Static energy in ( 2 + 1 + 1 )-flavor lattice QCD: Scale setting and charm effects

Brambilla, Nora; Delgado, Rafael L.; Kronfeld, Andreas S.; Leino, Viljami; Petreczky, Peter; Steinbeißer, Sebastian; Vairo, Antonio; Weber, Johannes H.

doi:10.1103/PhysRevD.107.074503

Title: Static energy in ( $2 + 1 + 1$ )-flavor lattice QCD: Scale setting and charm effects

Abstract

We present results for the static energy in (2 + 1 + 1 )-flavor QCD over a wide range of lattice spacings and several quark masses, including the physical quark mass, with ensembles of lattice-gauge-field configurations made available by the MILC Collaboration. We obtain results for the static energy out to distances of nearly 1 fm, allowing us to perform a simultaneous determination of the scales r₁ and r₀, as well as the string tension σ. For the smallest three lattice spacings we also determine the scale r₂. Our results for r₀ r₁ and r₀$$\sqrt{σ}$$ agree with published (2 + 1)-flavor results. However, our result for r₁/r₂ differs significantly from the value obtained in the (2 + 1 -flavor case, which is most likely due to the effect of the charm quark. We also report results for r₀, r₁, and r₂ in fm, with the former two being slightly lower than published (2 + 1)-flavor results. We study in detail the effect of the charm quark on the static energy by comparing our results on the finest two lattices with the previously published (2 + 1)-flavor QCD results at similar lattice spacing. We find that for r > 0.2 fm our results on the static energy agree with the (2 + 1)-flavor result, implying the decoupling of the charm quark for these distances. For smaller distances, on the other hand, we find that the effect of the dynamical charm quark is noticeable. The lattice results agree well with the two-loop perturbative expression of the static energy incorporating finite charm mass effects. This is the first time that the decoupling of the charm quark is observed and quantitatively analyzed on lattice data of the static energy.

Authors:

;

; Petreczky, Peter;

; Vairo, Antonio;

; TUMQCD Collaboration

Publication Date:: Tue Apr 11 00:00:00 EDT 2023

Research Org.:: Brookhaven National Laboratory (BNL), Upton, NY (United States); Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP)

Contributing Org.:: TUMQCD Collaboration

OSTI Identifier:: 1969421

Alternate Identifier(s):: OSTI ID: 1874300

Report Number(s):: TUM-EFT 154/21; HU-EP-22/19-RTG; FERMILAB-PUB-22-438-T; arXiv:2206.03156
Journal ID: ISSN 2470-0010; PRVDAQ; 074503

Grant/Contract Number:: AC02-07CH11359; SC0012704

Resource Type:: Published Article

Journal Name:: Physical Review. D.

Additional Journal Information:: Journal Name: Physical Review. D. Journal Volume: 107 Journal Issue: 7; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; effective field theory; lattice QCD; lattice gauge theory; nonperturbative effects in field theory; nonrelativistic QCD; perturbation theory; perturbative QCD; quantum chromodynamics; strong interaction

Citation Formats


                    Brambilla, Nora, Delgado, Rafael L., Kronfeld, Andreas S., Leino, Viljami, Petreczky, Peter, Steinbeißer, Sebastian, Vairo, Antonio, Weber, Johannes H., and TUMQCD Collaboration. Static energy in ( 2 + 1 + 1 )-flavor lattice QCD: Scale setting and charm effects.  United States: N. p., 2023. 
Web.  doi:10.1103/PhysRevD.107.074503.

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                    Brambilla, Nora, Delgado, Rafael L., Kronfeld, Andreas S., Leino, Viljami, Petreczky, Peter, Steinbeißer, Sebastian, Vairo, Antonio, Weber, Johannes H., & TUMQCD Collaboration. Static energy in ( 2 + 1 + 1 )-flavor lattice QCD: Scale setting and charm effects.  United States.  https://doi.org/10.1103/PhysRevD.107.074503

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                    Brambilla, Nora, Delgado, Rafael L., Kronfeld, Andreas S., Leino, Viljami, Petreczky, Peter, Steinbeißer, Sebastian, Vairo, Antonio, Weber, Johannes H., and TUMQCD Collaboration. Tue .  
"Static energy in ( 2 + 1 + 1 )-flavor lattice QCD: Scale setting and charm effects".  United States.  https://doi.org/10.1103/PhysRevD.107.074503.

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@article{osti_1969421,

  title        = {Static energy in ( 2 + 1 + 1 )-flavor lattice QCD: Scale setting and charm effects},

  author       = {Brambilla, Nora and Delgado, Rafael L. and Kronfeld, Andreas S. and Leino, Viljami and Petreczky, Peter and Steinbeißer, Sebastian and Vairo, Antonio and Weber, Johannes H. and TUMQCD Collaboration},

  abstractNote = {We present results for the static energy in (2 + 1 + 1 )-flavor QCD over a wide range of lattice spacings and several quark masses, including the physical quark mass, with ensembles of lattice-gauge-field configurations made available by the MILC Collaboration. We obtain results for the static energy out to distances of nearly 1 fm, allowing us to perform a simultaneous determination of the scales r1 and r0, as well as the string tension σ. For the smallest three lattice spacings we also determine the scale r2. Our results for r0 r1 and r0$\sqrt{σ}$ agree with published (2 + 1)-flavor results. However, our result for r1/r2 differs significantly from the value obtained in the (2 + 1 -flavor case, which is most likely due to the effect of the charm quark. We also report results for r0, r1, and r2 in fm, with the former two being slightly lower than published (2 + 1)-flavor results. We study in detail the effect of the charm quark on the static energy by comparing our results on the finest two lattices with the previously published (2 + 1)-flavor QCD results at similar lattice spacing. We find that for r > 0.2 fm our results on the static energy agree with the (2 + 1)-flavor result, implying the decoupling of the charm quark for these distances. For smaller distances, on the other hand, we find that the effect of the dynamical charm quark is noticeable. The lattice results agree well with the two-loop perturbative expression of the static energy incorporating finite charm mass effects. This is the first time that the decoupling of the charm quark is observed and quantitatively analyzed on lattice data of the static energy.},

  doi          = {10.1103/PhysRevD.107.074503},

  journal      = {Physical Review. D.},

  number       = 7,

  volume       = 107,

  place        = {United States},

  year         = {Tue Apr 11 00:00:00 EDT 2023},

  month        = {Tue Apr 11 00:00:00 EDT 2023}

}

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Title: Static energy in ( 2 + 1 + 1 )-flavor lattice QCD: Scale setting and charm effects

Abstract

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Title: Static energy in ( $2 + 1 + 1$ )-flavor lattice QCD: Scale setting and charm effects

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journal, May 1980

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journal, October 2018

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journal, March 2018

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journal, July 2000

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journal, February 2002

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journal, November 2020

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journal, December 1979

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journal, October 2022

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journal, April 2018

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conference, June 2011

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journal, December 2000

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