Linear sigma model for multiflavor gauge theories
Abstract
We consider a linear sigma model describing $$2N_f^2$$ bosons ($$\sigma$$, a0, $$\eta$$' and π) as an approximate effective theory for a $SU(3)$ local gauge theory with $$N_f$$ Dirac fermions in the fundamental representation. The model has a renormalizable U(Nf)L Ⓧ invariant part, which has an approximate $$O(2N_f^2)$$ symmetry, and two additional terms, one describing the effects of a $$SU(N_f)_V$$ invariant mass term and the other the effects of the axial anomaly. We calculate the spectrum for arbitrary $$N_f$$. Using preliminary and published lattice results from the LatKMI collaboration, we found combinations of the masses that vary slowly with the explicit chiral symmetry breaking and $$N_f$$. This suggests that the anomaly term plays a leading role in the mass spectrum and that simple formulas such as $$M_\sigma^2\simeq (2/N_f-C_\sigma)M_{\eta'}^2$$ should apply in the chiral limit. Lattice measurements of $$M_{\eta'}^2$$ and of approximate constants such as $$C_\sigma$$ could help locating the boundary of the conformal window. Here, we show that our calculation can be adapted for arbitrary representations of the gauge group and in particular to the minimal model with two sextets, where similar patterns are likely to apply.
- Authors:
-
- Univ. of Iowa, Iowa City, IA (United States). Dept. of Physics and Astronomy
- Publication Date:
- Research Org.:
- Univ. of Iowa, Iowa City, IA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF)
- OSTI Identifier:
- 1660400
- Alternate Identifier(s):
- OSTI ID: 1412945
- Grant/Contract Number:
- SC0010113; PHY11-25915
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. D.
- Additional Journal Information:
- Journal Volume: 96; Journal Issue: 11; Journal ID: ISSN 2470-0010
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Dynamical symmetry breaking
Citation Formats
Meurice, Y. Linear sigma model for multiflavor gauge theories. United States: N. p., 2017.
Web. doi:10.1103/physrevd.96.114507.
Meurice, Y. Linear sigma model for multiflavor gauge theories. United States. https://doi.org/10.1103/physrevd.96.114507
Meurice, Y. Mon .
"Linear sigma model for multiflavor gauge theories". United States. https://doi.org/10.1103/physrevd.96.114507. https://www.osti.gov/servlets/purl/1660400.
@article{osti_1660400,
title = {Linear sigma model for multiflavor gauge theories},
author = {Meurice, Y.},
abstractNote = {We consider a linear sigma model describing $2N_f^2$ bosons ($\sigma$, a0, $\eta$' and π) as an approximate effective theory for a $SU(3)$ local gauge theory with $N_f$ Dirac fermions in the fundamental representation. The model has a renormalizable U(Nf)L Ⓧ invariant part, which has an approximate $O(2N_f^2)$ symmetry, and two additional terms, one describing the effects of a $SU(N_f)_V$ invariant mass term and the other the effects of the axial anomaly. We calculate the spectrum for arbitrary $N_f$. Using preliminary and published lattice results from the LatKMI collaboration, we found combinations of the masses that vary slowly with the explicit chiral symmetry breaking and $N_f$. This suggests that the anomaly term plays a leading role in the mass spectrum and that simple formulas such as $M_\sigma^2\simeq (2/N_f-C_\sigma)M_{\eta'}^2$ should apply in the chiral limit. Lattice measurements of $M_{\eta'}^2$ and of approximate constants such as $C_\sigma$ could help locating the boundary of the conformal window. Here, we show that our calculation can be adapted for arbitrary representations of the gauge group and in particular to the minimal model with two sextets, where similar patterns are likely to apply.},
doi = {10.1103/physrevd.96.114507},
journal = {Physical Review. D.},
number = 11,
volume = 96,
place = {United States},
year = {Mon Dec 11 00:00:00 EST 2017},
month = {Mon Dec 11 00:00:00 EST 2017}
}
Web of Science
Works referenced in this record:
Vacuum Structure and Chiral Charge Quantization in the Large N Limit
journal, October 1981
- Ohta, N.
- Progress of Theoretical Physics, Vol. 66, Issue 4
Light flavor-singlet scalars and walking signals in QCD on the lattice
journal, July 2017
- Aoki, Yasumichi; Aoyama, Tatsumi; Bennett, Ed
- Physical Review D, Vol. 96, Issue 1
The axial vector current in beta decay
journal, May 1960
- Gell-Mann, M.; Lévy, M.
- Il Nuovo Cimento, Vol. 16, Issue 4
The η problem in the large-N limit: Effective Lagrangian approach
journal, December 1980
- Kawarabayashi, Ken; Ohta, Nobuyoshi
- Nuclear Physics B, Vol. 175, Issue 3
Can the nearly conformal sextet gauge model hide the Higgs impostor?
journal, December 2012
- Fodor, Zoltán; Holland, Kieran; Kuti, Julius
- Physics Letters B, Vol. 718, Issue 2
Study of the and mesons with improved staggered fermions
journal, July 2012
- Gregory, Eric B.; Irving, Alan C.; Richards, Christopher M.
- Physical Review D, Vol. 86, Issue 1
Meson Vacuum Phenomenology in a Three-flavor Linear Sigma Model with (Axial-)Vector Mesons: Investigation of the U$(1)_A$ Anomaly Term
journal, January 2013
- Kovács, P.; Wolf, G.
- Acta Physica Polonica B Proceedings Supplement, Vol. 6, Issue 3
Existence of the critical endpoint in the vector meson extended linear sigma model
journal, June 2016
- Kovács, P.; Szép, Zs.; Wolf, Gy.
- Physical Review D, Vol. 93, Issue 11
Light composite scalar in eight-flavor QCD on the lattice
journal, June 2014
- Aoki, Yasumichi; Aoyama, Tatsumi; Kurachi, Masafumi
- Physical Review D, Vol. 89, Issue 11
Vacuum properties of mesons in a linear sigma model with vector mesons and global chiral invariance
journal, September 2010
- Parganlija, Denis; Giacosa, Francesco; Rischke, Dirk H.
- Physical Review D, Vol. 82, Issue 5
On the Partical Conservation of the U(1) Current
journal, November 1981
- Kawarabayashi, K.; Ohta, N.
- Progress of Theoretical Physics, Vol. 66, Issue 5
Vacuum Structure and Chiral Charge Quantization in the Large N Limit
journal, March 1982
- Ohta, N.
- Progress of Theoretical Physics, Vol. 67, Issue 3
Orientifold theory dynamics and symmetry breaking
journal, March 2005
- Sannino, Francesco; Tuominen, Kimmo
- Physical Review D, Vol. 71, Issue 5
Strongly interacting dynamics and the search for new physics at the LHC
journal, June 2016
- Appelquist, T.; Brower, R. C.; Fleming, G. T.
- Physical Review D, Vol. 93, Issue 11
Critical surface of the chiral quark model at nonzero baryon density
journal, January 2007
- Kovács, P.; Szép, Zs.
- Physical Review D, Vol. 75, Issue 2
Composite Higgs model at a conformal fixed point
journal, April 2016
- Brower, R. C.; Hasenfratz, A.; Rebbi, C.
- Physical Review D, Vol. 93, Issue 7
Light composite Higgs boson from higher representations versus electroweak precision measurements: Predictions for CERN LHC
journal, September 2005
- Dietrich, Dennis D.; Sannino, Francesco; Tuominen, Kimmo
- Physical Review D, Vol. 72, Issue 5
Technicolor and other QCD-like theories at next-to-next-to-leading order
journal, November 2009
- Bijnens, Johan; Lu, Jie
- Journal of High Energy Physics, Vol. 2009, Issue 11
Low-energy effective action for pions and a dilatonic meson
journal, September 2016
- Golterman, Maarten; Shamir, Yigal
- Physical Review D, Vol. 94, Issue 5
How instantons solve the U(1) problem
journal, September 1986
- 't Hooft, G.
- Physics Reports, Vol. 142, Issue 6
The physics of eight flavours
journal, December 2008
- Deuzeman, Albert; Lombardo, Maria Paola; Pallante, Elisabetta
- Physics Letters B, Vol. 670, Issue 1
On the phase structure of vector-like gauge theories with massless fermions
journal, March 1982
- Banks, T.; Zaks, A.
- Nuclear Physics B, Vol. 196, Issue 2
Conformal window of gauge theories with fermions in higher dimensional representations
journal, April 2007
- Dietrich, Dennis D.; Sannino, Francesco
- Physical Review D, Vol. 75, Issue 8
Computation of the quantum effects due to a four-dimensional pseudoparticle
journal, December 1976
- 't Hooft, G.
- Physical Review D, Vol. 14, Issue 12
and Mesons from Lattice QCD
journal, December 2010
- Christ, N. H.; Dawson, C.; Izubuchi, T.
- Physical Review Letters, Vol. 105, Issue 24
Is the effective Lagrangian for quantum chromodynamics a model?
journal, June 1980
- Rosenzweig, C.; Schechter, J.; Trahern, C. G.
- Physical Review D, Vol. 21, Issue 12
Dilaton EFT framework for lattice data
journal, July 2017
- Appelquist, Thomas; Ingoldby, James; Piai, Maurizio
- Journal of High Energy Physics, Vol. 2017, Issue 7
Phase structure of SU(3) gauge theory with two flavors of symmetric-representation fermions
journal, February 2009
- DeGrand, Thomas; Shamir, Yigal; Svetitsky, Benjamin
- Physical Review D, Vol. 79, Issue 3
Meson vacuum phenomenology in a three-flavor linear sigma model with (axial-)vector mesons
journal, January 2013
- Parganlija, D.; Kovács, P.; Wolf, Gy.
- Physical Review D, Vol. 87, Issue 1
Light Composite Scalar in Twelve-Flavor QCD on the Lattice
journal, October 2013
- Aoki, Yasumichi; Aoyama, Tatsumi; Kurachi, Masafumi
- Physical Review Letters, Vol. 111, Issue 16
Mass anomalous dimension in sextet QCD
journal, April 2013
- DeGrand, Thomas; Shamir, Yigal; Svetitsky, Benjamin
- Physical Review D, Vol. 87, Issue 7
General Treatment of the Breaking of Chiral Symmetry and Scale Invariance in the Model
journal, June 1971
- Schechter, J.; Ueda, Y.
- Physical Review D, Vol. 3, Issue 11
Chiral perturbation theory beyond one loop
journal, April 2007
- Bijnens, Johan
- Progress in Particle and Nuclear Physics, Vol. 58, Issue 2
A mixed action analysis of η and <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:msup><mml:mrow><mml:mi>η</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:math> mesons
journal, July 2015
- Ottnad, Konstantin; Urbach, Carsten; Zimmermann, Falk
- Nuclear Physics B, Vol. 896
Chiral dynamics in the large N limit
journal, January 1980
- Di Vecchia, P.; Veneziano, G.
- Nuclear Physics B, Vol. 171
Note on a sigma model connection with instanton dynamics
journal, May 2008
- Fariborz, Amir H.; Jora, Renata; Schechter, Joseph
- Physical Review D, Vol. 77, Issue 9
Lattice tests of beyond standard model dynamics
journal, January 2016
- DeGrand, Thomas
- Reviews of Modern Physics, Vol. 88, Issue 1
Breaking the Axial u(1) does not Enhance Second Class Decays
journal, September 1987
- Meurice, Y.
- Modern Physics Letters A, Vol. 02, Issue 09
Topology and higher dimensional representations
journal, August 2009
- Fodor, Zoltán; Holland, Kieran; Kuti, Julius
- Journal of High Energy Physics, Vol. 2009, Issue 08
Strong dynamics, composite Higgs and the conformal window
journal, August 2016
- Nogradi, Daniel; Patella, Agostino
- International Journal of Modern Physics A, Vol. 31, Issue 22
Works referencing / citing this record:
Lattice gauge theory for physics beyond the Standard Model
journal, November 2019
- Brower, Richard C.; Hasenfratz, Anna; Neil, Ethan T.
- The European Physical Journal A, Vol. 55, Issue 11
Nonperturbative investigations of SU(3) gauge theory with eight dynamical flavors
text, January 2019
- Appelquist, T.; Brower, R. C.; Fleming, G. T.
- American Physical Society
Lattice Gauge Theory for Physics Beyond the Standard Model
text, January 2019
- Brower, Richard C.; Hasenfratz, Anna; Neil, Ethan T.
- arXiv
Phase transitions in neutron stars and their links to gravitational waves
text, January 2019
- Orsaria, Milva G.; Malfatti, Germán; Mariani, Mauro
- arXiv