Nonperturbative β function of twelve-flavor SU(3) gauge theory

Hasenfratz, Anna; Schaich, David

doi:10.1007/jhep02(2018)132

Title: Nonperturbative β function of twelve-flavor SU(3) gauge theory

Abstract

We study the discrete β function of SU(3) gauge theory with N _f = 12 massless fermions in the fundamental representation. Using an nHYP-smeared staggered lattice action and an improved gradient flow running coupling ${\tilde{g}}_{c}^{2} (L)$ we determine the continuum-extrapolated discrete β function up to g _c ² ≈ 8.2. We observe an IR fixed point at g _* ² = 7.3(_-2 ^{+ 8} ) in the $c = \sqrt{8 t} / L = 0.25$ scheme, and g _* ² = 7.3( _-3 ^{+ 6} ) with c = 0.3, combining statistical and systematic uncertainties in quadrature. The systematic effects we investigate include the stability of the (a/L) → 0 extrapolations, the interpolation of ${\tilde{g}}_{c}^{2} (L)$ as a function of the bare coupling, the improvement of the gradient flow running coupling, and the discretization of the energy density. In an appendix we observe that the resulting systematic errors increase dramatically upon combining smaller c ≲ 0.2 with smaller L ≤ 12, leading to an IR fixed point at g _* ² = 5.9(1.9) in the c = 0.2 scheme, which resolves to g _* ² = 6.9( _-1 ^{+ 6} ) upon considering only L ≥ 16. At the IR fixed point we measure the leading irrelevant critical exponent to be γ _g _* = 0.26(2), comparable to perturbative estimates.

Authors:

Hasenfratz, Anna ^[1];

^[2]

Univ. of Colorado, Boulder, CO (United States). Dept. of Physics
Syracuse Univ., NY (United States). Dept. of Physics; Univ. of Bern (Switzerland). AEC Inst. for Theoretical Physics

Publication Date:: Wed Feb 21 00:00:00 EST 2018

Research Org.:: Syracuse Univ., NY (United States); Univ. of Colorado, Boulder, CO (United States)

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

OSTI Identifier:: 1505130

Grant/Contract Number:: SC0008669; SC0009998; SC0010005; CNS-0821794

Resource Type:: Accepted Manuscript

Journal Name:: Journal of High Energy Physics (Online)

Additional Journal Information:: Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 2; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; lattice quantum field theory; renormalization group; technicolor and composite models

Citation Formats


                    Hasenfratz, Anna, and Schaich, David. Nonperturbative β function of twelve-flavor SU(3) gauge theory.  United States: N. p., 2018. 
Web.  doi:10.1007/jhep02(2018)132.

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                    Hasenfratz, Anna, & Schaich, David. Nonperturbative β function of twelve-flavor SU(3) gauge theory.  United States.  https://doi.org/10.1007/jhep02(2018)132

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                    Hasenfratz, Anna, and Schaich, David. Wed .  
"Nonperturbative β function of twelve-flavor SU(3) gauge theory".  United States.  https://doi.org/10.1007/jhep02(2018)132.  https://www.osti.gov/servlets/purl/1505130.

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@article{osti_1505130,

  title        = {Nonperturbative β function of twelve-flavor SU(3) gauge theory},

  author       = {Hasenfratz, Anna and Schaich, David},

  abstractNote = {We study the discrete β function of SU(3) gauge theory with N f = 12 massless fermions in the fundamental representation. Using an nHYP-smeared staggered lattice action and an improved gradient flow running coupling g ~ c 2 ( L ) we determine the continuum-extrapolated discrete β function up to g c 2 ≈ 8.2. We observe an IR fixed point at g * 2 = 7.3( -2 + 8 ) in the c = 8 t / L = 0.25 scheme, and g * 2 = 7.3( -3 + 6 ) with c = 0.3, combining statistical and systematic uncertainties in quadrature. The systematic effects we investigate include the stability of the (a/L) → 0 extrapolations, the interpolation of g ~ c 2 ( L ) as a function of the bare coupling, the improvement of the gradient flow running coupling, and the discretization of the energy density. In an appendix we observe that the resulting systematic errors increase dramatically upon combining smaller c ≲ 0.2 with smaller L ≤ 12, leading to an IR fixed point at g * 2 = 5.9(1.9) in the c = 0.2 scheme, which resolves to g * 2 = 6.9( -1 + 6 ) upon considering only L ≥ 16. At the IR fixed point we measure the leading irrelevant critical exponent to be γ g * = 0.26(2), comparable to perturbative estimates.},

  doi          = {10.1007/jhep02(2018)132},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 2,

  volume       = 2018,

  place        = {United States},

  year         = {Wed Feb 21 00:00:00 EST 2018},

  month        = {Wed Feb 21 00:00:00 EST 2018}

}

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Title: Nonperturbative β function of twelve-flavor SU(3) gauge theory

Abstract

Citation Formats

QCD: Restoration of chiral symmetry and deconfinement for large N f journal, September 2013

One, two, zero: Scales of strong interactions journal, October 2014

The lattice gradient flow at tree-level and its improvement journal, September 2014

Phase structure of an SU ( N ) gauge theory with N f flavors journal, October 1998

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Search for the IR fixed point in the Twisted Polyakov Loop scheme conference, June 2010

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Flavor symmetry and the static potential with hypercubic blocking journal, July 2001

The bulk transition of QCD with twelve flavors and the role of improvement journal, March 2013

Nonperturbative β function of eight-flavor SU(3) gauge theory journal, June 2015

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The strong coupling bulk transition of twelve flavors conference, July 2012

Anomalous dimensions on the lattice journal, April 2016

Zero Temperature Chiral Phase Transition in SU( N ) Gauge Theories journal, August 1996

Mass anomalous dimension from Dirac eigenmode scaling in conformal and confining systems conference, December 2012

Conformal window of SU ( N ) gauge theories with fermions in higher dimensional representations journal, April 2007

Five-Loop Running of the QCD Coupling Constant journal, February 2017

On the particle spectrum and the conformal window journal, December 2014

Lattice QCD with 8 and 12 degenerate quark flavors conference, June 2010

The gradient flow coupling in the Schrödinger functional journal, October 2013

Infinite N phase transitions in continuum Wilson loop operators journal, March 2006

The five-loop beta function of Yang-Mills theory with fermions journal, February 2017

Fisher zeros and conformality in lattice models conference, December 2012

Strong dynamics, composite Higgs and the conformal window journal, August 2016

Multicritical phenomena in O ( n 1 ) ⊕ O ( n 2 ) -symmetric theories journal, February 2003

Symanzik improvement of the gradient flow in lattice gauge theories journal, January 2016

Twelve massless flavors and three colors below the conformal window journal, September 2011

Confining force and running coupling with twelve fundamental and two sextet fermions conference, December 2012

Lattice study of infrared behaviour in SU(3) gauge theory with twelve massless flavours journal, August 2012

Bulk and finite- temperature transitions in SU(3) gauge theories with many light fermions conference, December 2012

The Yang-Mills gradient flow in finite volume journal, November 2012

Improving the continuum limit of gradient flow step scaling journal, May 2014

On the phase structure of vector-like gauge theories with massless fermions journal, March 1982

The Banks–Zaks expansion in perturbative QCD: An update journal, December 2016

Infrared Fixed Point of the 12-Fermion SU(3) Gauge Model Based on 2-Lattice Monte Carlo Renomalization-Group Matching journal, February 2012

Lattice Study of the Conformal Window in QCD-like Theories journal, April 2008

Large scale separation and hadronic resonances from a new strongly interacting sector journal, October 2017

Nearly conformal gauge theories in finite volume journal, November 2009

IR fixed points in SU ( 3 ) gauge theories journal, September 2015

Lattice tests of beyond standard model dynamics journal, January 2016

Measurements of Higgs boson production and couplings in diboson final states with the ATLAS detector at the LHC journal, October 2013

Lattice QCD with Eight Degenerate Quark Flavors conference, June 2009

Properties of the twisted Polyakov loop coupling and the infrared fixed point in the SU(3) gauge theories journal, August 2013

Large scale separation and hadronic resonances from a new strongly interacting sector conference, March 2018

Measurements of Higgs boson production and couplings in diboson final states with the ATLAS detector at the LHC text, January 2013

Lattice Study of the Conformal Window in QCD-like Theories text, January 2007

Nearly conformal gauge theories in finite volume text, January 2009

Lattice QCD with 8 and 12 degenerate quark flavors text, January 2009

Mass anomalous dimension from Dirac eigenmode scaling in conformal and confining systems text, January 2012

The bulk transition of QCD with twelve flavors and the role of improvement text, January 2012

Confining force and running coupling with twelve fundamental and two sextet fermions preprint, January 2012

Improving the continuum limit of gradient flow step scaling text, January 2014

The lattice gradient flow at tree-level and its improvement text, January 2014

On the particle spectrum and the conformal window text, January 2014

One,Two,Zero: Scales of Strong Interactions text, January 2014

Symanzik improvement of the gradient flow in lattice gauge theories text, January 2015

Five-Loop Running of the QCD coupling constant text, January 2016

Strong dynamics, composite Higgs and the conformal window text, January 2016

The five-loop beta function of Yang-Mills theory with fermions text, January 2017

Flavor Symmetry and the Static Potential with Hypercubic Blocking text, January 2001

Evidence for a conformal phase in SU ( N ) gauge theories journal, October 2010

Mass anomalous dimension from Dirac eigenmode scaling in conformal and confining systems conference, December 2012

Determining the mass anomalous dimension through the eigenmodes of Dirac operator conference, April 2014

Improved gradient flow for step scaling function and scale setting conference, May 2015

The bulk transition of many-flavour QCD and the search for a UVFP at strong coupling text, January 2010

Lattice Simulations and Infrared Conformality text, January 2011

MCRG study of 12 fundamental flavors with mixed fundamental-adjoint gauge action preprint, January 2011

Fisher zeros and conformality in lattice models text, January 2012

The anomalous dimension at the infrared fixed point of Nf = 12 SU(3) theory preprint, January 2013

Finite size scaling of conformal theories in the presence of a near-marginal operator text, January 2014

Determination of the mass anomalous dimension for $N_f=12$ and $N_f=9$ SU($3$) gauge theories preprint, January 2014

IR fixed points in $SU(3)$ gauge Theories text, January 2015

Crawling technicolor journal, November 2019

QCD: Restoration of chiral symmetry and deconfinement for large $N_{f}$
journal, September 2013

One, two, zero: Scales of strong interactions
journal, October 2014

The lattice gradient flow at tree-level and its improvement
journal, September 2014

Phase structure of an $SU (N)$ gauge theory with $N_{f}$ flavors
journal, October 1998

Scale-dependent mass anomalous dimension from Dirac eigenmodes
journal, July 2013

Trivializing Maps, the Wilson Flow and the HMC Algorithm
journal, November 2009

The running coupling of 8 flavors and 3 colors
journal, June 2015

Infrared zero of $β$ and value of $γ_{m}$ for an SU(3) gauge theory at the five-loop level
journal, November 2016

Search for the IR fixed point in the Twisted Polyakov Loop scheme
conference, June 2010

Scheme-independent calculation of $γ_{\bar{ψ} ψ, I R}$ for an SU(3) gauge theory
journal, November 2016

Flavor symmetry and the static potential with hypercubic blocking
journal, July 2001

The bulk transition of QCD with twelve flavors and the role of improvement
journal, March 2013

Nonperturbative β function of eight-flavor SU(3) gauge theory
journal, June 2015

Asymptotic Behavior of Non-Abelian Gauge Theories to Two-Loop Order
journal, July 1974

Consistent Perturbative Fixed Point Calculations in QCD and Supersymmetric QCD
journal, August 2016

The strong coupling bulk transition of twelve flavors
conference, July 2012

Anomalous dimensions on the lattice
journal, April 2016

Zero Temperature Chiral Phase Transition in SU( N ) Gauge Theories
journal, August 1996

Mass anomalous dimension from Dirac eigenmode scaling in conformal and confining systems
conference, December 2012

Conformal window of $SU (N)$ gauge theories with fermions in higher dimensional representations
journal, April 2007

Five-Loop Running of the QCD Coupling Constant
journal, February 2017

On the particle spectrum and the conformal window
journal, December 2014

Lattice QCD with 8 and 12 degenerate quark flavors
conference, June 2010

The gradient flow coupling in the Schrödinger functional
journal, October 2013

Infinite N phase transitions in continuum Wilson loop operators
journal, March 2006

The five-loop beta function of Yang-Mills theory with fermions
journal, February 2017

Fisher zeros and conformality in lattice models
conference, December 2012

Strong dynamics, composite Higgs and the conformal window
journal, August 2016

Multicritical phenomena in $O {(n}_{1}) \oplus O {(n}_{2})$ -symmetric theories
journal, February 2003

Symanzik improvement of the gradient flow in lattice gauge theories
journal, January 2016

Twelve massless flavors and three colors below the conformal window
journal, September 2011

Confining force and running coupling with twelve fundamental and two sextet fermions
conference, December 2012

Lattice study of infrared behaviour in SU(3) gauge theory with twelve massless flavours
journal, August 2012

Bulk and finite- temperature transitions in SU(3) gauge theories with many light fermions
conference, December 2012

The Yang-Mills gradient flow in finite volume
journal, November 2012

Improving the continuum limit of gradient flow step scaling
journal, May 2014

On the phase structure of vector-like gauge theories with massless fermions
journal, March 1982

The Banks–Zaks expansion in perturbative QCD: An update
journal, December 2016

Infrared Fixed Point of the 12-Fermion SU(3) Gauge Model Based on 2-Lattice Monte Carlo Renomalization-Group Matching
journal, February 2012

Lattice Study of the Conformal Window in QCD-like Theories
journal, April 2008

Large scale separation and hadronic resonances from a new strongly interacting sector
journal, October 2017

Nearly conformal gauge theories in finite volume
journal, November 2009

IR fixed points in $SU (3)$ gauge theories
journal, September 2015

Lattice tests of beyond standard model dynamics
journal, January 2016

Measurements of Higgs boson production and couplings in diboson final states with the ATLAS detector at the LHC
journal, October 2013

Lattice QCD with Eight Degenerate Quark Flavors
conference, June 2009

Properties of the twisted Polyakov loop coupling and the infrared fixed point in the SU(3) gauge theories
journal, August 2013

Large scale separation and hadronic resonances from a new strongly interacting sector
conference, March 2018

Measurements of Higgs boson production and couplings in diboson final states with the ATLAS detector at the LHC
text, January 2013

Lattice Study of the Conformal Window in QCD-like Theories
text, January 2007

Nearly conformal gauge theories in finite volume
text, January 2009

Lattice QCD with 8 and 12 degenerate quark flavors
text, January 2009

Mass anomalous dimension from Dirac eigenmode scaling in conformal and confining systems
text, January 2012

The bulk transition of QCD with twelve flavors and the role of improvement
text, January 2012

Confining force and running coupling with twelve fundamental and two sextet fermions
preprint, January 2012

Improving the continuum limit of gradient flow step scaling
text, January 2014

The lattice gradient flow at tree-level and its improvement
text, January 2014

On the particle spectrum and the conformal window
text, January 2014

One,Two,Zero: Scales of Strong Interactions
text, January 2014

Symanzik improvement of the gradient flow in lattice gauge theories
text, January 2015

Five-Loop Running of the QCD coupling constant
text, January 2016

Strong dynamics, composite Higgs and the conformal window
text, January 2016

The five-loop beta function of Yang-Mills theory with fermions
text, January 2017

Flavor Symmetry and the Static Potential with Hypercubic Blocking
text, January 2001

Evidence for a conformal phase in $SU (N)$ gauge theories
journal, October 2010

Mass anomalous dimension from Dirac eigenmode scaling in conformal and confining systems
conference, December 2012

Determining the mass anomalous dimension through the eigenmodes of Dirac operator
conference, April 2014

Improved gradient flow for step scaling function and scale setting
conference, May 2015

The bulk transition of many-flavour QCD and the search for a UVFP at strong coupling
text, January 2010

Lattice Simulations and Infrared Conformality
text, January 2011

MCRG study of 12 fundamental flavors with mixed fundamental-adjoint gauge action
preprint, January 2011

Fisher zeros and conformality in lattice models
text, January 2012

The anomalous dimension at the infrared fixed point of Nf = 12 SU(3) theory
preprint, January 2013

Finite size scaling of conformal theories in the presence of a near-marginal operator
text, January 2014

Determination of the mass anomalous dimension for $N_f=12$ and $N_f=9$ SU($3$) gauge theories
preprint, January 2014

IR fixed points in $SU(3)$ gauge Theories
text, January 2015

Crawling technicolor
journal, November 2019

Gradient flow step-scaling function for SU(3) with twelve flavors
journal, December 2019

Infrared fixed point of SU(2) gauge theory with six flavors
journal, June 2018

Slope of the beta function at the fixed point of SU(2) gauge theory with six or eight flavors
journal, September 2018