Carlo as a solid and efficient method for a precise lattice determination of the hadronic contribution to a µ .

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Frequency-splitting estimators of single-propagator traces

Cited by 34 publications

References 45 publications

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

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

The anomalous magnetic moment of the muon: status of lattice QCD calculations

A novel computational paradigm for a precise determination of the hadronic contribution to $(g-2)_\mu$ from lattice QCD

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