skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Linear sigma EFT for nearly conformal gauge theories

Abstract

Here, we construct a generalized linear sigma model as an effective field theory (EFT) to describe nearly conformal gauge theories at low energies. The work is motivated by recent lattice studies of gauge theories near the conformal window, which have shown that the lightest flavor-singlet scalar state in the spectrum (σ) can be much lighter than the vector state (ρ) and nearly degenerate with the PNGBs (π) over a large range of quark masses. The EFT incorporates this feature. We highlight the crucial role played by the terms in the potential that explicitly break chiral symmetry. The explicit breaking can be large enough so that a limited set of additional terms in the potential can no longer be neglected, with the EFT still weakly coupled in this new range. The additional terms contribute importantly to the scalar and pion masses. In particular, they relax the inequality M 2 σ ≥ 3M 2 π, allowing for consistency with current lattice data.

Authors:
 [1];  [2];  [1];  [3];  [4];  [1];  [5];  [6];  [2];  [7];  [8];  [9];  [10];  [4]
  1. Yale Univ., New Haven, CT (United States)
  2. Boston Univ., Boston, MA (United States)
  3. Yale Univ., New Haven, CT (United States); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of Bern, Bern (Switzerland)
  4. Univ. of Colorado, Boulder, CO (United States)
  5. Univ. of California, Davis, CA (United States)
  6. Argonne National Lab. (ANL), Argonne, IL (United States)
  7. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Brookhaven National Lab. (BNL), Upton, NY (United States)
  8. Univ. of Bern, Bern (Switzerland)
  9. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
  10. Boston Univ., Boston, MA (United States); NVIDIA Corp., Santa Clara, CA (United States)
Publication Date:
Research Org.:
Brookhaven National Lab. (BNL), Upton, NY (United States); Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26); RIKEN; National Science Foundation (NSF); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
Contributing Org.:
Lattice Strong Dynamics (LSD) Collaboration
OSTI Identifier:
1488639
Alternate Identifier(s):
OSTI ID: 1489357; OSTI ID: 1573356
Report Number(s):
RBRC-1291; BNL-210838-2019-JAAM
Journal ID: ISSN 2470-0010; PRVDAQ
Grant/Contract Number:  
SC0012704; SC0010005; SC0010025; SC0014664; AC52-07NA27344; AC02-06CH11357
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 98; Journal Issue: 11; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Citation Formats

Appelquist, Thomas, Brower, R. C., Fleming, G. T., Gasbarro, Andrew, Hasenfratz, A., Ingoldby, James, Kiskis, J., Osborn, J. C., Rebbi, C., Rinaldi, Enrico, Schaich, D., Vranas, P., Weinberg, E., and Witzel, O. Linear sigma EFT for nearly conformal gauge theories. United States: N. p., 2018. Web. doi:10.1103/PhysRevD.98.114510.
Appelquist, Thomas, Brower, R. C., Fleming, G. T., Gasbarro, Andrew, Hasenfratz, A., Ingoldby, James, Kiskis, J., Osborn, J. C., Rebbi, C., Rinaldi, Enrico, Schaich, D., Vranas, P., Weinberg, E., & Witzel, O. Linear sigma EFT for nearly conformal gauge theories. United States. doi:10.1103/PhysRevD.98.114510.
Appelquist, Thomas, Brower, R. C., Fleming, G. T., Gasbarro, Andrew, Hasenfratz, A., Ingoldby, James, Kiskis, J., Osborn, J. C., Rebbi, C., Rinaldi, Enrico, Schaich, D., Vranas, P., Weinberg, E., and Witzel, O. Thu . "Linear sigma EFT for nearly conformal gauge theories". United States. doi:10.1103/PhysRevD.98.114510.
@article{osti_1488639,
title = {Linear sigma EFT for nearly conformal gauge theories},
author = {Appelquist, Thomas and Brower, R. C. and Fleming, G. T. and Gasbarro, Andrew and Hasenfratz, A. and Ingoldby, James and Kiskis, J. and Osborn, J. C. and Rebbi, C. and Rinaldi, Enrico and Schaich, D. and Vranas, P. and Weinberg, E. and Witzel, O.},
abstractNote = {Here, we construct a generalized linear sigma model as an effective field theory (EFT) to describe nearly conformal gauge theories at low energies. The work is motivated by recent lattice studies of gauge theories near the conformal window, which have shown that the lightest flavor-singlet scalar state in the spectrum (σ) can be much lighter than the vector state (ρ) and nearly degenerate with the PNGBs (π) over a large range of quark masses. The EFT incorporates this feature. We highlight the crucial role played by the terms in the potential that explicitly break chiral symmetry. The explicit breaking can be large enough so that a limited set of additional terms in the potential can no longer be neglected, with the EFT still weakly coupled in this new range. The additional terms contribute importantly to the scalar and pion masses. In particular, they relax the inequality M2σ ≥ 3M2π, allowing for consistency with current lattice data.},
doi = {10.1103/PhysRevD.98.114510},
journal = {Physical Review D},
number = 11,
volume = 98,
place = {United States},
year = {2018},
month = {12}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1103/PhysRevD.98.114510

Citation Metrics:
Cited by: 2 works
Citation information provided by
Web of Science

Figures / Tables:

TABLE I. TABLE I.: Operator content of the leading-order (D ≤ 4) breaking potential when α = 1, corresponding to a relatively large amount of chiral symmetry breaking. We show that this amount is required to fit currently available lattice data.

Save / Share:

Works referenced in this record:

The twelve-flavor β-function and dilaton tests of the sextet scalar
journal, January 2018


Light flavor-singlet scalars and walking signals in N f = 8 QCD on the lattice
journal, July 2017


Symmetry Breaking and Spin-Zero Mass Spectrum
journal, January 1971


General Treatment of the Breaking of Chiral Symmetry and Scale Invariance in the SU(3) σ Model
journal, August 1973


Behavior of Current Divergences under SU 3 × SU 3
journal, November 1968


Chiral effective theory with a light scalar and lattice QCD
journal, January 2013


Large-mass regime of the dilaton-pion low-energy effective theory
journal, September 2018


Light composite scalar in eight-flavor QCD on the lattice
journal, June 2014


Strongly interacting dynamics and the search for new physics at the LHC
journal, June 2016


Lattice simulations with eight flavors of domain wall fermions in SU(3) gauge theory
journal, December 2014


Composite Higgs model at a conformal fixed point
journal, April 2016


Isoscalar π π Scattering and the σ Meson Resonance from QCD
journal, January 2017


Mass splittings in a linear sigma model for multiflavor gauge theories
journal, November 2018


Chiral perturbation theory
journal, June 1995


Low-energy effective action for pions and a dilatonic meson
journal, September 2016


Recent results from SU(2) with one adjoint Dirac fermion
journal, December 2017

  • Athenodorou, A.; Bennett, E.; Bergner, G.
  • International Journal of Modern Physics A, Vol. 32, Issue 35
  • DOI: 10.1142/S0217751X17470066

Extraction of isoscalar π π phase shifts from lattice QCD
journal, July 2018


Study of the change from walking to non-walking behavior in a vectorial gauge theory as a function of N f
journal, December 2006


Can a Linear Sigma Model Describe Walking Gauge Theories at Low Energies?
journal, January 2018


Currents and symmetry breaking
journal, November 1967


Extending chiral perturbation theory with an isosinglet scalar
journal, February 2017


Isoscalar π π , K K ¯ , η η scattering and the σ , f 0 , f 2 mesons from QCD
journal, March 2018


Linear sigma model for multiflavor gauge theories
journal, December 2017


Looking behind the Standard Model with lattice gauge theory
journal, January 2018


Dilaton EFT framework for lattice data
journal, July 2017

  • Appelquist, Thomas; Ingoldby, James; Piai, Maurizio
  • Journal of High Energy Physics, Vol. 2017, Issue 7
  • DOI: 10.1007/JHEP07(2017)035

General Treatment of the Breaking of Chiral Symmetry and Scale Invariance in the SU ( 3 )   σ Model
journal, June 1971


Isospin-0 π π s-wave scattering length from twisted mass lattice QCD
journal, September 2017


Lattice tests of beyond standard model dynamics
journal, January 2016


Analysis of a dilaton EFT for lattice data
journal, March 2018

  • Appelquist, Thomas; Ingoldby, James; Piai, Maurizio
  • Journal of High Energy Physics, Vol. 2018, Issue 3
  • DOI: 10.1007/JHEP03(2018)039

    Figures / Tables found in this record:

      Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.