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Exponential Error Reduction for Glueball Calculations Using a Two-Level Algorithm in Pure Gauge Theory

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arxiv 2406.12656 v1 pith:TXFEROSN submitted 2024-06-18 hep-lat

Lorenzo Barca , Francesco Knechtli , Sofie Martins , Michael Peardon , Stefan Schaefer , Juan Andrés Urrea-Niño This is my paper · ORCID
classification hep-lat
keywords algorithmglueballreductionstandardcalculationschannelsdistancesexponential
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

This study explores the application of a two-level algorithm to enhance the signal-to-noise ratio of glueball calculations in four-dimensional $\mathrm{SU(3)}$ pure gauge theory. Our findings demonstrate that the statistical errors exhibit an exponential reduction, enabling reliable extraction of effective masses at distances where current standard methods would demand exponentially more samples. However, at shorter distances, standard methods prove more efficient due to a saturation of the variance reduction using the multi-level method. We discuss the physical distance at which the multi-level sampling is expected to outperform the standard algorithm, supported by numerical evidence across different lattice spacings and glueball channels. Additionally, we construct a variational basis comprising 35 Wilson loops up to length 12 and 5 smearing sizes each, presenting results for the first state in the spectrum for the scalar, pseudoscalar, and tensor channels.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Lattice evidence that scalar glueballs are small

    hep-lat 2025-08 conditional novelty 8.0 of 10

    First lattice extraction of scalar glueball gravitational form factors gives a mass radius of 0.263(31) fm, smaller than typical hadrons.

  2. Scaling and Luescher Term in a non-Abelian (2+1)d SU$(2)$ Quantum Link Model

    hep-lat 2026-02 conditional novelty 6.0 of 10

    In an SU(2) quantum link model on a hexagonal lattice, the static quark potential shows a coupling-dependent Lüscher term and logarithmically growing string width, indicating a rough confining string with no continuum limit.

  3. Flavor mixing in charmonium and light mesons with optimal distillation profiles

    hep-lat 2025-02 conditional novelty 6.0 of 10

    In two lattice QCD ensembles, flavor-singlet charmonium and light-meson operators mix with each other and with gluonic operators, and adding a two-pion operator reveals an additional low-lying state.

  4. Test of a two-level algorithm for the glueball spectrum in $SU(N_c)$ Yang-Mills theory

    hep-lat 2025-01 conditional novelty 4.0 of 10

    A new implementation of the two-level algorithm for SU(N_c) gauge theory produces glueball masses consistent with established lattice values and shows improved error scaling at large time separations.

  5. Update on Glueballs

    hep-lat 2025-02 unverdicted novelty 2.0 of 10

    A lattice QCD review concludes that, based on exploratory calculations, no scalar hadron below roughly 2 GeV appears to be predominantly a glueball.

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