An analysis of systematic effects in finite size scaling studies using the gradient flow

Nada, Alessandro; Ramos, Alberto

doi:10.1140/epjc/s10052-020-08759-1

Cited by 99 publications

(28 citation statements)

References 34 publications

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“…This procedure is similar to the approach taken in [38], and we encourage the reader interested in the details to consult that reference.…”

Section: Determination Of λ(μ Had )mentioning

confidence: 99%

“…After this non-perturbative conversion, the known 3-loop β-function in the SF scheme [51,52,53] can be used to determine the ratio Λ MS /(2µ had ). This procedure is similar to the approach taken in [38], and we encourage the reader interested in the details to consult that reference.…”

Section: Msmentioning

confidence: 99%

“…Finally, due to the use of an asymmetrical torus, the memory footprint required to simulate this scheme in a computer is reduced. The computing power stays roughly the same because with this geometry the observables show a larger variance [38], but this scheme allows for a better usage of current GPU clusters.…”

Section: Introductionmentioning

confidence: 99%

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Memory efficient finite volume schemes with twisted boundary conditions

et al. 2021

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In this paper we explore a finite volume renormalization scheme that combines three main ingredients: a coupling based on the gradient flow, the use of twisted boundary conditions and a particular asymmetric geometry, that for SU(N) gauge theories consists on a hypercubic box of size $$l^2 \times (Nl)^2$$ l 2 × ( N l ) 2 , a choice motivated by the study of volume independence in large N gauge theories. We argue that this scheme has several advantages that make it particularly suited for precision determinations of the strong coupling, among them translational invariance, an analytic expansion in the coupling and a reduced memory footprint with respect to standard simulations on symmetric lattices, allowing for a more efficient use of current GPU clusters. We test this scheme numerically with a determination of the $$\Lambda $$ Λ parameter in the SU(3) pure gauge theory. We show that the use of an asymmetric geometry has no significant impact in the size of scaling violations, obtaining a value $$\Lambda _{\overline{\mathrm{MS}}}\sqrt{8 t_0} =0.603(17)$$ Λ MS ¯ 8 t 0 = 0.603 ( 17 ) in good agreement with the existing literature. The role of topology freezing, that is relevant for the determination of the coupling in this particular scheme and for large N applications, is discussed in detail.

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“…This procedure is similar to the approach taken in [38], and we encourage the reader interested in the details to consult that reference.…”

Section: Determination Of λ(μ Had )mentioning

confidence: 99%

Section: Msmentioning

confidence: 99%

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Memory efficient finite volume schemes with twisted boundary conditions

et al. 2021

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“…Eq. ( 1) defers this computation to the pure gauge theory, where very high precision can be achieved [15,16]. We computed a finite volume coupling in a setting with f = 3 mass-degenerate heavy quarks for values of the quark mass ranging from charm to above the bottom and already provided a proof of principle that Eq.…”

Section: Introductionmentioning

confidence: 99%

“…A solution to this multiscale problem has been known for 30 years in the form of the recursive step-scaling method [13]. The method has since been applied to the running of the coupling in QCD with N f = 0 [2,3,14,15], N f = 2 [16,17], N f = 3 [5,18] and N f = 4 [19,20] quark flavours (for a review cf. [21]), and in various candidate models of physics beyond the Standard Model (for reviews, cf.…”

Section: Introductionmentioning

confidence: 99%

Results for $\alpha_s$ from the decoupling strategy

Höllwieser¹,

Brida²,

Knechtli³

et al. 2022

Proceedings of the 38th International Symposium on Lattice Field Theory — PoS(LATTICE2021)

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We present analysis details and new results for the strong coupling ( ), determined by the decoupling strategy. We measure a massive gradient flow (GF) coupling defined in finite volume with Schrödinger functional (SF) boundary conditions in a theory with f = 3 degenerate heavy quarks of mass . The massive couplings are matched to effective couplings in pure gauge. Using the running in the pure gauge theory and the perturbative relation of the Lambda parameters, the Lambda parameter of the three flavor theory is obtained by an extrapolation to infinite M. Our final result is compatible both with the FLAG average and with the previous ALPHA result, albeit with a slightly smaller, yet still statistics dominated, error. This constitutes a non-trivial check, as the decoupling strategy is conceptually very different from the 3-flavor QCD step-scaling method, and so are most of its systematic errors. These include the uncertainties of the decoupling and continuum limits, which we discuss in some detail. Furthermore, by relying on decoupling once again, we could estimate the small ( ) and (1/ ) contaminations to the massive GF coupling stemming from the SF boundaries by means of pure gauge simulations.

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Large‐scale asymmetry in galaxy spin directions: Analysis of galaxies with spectra in DES, SDSS, and DESI Legacy Survey

Shamir

2022

Astron Nachr

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Multiple previous studies using several different probes have shown considerable evidence for the existence of cosmological‐scale anisotropy and a Hubble‐scale axis. One of the probes that show such evidence is the distribution of the directions toward which galaxies spin. The advantage of the analysis of the distribution of galaxy spin directions compared to the cosmic microwave background anisotropy is that the ratio of galaxy spin directions is a relative measurement, and therefore less sensitive to background contamination such as Milky Way obstruction. Another advantage is that many spiral galaxies have spectra, and therefore allow to analyze the location of such axis relative to Earth. This paper shows an analysis of the distribution of the spin directions of over 90K galaxies with spectra. That analysis is also compared to previous analyses using the Earth‐based Sloan Digital Sky Survey, Panoramic Survey Telescope and Rapid Response System, and Dark Energy Spectroscopic Instrument Legacy Survey, as well as space‐based data collected by Hubble Space Telescope. The results show very good agreement between the distribution patterns observed with the different telescopes. The dipole or quadrupole axes formed by the spin directions of the galaxies with spectra do not necessarily go directly through Earth.

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An analysis of systematic effects in finite size scaling studies using the gradient flow

Abstract: We propose a new strategy for the determination of the step scaling function $$\sigma (u)$$ σ ( u ) in finite size scaling studies using the gradient flow. In this approach the determination of $$\sigma (u)$$ σ ( u ) is broken in two pieces: a c… Show more

Cited by 99 publications

References 34 publications

Memory efficient finite volume schemes with twisted boundary conditions

Memory efficient finite volume schemes with twisted boundary conditions

Results for $\alpha_s$ from the decoupling strategy

Large‐scale asymmetry in galaxy spin directions: Analysis of galaxies with spectra in DES, SDSS, and DESI Legacy Survey

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