Abstract
We provide a unified description, both at the effective and fundamental Lagrangian level, of models of composite Higgs dynamics where the Higgs itself can emerge, depending on the way the electroweak symmetry is embedded, either as a pseudo-Goldstone boson or as a massive excitation of the condensate. We show that, in general, these states mix with repercussions on the electroweak physics and phenomenology. Our results will help clarify the main differences, similarities, benefits and shortcomings of the different ways one can naturally realize a composite nature of the electroweak sector of the Standard Model. We will analyze the minimal underlying realization in terms of fundamental strongly coupled gauge theories supporting the flavor symmetry breaking pattern SU(4)/Sp(4) ~ SO(6)/SO(5). The most minimal fundamental description consists of an SU(2) gauge theory with two Dirac fermions transforming according to the fundamental representation of the gauge group. This minimal choice enables us to use recent first principle lattice results to make the first predictions for the massive spectrum for models of composite (Goldstone) Higgs dynamics. These results are of the utmost relevance to guide searches of new physics at the Large Hadron Collider.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
O. Antipin, M. Mojaza and F. Sannino, Natural Conformal Extensions of the Standard Model, arXiv:1310.0957 [INSPIRE].
S. Weinberg, Implications of Dynamical Symmetry Breaking, Phys. Rev. D 13 (1976) 974 [INSPIRE].
L. Susskind, Dynamics of Spontaneous Symmetry Breaking in the Weinberg-Salam Theory, Phys. Rev. D 20 (1979) 2619 [INSPIRE].
D.B. Kaplan and H. Georgi, SU(2) × U(1) Breaking by Vacuum Misalignment, Phys. Lett. B 136 (1984) 183 [INSPIRE].
D.B. Kaplan, H. Georgi and S. Dimopoulos, Composite Higgs Scalars, Phys. Lett. B 136 (1984) 187 [INSPIRE].
R. Foadi, M.T. Frandsen and F. Sannino, 125 GeV Higgs from a not so light Technicolor Scalar, Phys. Rev. D 87 (2013) 095001 [arXiv:1211.1083] [INSPIRE].
M.E. Peskin, The Alignment of the Vacuum in Theories of Technicolor, Nucl. Phys. B 175 (1980) 197 [INSPIRE].
J. Preskill, Subgroup Alignment in Hypercolor Theories, Nucl. Phys. B 177 (1981) 21 [INSPIRE].
D.A. Kosower, Symmetry breaking patterns in pseudoreal and real gauge theories, Phys. Lett. B 144 (1984) 215 [INSPIRE].
F. Sannino and K. Tuominen, Orientifold theory dynamics and symmetry breaking, Phys. Rev. D 71 (2005) 051901 [hep-ph/0405209] [INSPIRE].
D.D. Dietrich and F. Sannino, Conformal window of SU(N) gauge theories with fermions in higher dimensional representations, Phys. Rev. D 75 (2007) 085018 [hep-ph/0611341] [INSPIRE].
F. Sannino, Conformal Windows of SP(2N) and SO(N) Gauge Theories, Phys. Rev. D 79 (2009) 096007 [arXiv:0902.3494] [INSPIRE].
M. Mojaza, C. Pica, T.A. Ryttov and F. Sannino, Exceptional and Spinorial Conformal Windows, Phys. Rev. D 86 (2012) 076012 [arXiv:1206.2652] [INSPIRE].
S. Catterall and F. Sannino, Minimal walking on the lattice, Phys. Rev. D 76 (2007) 034504 [arXiv:0705.1664] [INSPIRE].
S. Catterall, J. Giedt, F. Sannino and J. Schneible, Phase diagram of SU(2) with 2 flavors of dynamical adjoint quarks, JHEP 11 (2008) 009 [arXiv:0807.0792] [INSPIRE].
L. Del Debbio, M.T. Frandsen, H. Panagopoulos and F. Sannino, Higher representations on the lattice: Perturbative studies, JHEP 06 (2008) 007 [arXiv:0802.0891] [INSPIRE].
L. Del Debbio, A. Patella and C. Pica, Higher representations on the lattice: Numerical simulations. SU(2) with adjoint fermions, Phys. Rev. D 81 (2010) 094503 [arXiv:0805.2058] [INSPIRE].
S. Catterall, J. Giedt, F. Sannino and J. Schneible, Probes of nearly conformal behavior in lattice simulations of minimal walking technicolor, arXiv:0910.4387 [INSPIRE].
A.J. Hietanen, K. Rummukainen and K. Tuominen, Evolution of the coupling constant in SU(2) lattice gauge theory with two adjoint fermions, Phys. Rev. D 80 (2009) 094504 [arXiv:0904.0864] [INSPIRE].
L. Del Debbio, B. Lucini, A. Patella, C. Pica and A. Rago, Conformal versus confining scenario in SU(2) with adjoint fermions, Phys. Rev. D 80 (2009) 074507 [arXiv:0907.3896] [INSPIRE].
J.B. Kogut and D.K. Sinclair, Thermodynamics of lattice QCD with 2 flavours of colour-sextet quarks: A model of walking/conformal Technicolor, Phys. Rev. D 81 (2010) 114507 [arXiv:1002.2988] [INSPIRE].
T. Karavirta, J. Rantaharju, K. Rummukainen and K. Tuominen, Determining the conformal window: SU(2) gauge theory with N f = 4, 6 and 10 fermion flavours, JHEP 05 (2012) 003 [arXiv:1111.4104] [INSPIRE].
R. Lewis, C. Pica and F. Sannino, Light Asymmetric Dark Matter on the Lattice: SU(2) Technicolor with Two Fundamental Flavors, Phys. Rev. D 85 (2012) 014504 [arXiv:1109.3513] [INSPIRE].
A. Hietanen, C. Pica, F. Sannino and U.I. Sondergaard, Isotriplet Dark Matter on the Lattice: SO(4)-gauge theory with two Vector Wilson fermions, PoS(LATTICE 2012)065 [arXiv:1211.0142] [INSPIRE].
A. Hietanen, C. Pica, F. Sannino and U.I. Sondergaard, Orthogonal Technicolor with Isotriplet Dark Matter on the Lattice, Phys. Rev. D 87 (2013) 034508 [arXiv:1211.5021] [INSPIRE].
A. Hietanen, R. Lewis, C. Pica and F. Sannino, Composite Goldstone Dark Matter: Experimental Predictions from the Lattice, arXiv:1308.4130 [INSPIRE].
A. Hietanen, C. Pica, F. Sannino and U. Søndergaard, Predictions for LHC from SO(4) MWT, arXiv:1311.3841 [INSPIRE].
J. Mrazek, A. Pomarol, R. Rattazzi, M. Redi, J. Serra and A. Wulzer, The Other Natural Two Higgs Doublet Model, Nucl. Phys. B 853 (2011) 1 [arXiv:1105.5403] [INSPIRE].
B. Bellazzini, C. Csáki and J. Serra, Composite Higgses, arXiv:1401.2457 [INSPIRE].
K. Agashe, R. Contino and A. Pomarol, The minimal composite Higgs model, Nucl. Phys. B 719 (2005) 165 [hep-ph/0412089] [INSPIRE].
F. Caracciolo, A. Parolini and M. Serone, UV Completions of Composite Higgs Models with Partial Compositeness, JHEP 02 (2013) 066 [arXiv:1211.7290] [INSPIRE].
R. Foadi, M.T. Frandsen, T.A. Ryttov and F. Sannino, Minimal Walking Technicolor: Set Up for Collider Physics, Phys. Rev. D 76 (2007) 055005 [arXiv:0706.1696] [INSPIRE].
M.T. Frandsen and F. Sannino, iTIMP: isotriplet Technicolor Interacting Massive Particle as Dark Matter, Phys. Rev. D 81 (2010) 097704 [arXiv:0911.1570] [INSPIRE].
T. Appelquist, P.S. Rodrigues da Silva and F. Sannino, Enhanced global symmetries and the chiral phase transition, Phys. Rev. D 60 (1999) 116007 [hep-ph/9906555] [INSPIRE].
Z.-y. Duan, P.S. Rodrigues da Silva and F. Sannino, Enhanced global symmetry constraints on epsilon terms, Nucl. Phys. B 592 (2001) 371 [hep-ph/0001303] [INSPIRE].
T.A. Ryttov and F. Sannino, Ultra Minimal Technicolor and its Dark Matter TIMP, Phys. Rev. D 78 (2008) 115010 [arXiv:0809.0713] [INSPIRE].
E. Katz, A.E. Nelson and D.G.E. Walker, The Intermediate Higgs, JHEP 08 (2005) 074 [hep-ph/0504252] [INSPIRE].
B. Gripaios, A. Pomarol, F. Riva and J. Serra, Beyond the Minimal Composite Higgs Model, JHEP 04 (2009) 070 [arXiv:0902.1483] [INSPIRE].
J. Galloway, J.A. Evans, M.A. Luty and R.A. Tacchi, Minimal Conformal Technicolor and Precision Electroweak Tests, JHEP 10 (2010) 086 [arXiv:1001.1361] [INSPIRE].
J. Barnard, T. Gherghetta and T.S. Ray, UV descriptions of composite Higgs models without elementary scalars, JHEP 02 (2014) 002 [arXiv:1311.6562] [INSPIRE].
G. Ferretti and D. Karateev, Fermionic UV completions of Composite Higgs models, JHEP 03 (2014) 077 [arXiv:1312.5330] [INSPIRE].
P. Batra and Z. Chacko, Symmetry Breaking Patterns for the Little Higgs from Strong Dynamics, Phys. Rev. D 77 (2008) 055015 [arXiv:0710.0333] [INSPIRE].
L. Vecchi, The Natural Composite Higgs, arXiv:1304.4579 [INSPIRE].
M. Frigerio, A. Pomarol, F. Riva and A. Urbano, Composite Scalar Dark Matter, JHEP 07 (2012) 015 [arXiv:1204.2808] [INSPIRE].
Y. Hosotani, P. Ko and M. Tanaka, Stable Higgs Bosons as Cold Dark Matter, Phys. Lett. B 680 (2009) 179 [arXiv:0908.0212] [INSPIRE].
S.B. Gudnason, C. Kouvaris and F. Sannino, Towards working technicolor: Effective theories and dark matter, Phys. Rev. D 73 (2006) 115003 [hep-ph/0603014] [INSPIRE].
S.B. Gudnason, C. Kouvaris and F. Sannino, Dark Matter from new Technicolor Theories, Phys. Rev. D 74 (2006) 095008 [hep-ph/0608055] [INSPIRE].
E. Nardi, F. Sannino and A. Strumia, Decaying Dark Matter can explain the e ± excesses, JCAP 01 (2009) 043 [arXiv:0811.4153] [INSPIRE].
R. Foadi, M.T. Frandsen and F. Sannino, Technicolor Dark Matter, Phys. Rev. D 80 (2009) 037702 [arXiv:0812.3406] [INSPIRE].
E. Del Nobile, C. Kouvaris and F. Sannino, Interfering Composite Asymmetric Dark Matter for DAMA and CoGeNT, Phys. Rev. D 84 (2011) 027301 [arXiv:1105.5431] [INSPIRE].
D.D. Dietrich and M. Jarvinen, Pion masses in quasiconformal gauge field theories, Phys. Rev. D 79 (2009) 057903 [arXiv:0901.3528] [INSPIRE].
T.A. Ryttov and F. Sannino, Conformal House, Int. J. Mod. Phys. A 25 (2010) 4603 [arXiv:0906.0307] [INSPIRE].
N. Chen, T.A. Ryttov and R. Shrock, Patterns of Dynamical Gauge Symmetry Breaking, Phys. Rev. D 82 (2010) 116006 [arXiv:1010.3736] [INSPIRE].
T. Appelquist, Z.-y. Duan and F. Sannino, Phases of chiral gauge theories, Phys. Rev. D 61 (2000) 125009 [hep-ph/0001043] [INSPIRE].
K. Yamawaki, M. Bando and K.-i. Matumoto, Scale Invariant Technicolor Model and a Technidilaton, Phys. Rev. Lett. 56 (1986) 1335 [INSPIRE].
D.D. Dietrich, F. Sannino and K. Tuominen, Light composite Higgs from higher representations versus electroweak precision measurements: Predictions for CERN LHC, Phys. Rev. D 72 (2005) 055001 [hep-ph/0505059] [INSPIRE].
T. Appelquist and Y. Bai, A Light Dilaton in Walking Gauge Theories, Phys. Rev. D 82 (2010) 071701 [arXiv:1006.4375] [INSPIRE].
V.P. Gusynin and V.A. Miransky, Nonperturbative scale anomaly in gauge theories, Sov. Phys. JETP 68 (1989) 232 [INSPIRE].
B. Holdom and J. Terning, A Light Dilaton in Gauge Theories?, Phys. Lett. B 187 (1987) 357 [INSPIRE].
B. Holdom and J. Terning, No Light Dilaton in Gauge Theories, Phys. Lett. B 200 (1988) 338 [INSPIRE].
M. Harada, M. Kurachi and K. Yamawaki, Meson masses in large-N f QCD from Bethe-Salpeter equation, Phys. Rev. D 68 (2003) 076001 [hep-ph/0305018] [INSPIRE].
M. Kurachi and R. Shrock, Study of the Change from Walking to Non-Walking Behavior in a Vectorial Gauge Theory as a Function of N(f), JHEP 12 (2006) 034 [hep-ph/0605290] [INSPIRE].
A. Doff, A.A. Natale and P.S. Rodrigues da Silva, Light composite Higgs from an effective action for technicolor, Phys. Rev. D 77 (2008) 075012 [arXiv:0802.1898] [INSPIRE].
A. Doff and A.A. Natale, Mass and width of a composite Higgs boson, Phys. Lett. B 677 (2009) 301 [arXiv:0902.2379] [INSPIRE].
A. Doff, A.A. Natale and P.S. Rodrigues da Silva, Light composite Higgs boson from the normalized Bethe-Salpeter equation, Phys. Rev. D 80 (2009) 055005 [arXiv:0905.2981] [INSPIRE].
A. Doff and A.A. Natale, Scalar bosons in Minimal and Ultraminimal Technicolor: Masses, trilinear couplings and widths, Phys. Rev. D 81 (2010) 095014 [arXiv:0912.1003] [INSPIRE].
F. Sannino and M. Shifman, Effective Lagrangians for orientifold theories, Phys. Rev. D 69 (2004) 125004 [hep-th/0309252] [INSPIRE].
D.K. Hong, S.D.H. Hsu and F. Sannino, Composite Higgs from higher representations, Phys. Lett. B 597 (2004) 89 [hep-ph/0406200] [INSPIRE].
B. Grinstein and P. Uttayarat, A Very Light Dilaton, JHEP 07 (2011) 038 [arXiv:1105.2370] [INSPIRE].
O. Antipin, M. Mojaza and F. Sannino, Light Dilaton at Fixed Points and Ultra Light Scale Super Yang-Mills, Phys. Lett. B 712 (2012) 119 [arXiv:1107.2932] [INSPIRE].
O. Antipin, M. Mojaza and F. Sannino, Jumping out of the light-Higgs conformal window, Phys. Rev. D 87 (2013) 096005 [arXiv:1208.0987] [INSPIRE].
Z. Fodor, K. Holland, J. Kuti, D. Nogradi and C.H. Wong, Can a light Higgs impostor hide in composite gauge models?, arXiv:1401.2176 [INSPIRE].
Z. Fodor, K. Holland, J. Kuti, D. Nogradi, C. Schroeder and C.H. Wong, The sextet gauge model, light Higgs and the dilaton, PoS(LATTICE 2012)024 [arXiv:1211.6164] [INSPIRE].
F. Sannino, Jumping Dynamics, Mod. Phys. Lett. A 28 (2013) 1350127 [arXiv:1205.4246] [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: 1402.0233
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, 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 license, and indicate if changes were made.
About this article
Cite this article
Cacciapaglia, G., Sannino, F. Fundamental composite (Goldstone) Higgs dynamics. J. High Energ. Phys. 2014, 111 (2014). https://doi.org/10.1007/JHEP04(2014)111
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2014)111