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A non-perturbative exploration of the high energy regime in $N_\text{f}=3$ QCD

Using continuum extrapolated lattice data we trace a family of running couplings in three-flavour QCD over a large range of scales from about 4 to 128 GeV. The scale is set by the finite space time volume so that recursive finite size techniques can be applied, and Schrödinger functional (SF) bounda...

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Autores principales: Dalla Brida, Mattia, Fritzsch, Patrick, Korzec, Tomasz, Ramos, Alberto, Sint, Stefan, Sommer, Rainer
Lenguaje:eng
Publicado: 2018
Materias:
Acceso en línea:https://dx.doi.org/10.1140/epjc/s10052-018-5838-5
http://cds.cern.ch/record/2310808
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author Dalla Brida, Mattia
Fritzsch, Patrick
Korzec, Tomasz
Ramos, Alberto
Sint, Stefan
Sommer, Rainer
author_facet Dalla Brida, Mattia
Fritzsch, Patrick
Korzec, Tomasz
Ramos, Alberto
Sint, Stefan
Sommer, Rainer
author_sort Dalla Brida, Mattia
collection CERN
description Using continuum extrapolated lattice data we trace a family of running couplings in three-flavour QCD over a large range of scales from about 4 to 128 GeV. The scale is set by the finite space time volume so that recursive finite size techniques can be applied, and Schrödinger functional (SF) boundary conditions enable direct simulations in the chiral limit. Compared to earlier studies we have improved on both statistical and systematic errors. Using the SF coupling to implicitly define a reference scale $1/L_0\approx 4$  GeV through $\bar{g}^2(L_0) =2.012$ , we quote $L_0 \Lambda ^{N_\mathrm{f}=3}_{{\overline{\mathrm{MS}}}} =0.0791(21)$ . This error is dominated by statistics, in particular, the remnant perturbative uncertainty is negligible and very well controlled, by connecting to infinite renormalization scale from different scales $2^n/L_0$ for $n=0,1,\ldots ,5$ . An intermediate step in this connection may involve any member of a one-parameter family of SF couplings. This provides an excellent opportunity for tests of perturbation theory some of which have been published in a letter (ALPHA collaboration, M. Dalla Brida et al. in Phys Rev Lett 117(18):182001, 2016). The results indicate that for our target precision of 3 per cent in $L_0 \Lambda ^{N_\mathrm{f}=3}_{{\overline{\mathrm{MS}}}}$ , a reliable estimate of the truncation error requires non-perturbative data for a sufficiently large range of values of $\alpha _s=\bar{g}^2/(4\pi )$ . In the present work we reach this precision by studying scales that vary by a factor $2^5= 32$ , reaching down to $\alpha _s\approx 0.1$ . We here provide the details of our analysis and an extended discussion.
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spelling cern-23108082023-08-11T04:19:35Zdoi:10.1140/epjc/s10052-018-5838-5http://cds.cern.ch/record/2310808engDalla Brida, MattiaFritzsch, PatrickKorzec, TomaszRamos, AlbertoSint, StefanSommer, RainerA non-perturbative exploration of the high energy regime in $N_\text{f}=3$ QCDhep-phParticle Physics - Phenomenologyhep-latParticle Physics - LatticeUsing continuum extrapolated lattice data we trace a family of running couplings in three-flavour QCD over a large range of scales from about 4 to 128 GeV. The scale is set by the finite space time volume so that recursive finite size techniques can be applied, and Schrödinger functional (SF) boundary conditions enable direct simulations in the chiral limit. Compared to earlier studies we have improved on both statistical and systematic errors. Using the SF coupling to implicitly define a reference scale $1/L_0\approx 4$  GeV through $\bar{g}^2(L_0) =2.012$ , we quote $L_0 \Lambda ^{N_\mathrm{f}=3}_{{\overline{\mathrm{MS}}}} =0.0791(21)$ . This error is dominated by statistics, in particular, the remnant perturbative uncertainty is negligible and very well controlled, by connecting to infinite renormalization scale from different scales $2^n/L_0$ for $n=0,1,\ldots ,5$ . An intermediate step in this connection may involve any member of a one-parameter family of SF couplings. This provides an excellent opportunity for tests of perturbation theory some of which have been published in a letter (ALPHA collaboration, M. Dalla Brida et al. in Phys Rev Lett 117(18):182001, 2016). The results indicate that for our target precision of 3 per cent in $L_0 \Lambda ^{N_\mathrm{f}=3}_{{\overline{\mathrm{MS}}}}$ , a reliable estimate of the truncation error requires non-perturbative data for a sufficiently large range of values of $\alpha _s=\bar{g}^2/(4\pi )$ . In the present work we reach this precision by studying scales that vary by a factor $2^5= 32$ , reaching down to $\alpha _s\approx 0.1$ . We here provide the details of our analysis and an extended discussion.Using continuum extrapolated lattice data we trace a family of running couplings in three-flavour QCD over a large range of scales from about 4 to 128 GeV. The scale is set by the finite space time volume so that recursive finite size techniques can be applied, and Schr\"odinger functional (SF) boundary conditions enable direct simulations in the chiral limit. Compared to earlier studies we have improved on both statistical and systematic errors. Using the SF coupling to implicitly define a reference scale $1/L_0\approx 4$ GeV through $\bar{g}^2(L_0) =2.012$, we quote $L_0 \Lambda^{N_{\rm f}=3}_{\overline{\rm MS}} =0.0791(21)$. This error is dominated by statistics; in particular, the remnant perturbative uncertainty is negligible and very well controlled, by connecting to infinite renormalization scale from different scales $2^n/L_0$ for $n=0,1,\ldots,5$. An intermediate step in this connection may involve any member of a one-parameter family of SF couplings. This provides an excellent opportunity for tests of perturbation theory some of which have been published in a letter [1]. The results indicate that for our target precision of 3 per cent in $L_0 \Lambda^{N_{\rm f}=3}_{\overline{\rm MS}}$, a reliable estimate of the truncation error requires non-perturbative data for a sufficiently large range of values of $\alpha_s=\bar{g}^2/(4\pi)$. In the present work we reach this precision by studying scales that vary by a factor $2^5= 32$, reaching down to $\alpha_s\approx 0.1$. We here provide the details of our analysis and an extended discussion.arXiv:1803.10230CERN-TH-2018-060DESY 18-044WUB/18-01DESY-18-044WUB-18-01oai:cds.cern.ch:23108082018-03-27
spellingShingle hep-ph
Particle Physics - Phenomenology
hep-lat
Particle Physics - Lattice
Dalla Brida, Mattia
Fritzsch, Patrick
Korzec, Tomasz
Ramos, Alberto
Sint, Stefan
Sommer, Rainer
A non-perturbative exploration of the high energy regime in $N_\text{f}=3$ QCD
title A non-perturbative exploration of the high energy regime in $N_\text{f}=3$ QCD
title_full A non-perturbative exploration of the high energy regime in $N_\text{f}=3$ QCD
title_fullStr A non-perturbative exploration of the high energy regime in $N_\text{f}=3$ QCD
title_full_unstemmed A non-perturbative exploration of the high energy regime in $N_\text{f}=3$ QCD
title_short A non-perturbative exploration of the high energy regime in $N_\text{f}=3$ QCD
title_sort non-perturbative exploration of the high energy regime in $n_\text{f}=3$ qcd
topic hep-ph
Particle Physics - Phenomenology
hep-lat
Particle Physics - Lattice
url https://dx.doi.org/10.1140/epjc/s10052-018-5838-5
http://cds.cern.ch/record/2310808
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