Abstract
We consider scalegenesis, spontaneous scale symmetry breaking, by the scalar-bilinear condensation in SU(N) scalar gauge theory. In an effective field theory approach to the scalar-bilinear condensation at finite temperature, we include the Polyakov loop to take into account the confinement effect. The theory with N = 3, 4, 5 and 6 is investigated, and we find that in all these cases the scale phase transition is a first-order phase transition. We also calculate the latent heat at and slightly below the critical temperature. Comparing the results with those obtained without the Polyakov loop effect, we find that the Polyakov effect can considerably increase the latent heat in some cases, which would mean a large increase in the energy density of the gravitational waves background, if it were produced by the scale phase transition.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
E. Gildener, Gauge symmetry hierarchies, Phys. Rev. D 14 (1976) 1667 [INSPIRE].
S. Weinberg, Gauge hierarchies, Phys. Lett. 82B (1979) 387 [INSPIRE].
K.-Y. Oda and M. Yamada, Non-minimal coupling in Higgs-Yukawa model with asymptotically safe gravity, Class. Quant. Grav. 33 (2016) 125011 [arXiv:1510.03734] [INSPIRE].
C. Wetterich and M. Yamada, Gauge hierarchy problem in asymptotically safe gravity-the resurgence mechanism, Phys. Lett. B 770 (2017) 268 [arXiv:1612.03069] [INSPIRE].
Y. Hamada and M. Yamada, Asymptotic safety of higher derivative quantum gravity non-minimally coupled with a matter system, JHEP 08 (2017) 070 [arXiv:1703.09033] [INSPIRE].
A. Eichhorn, Y. Hamada, J. Lumma and M. Yamada, Quantum gravity fluctuations flatten the Planck-scale Higgs potential, Phys. Rev. D 97 (2018) 086004 [arXiv:1712.00319] [INSPIRE].
M. Niedermaier and M. Reuter, Gravitational radiation from post-newtonian sources and inspiralling compact binaries, Living Rev. Rel. 9 (2006) 5.
M. Niedermaier, The asymptotic safety scenario in quantum gravity: an introduction, Class. Quant. Grav. 24 (2007) R171 [gr-qc/0610018] [INSPIRE].
R. Percacci, Asymptotic safety, arXiv:0709.3851 [INSPIRE].
M. Reuter and F. Saueressig, Quantum Einstein gravity, New J. Phys. 14 (2012) 055022 [arXiv:1202.2274] [INSPIRE].
A. Codello, R. Percacci and C. Rahmede, Investigating the ultraviolet properties of gravity with a wilsonian renormalization group equation, Annals Phys. 324 (2009) 414 [arXiv:0805.2909] [INSPIRE].
A. Eichhorn, Status of the asymptotic safety paradigm for quantum gravity and matter, in the proceedings of Black Holes, Gravitational Waves and Spacetime Singularities, May 9–12, Rome, Italy (2017), arXiv:1709.03696 [INSPIRE].
R. Percacci, An introduction to covariant quantum gravity and asymptotic safety, Years of General Relativity volume 3, World Scientific, Singapore (2017).
C. Wetterich, Fine tuning problem and the renormalization group, Phys. Lett. 140B (1984) 215 [INSPIRE].
W.A. Bardeen, On naturalness in the standard model, in the proceedings of Ontake Summer Institute on Particle Physics, August 27–September 2, Ontake Mountain, Japan (1995).
H. Aoki and S. Iso, Revisiting the naturalness problem - Who is afraid of quadratic divergences?, Phys. Rev. D 86 (2012) 013001 [arXiv:1201.0857] [INSPIRE].
S.R. Coleman and E.J. Weinberg, Radiative corrections as the origin of spontaneous symmetry breaking, Phys. Rev. D 7 (1973) 1888 [INSPIRE].
T. Hur and P. Ko, Scale invariant extension of the standard model with strongly interacting hidden sector, Phys. Rev. Lett. 106 (2011) 141802 [arXiv:1103.2571] [INSPIRE].
M. Heikinheimo et al., Physical naturalness and dynamical breaking of classical scale invariance, Mod. Phys. Lett. A 29 (2014) 1450077 [arXiv:1304.7006] [INSPIRE].
M. Holthausen, J. Kubo, K.S. Lim and M. Lindner, Electroweak and conformal symmetry breaking by a strongly coupled hidden sector, JHEP 12 (2013) 076 [arXiv:1310.4423] [INSPIRE].
J. Kubo, K.S. Lim and M. Lindner, Gamma-ray line from Nambu-Goldstone dark matter in a scale invariant extension of the standard model, JHEP 09 (2014) 016 [arXiv:1405.1052] [INSPIRE].
M. Heikinheimo and C. Spethmann, Galactic centre GeV photons from dark technicolor, JHEP 12 (2014) 084 [arXiv:1410.4842] [INSPIRE].
C.D. Carone and R. Ramos, Dark chiral symmetry breaking and the origin of the electroweak scale, Phys. Lett. B 746 (2015) 424 [arXiv:1505.04448] [INSPIRE].
Y. Ametani, M. Aoki, H. Goto and J. Kubo, Nambu-Goldstone dark matter in a scale invariant bright hidden sector, Phys. Rev. D 91 (2015) 115007 [arXiv:1505.00128] [INSPIRE].
J. Kubo and M. Yamada, Genesis of electroweak and dark matter scales from a bilinear scalar condensate, Phys. Rev. D 93 (2016) 075016 [arXiv:1505.05971] [INSPIRE].
N. Haba, H. Ishida, N. Kitazawa and Y. Yamaguchi, A new dynamics of electroweak symmetry breaking with classically scale invariance, Phys. Lett. B 755 (2016) 439 [arXiv:1512.05061] [INSPIRE].
H. Hatanaka, D.-W. Jung and P. Ko, AdS/QCD approach to the scale-invariant extension of the standard model with a strongly interacting hidden sector, JHEP 08 (2016) 094 [arXiv:1606.02969] [INSPIRE].
H. Ishida, S. Matsuzaki, S. Okawa and Y. Omura, Scale generation via dynamically induced multiple seesaw mechanisms, Phys. Rev. D 95 (2017) 075033 [arXiv:1701.00598] [INSPIRE].
N. Haba and T. Yamada, Strong dynamics in a classically scale invariant extension of the standard model with a flat potential, Phys. Rev. D 95 (2017) 115016 [arXiv:1701.02146] [INSPIRE].
N. Haba and T. Yamada, Multiple-point principle realized with strong dynamics, Phys. Rev. D 95 (2017) 115015 [arXiv:1703.04235] [INSPIRE].
K. Tsumura, M. Yamada and Y. Yamaguchi, Gravitational wave from dark sector with dark pion, JCAP 07 (2017) 044 [arXiv:1704.00219] [INSPIRE].
M. Aoki, H. Goto and J. Kubo, Gravitational waves from hidden QCD phase transition, Phys. Rev. D 96 (2017) 075045 [arXiv:1709.07572] [INSPIRE].
K. Osterwalder and E. Seiler, Gauge field theories on the lattice, Annals Phys. 110 (1978) 440 [INSPIRE].
E.H. Fradkin and S.H. Shenker, Phase diagrams of lattice gauge theories with Higgs fields, Phys. Rev. D 19 (1979) 3682 [INSPIRE].
Y. Nambu and G. Jona-Lasinio, Dynamical model of elementary particles based on an analogy with superconductivity. I, Phys. Rev. 122 (1961) 345.
Y. Nambu and G. Jona-Lasinio, Dynamical model of elementary particles based on an analogy with superconductivity. II, Phys. Rev. 124 (1961) 246.
J. Kubo, Q.M.B. Soesanto and M. Yamada, Non-perturbative electroweak-scalegenesis on the test bench of dark matter detection, Eur. Phys. J. C 78 (2018) 218 [arXiv:1712.06324] [INSPIRE].
J. Kubo and M. Yamada, Scale and electroweak first-order phase transitions, PTEP 2015 (2015) 093B01 [arXiv:1506.06460] [INSPIRE].
J. Kubo and M. Yamada, Scale genesis and gravitational wave in a classically scale invariant extension of the standard model, JCAP 12 (2016) 001 [arXiv:1610.02241] [INSPIRE].
N. Seto, S. Kawamura and T. Nakamura, Possibility of direct measurement of the acceleration of the universe using 0.1 Hz band laser interferometer gravitational wave antenna in space, Phys. Rev. Lett. 87 (2001) 221103 [astro-ph/0108011] [INSPIRE].
S. Kawamura et al., The Japanese space gravitational wave antenna DECIGO, Class. Quant. Grav. 23 (2006) S125 [INSPIRE].
S. Kawamura et al., The Japanese space gravitational wave antenna: DECIGO, Class. Quant. Grav. 28 (2011) 094011 [INSPIRE].
eLISA collaboration, P.A. Seoane et al., The gravitational universe, arXiv:1305.5720 [INSPIRE].
N. Weiss, The effective potential for the order parameter of gauge theories at finite temperature, Phys. Rev. D 24 (1981) 475 [INSPIRE].
R.D. Pisarski, Quark gluon plasma as a condensate of SU(3) Wilson lines, Phys. Rev. D 62 (2000) 111501 [hep-ph/0006205] [INSPIRE].
A. Dumitru and R.D. Pisarski, Event-by-event fluctuations from decay of a Polyakov loop condensate, Phys. Lett. B 504 (2001) 282 [hep-ph/0010083] [INSPIRE].
A. Dumitru and R.D. Pisarski, Degrees of freedom and the deconfining phase transition, Phys. Lett. B 525 (2002) 95 [hep-ph/0106176] [INSPIRE].
R.D. Pisarski, Tests of the Polyakov loops model, Nucl. Phys. A 702 (2002) 151 [hep-ph/0112037] [INSPIRE].
F. Sannino, Higher representations: confinement and large N , Phys. Rev. D 72 (2005) 125006 [hep-th/0507251] [INSPIRE].
F. Marhauser and J.M. Pawlowski, Confinement in Polyakov gauge, arXiv:0812.1144 [INSPIRE].
J. Braun, A. Eichhorn, H. Gies and J.M. Pawlowski, On the nature of the phase transition in SU(N), Sp(2) and E 7 Yang-Mills theory, Eur. Phys. J. C 70 (2010) 689 [arXiv:1007.2619] [INSPIRE].
K. Fukushima, Chiral effective model with the Polyakov loop, Phys. Lett. B 591 (2004) 277 [hep-ph/0310121] [INSPIRE].
C. Ratti, M.A. Thaler and W. Weise, Phases of QCD: lattice thermodynamics and a field theoretical model, Phys. Rev. D 73 (2006) 014019 [hep-ph/0506234] [INSPIRE].
S. Roessner, C. Ratti and W. Weise, Polyakov loop, diquarks and the two-flavour phase diagram, Phys. Rev. D 75 (2007) 034007 [hep-ph/0609281] [INSPIRE].
K. Fukushima, Phase diagrams in the three-flavor Nambu-Jona-Lasinio model with the Polyakov loop, Phys. Rev. D 77 (2008) 114028 [Erratum ibid. D 78 (2008) 039902] [arXiv:0803.3318] [INSPIRE].
T.K. Herbst, J.M. Pawlowski and B.-J. Schaefer, The phase structure of the Polyakov-quark-meson model beyond mean field, Phys. Lett. B 696 (2011) 58 [arXiv:1008.0081] [INSPIRE].
K. Fukushima and T. Hatsuda, The phase diagram of dense QCD, Rept. Prog. Phys. 74 (2011) 014001 [arXiv:1005.4814] [INSPIRE].
K. Fukushima and C. Sasaki, The phase diagram of nuclear and quark matter at high baryon density, Prog. Part. Nucl. Phys. 72 (2013) 99 [arXiv:1301.6377] [INSPIRE].
K. Fukushima and V. Skokov, Polyakov loop modeling for hot QCD, Prog. Part. Nucl. Phys. 96 (2017) 154 [arXiv:1705.00718] [INSPIRE].
W.A. Bardeen, C.N. Leung and S.T. Love, The dilaton and chiral symmetry breaking, Phys. Rev. Lett. 56 (1986) 1230 [INSPIRE].
A.M. Polyakov, Thermal properties of gauge fields and quark liberation, Phys. Lett. B 72 (1978) 477.
L. Susskind, Lattice models of quark confinement at high temperature, Phys. Rev. D 20 (1979) 2610 [INSPIRE].
B. Svetitsky and L.G. Yaffe, Critical behavior at finite temperature confinement transitions, Nucl. Phys. B 210 (1982) 423 [INSPIRE].
B. Svetitsky, Symmetry aspects of finite temperature confinement transitions, Phys. Rept. 132 (1986) 1 [INSPIRE].
J. Greensite, The confinement problem in lattice gauge theory, Prog. Part. Nucl. Phys. 51 (2003) 1 [hep-lat/0301023] [INSPIRE].
M. Fukugita and A. Ukawa, Deconfining and chiral transitions of finite temperature quantum chromodynamics in the presence of dynamical quark loops, Phys. Rev. Lett. 57 (1986) 503 [INSPIRE].
F. Karsch and E. Laermann, Susceptibilities, the specific heat and a cumulant in two flavor QCD, Phys. Rev. D 50 (1994) 6954 [hep-lat/9406008] [INSPIRE].
JLQCD collaboration, S. Aoki et al., Scaling study of the two flavor chiral phase transition with the Kogut-Susskind quark action in lattice QCD, Phys. Rev. D 57 (1998) 3910 [hep-lat/9710048] [INSPIRE].
F. Karsch, E. Laermann and A. Peikert, Quark mass and flavor dependence of the QCD phase transition, Nucl. Phys. B 605 (2001) 579 [hep-lat/0012023] [INSPIRE].
C.R. Allton et al., The QCD thermal phase transition in the presence of a small chemical potential, Phys. Rev. D 66 (2002) 074507 [hep-lat/0204010] [INSPIRE].
L.M. Haas et al., Improved Polyakov-loop potential for effective models from functional calculations, Phys. Rev. D 87 (2013) 076004 [arXiv:1302.1993] [INSPIRE].
K.-I. Kondo, Confinement-deconfinement phase transition and gauge-invariant gluonic mass in Yang-Mills theory, arXiv:1508.02656 [INSPIRE].
M. Shirogane et al., Latent heat at the first order phase transition point of SU(3) gauge theory, Phys. Rev. D 94 (2016) 014506 [arXiv:1605.02997] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1808.02413
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Kubo, J., Yamada, M. Scale and confinement phase transitions in scale invariant SU(N) scalar gauge theory. J. High Energ. Phys. 2018, 3 (2018). https://doi.org/10.1007/JHEP10(2018)003
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2018)003