Abstract
We study in detail the vacuum structure of a composite two Higgs doublet model based on a minimal underlying theory with 3 Dirac fermions in pseudo-real representations of the condensing gauge interactions, leading to the SU(6)/Sp(6) symmetry breaking pattern. We find that, independently on the source of top mass, the most general CP-conserving vacuum is characterised by three non-vanishing angles. A special case occurs if the Yukawas are aligned, leading to a single angle. In the latter case, a Dark Matter candidate arises, protected by a global U(1) symmetry.
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References
P.W. Higgs, Broken Symmetries and the Masses of Gauge Bosons, Phys. Rev. Lett. 13 (1964) 508 [INSPIRE].
S. Weinberg, Implications of Dynamical Symmetry Breaking, Phys. Rev. D 13 (1976) 974 [INSPIRE].
S. Dimopoulos and L. Susskind, Mass Without Scalars, Nucl. Phys. B 155 (1979) 237 [INSPIRE].
F. Sannino and K. Tuominen, Orientifold theory dynamics and symmetry breaking, Phys. Rev. D 71 (2005) 051901 [hep-ph/0405209] [INSPIRE].
S. Catterall and F. Sannino, Minimal walking on the lattice, Phys. Rev. D 76 (2007) 034504 [arXiv:0705.1664] [INSPIRE].
J. Rantaharju, C. Pica and F. Sannino, Ideal Walking Dynamics via a Gauged NJLS Model, Phys. Rev. D 96 (2017) 014512 [arXiv:1704.03977] [INSPIRE].
R. Foadi, M.T. Frandsen and F. Sannino, 125 GeV Higgs boson from a not so light technicolor scalar, Phys. Rev. D 87 (2013) 095001 [arXiv:1211.1083] [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].
J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
R. Contino, Y. Nomura and A. Pomarol, Higgs as a holographic pseudoGoldstone boson, Nucl. Phys. B 671 (2003) 148 [hep-ph/0306259] [INSPIRE].
R. Contino, The Higgs as a Composite Nambu-Goldstone Boson, in Physics of the large and the small, TASI 09, proceedings of the Theoretical Advanced Study Institute in Elementary Particle Physics, Boulder, Colorado, U.S.A., 1–26 June 2009, pp. 235–306 (2011) [https://doi.org/10.1142/9789814327183_0005] [arXiv:1005.4269] [INSPIRE].
B. Bellazzini, C. Csáki and J. Serra, Composite Higgses, Eur. Phys. J. C 74 (2014) 2766 [arXiv:1401.2457] [INSPIRE].
G. Panico and A. Wulzer, The Composite Nambu-Goldstone Higgs, Lect. Notes Phys. 913 (2016) 1 [arXiv:1506.01961] [INSPIRE].
G. Cacciapaglia and F. Sannino, Fundamental Composite (Goldstone) Higgs Dynamics, JHEP 04 (2014) 111 [arXiv:1402.0233] [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].
G. von Gersdorff, E. Pontón and R. Rosenfeld, The Dynamical Composite Higgs, JHEP 06 (2015) 119 [arXiv:1502.07340] [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].
M. Frigerio, A. Pomarol, F. Riva and A. Urbano, Composite Scalar Dark Matter, JHEP 07 (2012) 015 [arXiv:1204.2808] [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].
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].
A. Hietanen, R. Lewis, C. Pica and F. Sannino, Fundamental Composite Higgs Dynamics on the Lattice: SU(2) with Two Flavors, JHEP 07 (2014) 116 [arXiv:1404.2794] [INSPIRE].
V. Drach, A. Hietanen, C. Pica, J. Rantaharju and F. Sannino, Template Composite Dark Matter: SU(2) gauge theory with 2 fundamental flavours, PoS(LATTICE2015)234 (2016) [arXiv:1511.04370] [INSPIRE].
R. Arthur, V. Drach, M. Hansen, A. Hietanen, C. Pica and F. Sannino, SU(2) gauge theory with two fundamental flavors: A minimal template for model building, Phys. Rev. D 94 (2016) 094507 [arXiv:1602.06559] [INSPIRE].
R. Arthur, V. Drach, A. Hietanen, C. Pica and F. Sannino, SU(2) Gauge Theory with Two Fundamental Flavours: Scalar and Pseudoscalar Spectrum, arXiv:1607.06654 [INSPIRE].
N. Bizot, M. Frigerio, M. Knecht and J.-L. Kneur, Nonperturbative analysis of the spectrum of meson resonances in an ultraviolet-complete composite-Higgs model, Phys. Rev. D 95 (2017) 075006 [arXiv:1610.09293] [INSPIRE].
T. Ma and G. Cacciapaglia, Fundamental Composite 2HDM: SU(N) with 4 flavours, JHEP 03 (2016) 211 [arXiv:1508.07014] [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].
E. Bertuzzo, T.S. Ray, H. de Sandes and C.A. Savoy, On Composite Two Higgs Doublet Models, JHEP 05 (2013) 153 [arXiv:1206.2623] [INSPIRE].
S. De Curtis, S. Moretti, K. Yagyu and E. Yildirim, Theory and Phenomenology of Composite 2-Higgs Doublet Models, PoS(CHARGED2016)018 (2016) [arXiv:1612.05125] [INSPIRE].
M. Chala, h → γγ excess and Dark Matter from Composite Higgs Models, JHEP 01 (2013) 122 [arXiv:1210.6208] [INSPIRE].
Y. Wu, T. Ma, B. Zhang and G. Cacciapaglia, Composite Dark Matter and Higgs, JHEP 11 (2017) 058 [arXiv:1703.06903] [INSPIRE].
G. Ballesteros, A. Carmona and M. Chala, Exceptional Composite Dark Matter, Eur. Phys. J. C 77 (2017) 468 [arXiv:1704.07388] [INSPIRE].
R. Balkin, M. Ruhdorfer, E. Salvioni and A. Weiler, Charged Composite Scalar Dark Matter, JHEP 11 (2017) 094 [arXiv:1707.07685] [INSPIRE].
H. Georgi and D.B. Kaplan, Composite Higgs and Custodial SU(2), Phys. Lett. B 145 (1984) 216 [INSPIRE].
A. Pomarol and R. Vega, Constraints on CP-violation in the Higgs sector from the rho parameter, Nucl. Phys. B 413 (1994) 3 [hep-ph/9305272] [INSPIRE].
B. Grzadkowski, M. Maniatis and J. Wudka, The bilinear formalism and the custodial symmetry in the two-Higgs-doublet model, JHEP 11 (2011) 030 [arXiv:1011.5228] [INSPIRE].
I. Low, W. Skiba and D. Tucker-Smith, Little Higgses from an antisymmetric condensate, Phys. Rev. D 66 (2002) 072001 [hep-ph/0207243] [INSPIRE].
T. Brown, C. Frugiuele and T. Gregoire, UV friendly T-parity in the SU(6)/Sp(6) little Higgs model, JHEP 06 (2011) 108 [arXiv:1012.2060] [INSPIRE].
M.E. Peskin and T. Takeuchi, Estimation of oblique electroweak corrections, Phys. Rev. D 46 (1992) 381 [INSPIRE].
E. Eichten and K.D. Lane, Dynamical Breaking of Weak Interaction Symmetries, Phys. Lett. B 90 (1980) 125 [INSPIRE].
R. Rattazzi, V.S. Rychkov, E. Tonni and A. Vichi, Bounding scalar operator dimensions in 4D CFT, JHEP 12 (2008) 031 [arXiv:0807.0004] [INSPIRE].
V.S. Rychkov and A. Vichi, Universal Constraints on Conformal Operator Dimensions, Phys. Rev. D 80 (2009) 045006 [arXiv:0905.2211] [INSPIRE].
O. Antipin, E. Mølgaard and F. Sannino, Higgs Critical Exponents and Conformal Bootstrap in Four Dimensions, JHEP 06 (2015) 030 [arXiv:1406.6166] [INSPIRE].
G. Cacciapaglia, H. Cai, T. Flacke, S.J. Lee, A. Parolini and H. Serôdio, Anarchic Yukawas and top partial compositeness: the flavour of a successful marriage, JHEP 06 (2015) 085 [arXiv:1501.03818] [INSPIRE].
G. Panico and A. Pomarol, Flavor hierarchies from dynamical scales, JHEP 07 (2016) 097 [arXiv:1603.06609] [INSPIRE].
G. Cacciapaglia and F. Sannino, An Ultraviolet Chiral Theory of the Top for the Fundamental Composite (Goldstone) Higgs, Phys. Lett. B 755 (2016) 328 [arXiv:1508.00016] [INSPIRE].
E.H. Simmons, Phenomenology of a Technicolor Model With Heavy Scalar Doublet, Nucl. Phys. B 312 (1989) 253 [INSPIRE].
S. Samuel, Bosonic Technicolor, Nucl. Phys. B 347 (1990) 625 [INSPIRE].
O. Antipin and M. Redi, The Half-composite Two Higgs Doublet Model and the Relaxion, JHEP 12 (2015) 031 [arXiv:1508.01112] [INSPIRE].
A. Agugliaro, O. Antipin, D. Becciolini, S. De Curtis and M. Redi, UV complete composite Higgs models, Phys. Rev. D 95 (2017) 035019 [arXiv:1609.07122] [INSPIRE].
D.B. Kaplan, Flavor at SSC energies: A New mechanism for dynamically generated fermion masses, Nucl. Phys. B 365 (1991) 259 [INSPIRE].
F. Sannino, A. Strumia, A. Tesi and E. Vigiani, Fundamental partial compositeness, JHEP 11 (2016) 029 [arXiv:1607.01659] [INSPIRE].
G.M. Pelaggi, F. Sannino, A. Strumia and E. Vigiani, Naturalness of asymptotically safe Higgs, Front. in Phys. 5 (2017) 49 [arXiv:1701.01453] [INSPIRE].
G. Cacciapaglia, H. Gertov, F. Sannino and A.E. Thomsen, Minimal Fundamental Partial Compositeness, Phys. Rev. D 98 (2018) 015006 [arXiv:1704.07845] [INSPIRE].
F. Sannino, P. Stangl, D.M. Straub and A.E. Thomsen, Flavor Physics and Flavor Anomalies in Minimal Fundamental Partial Compositeness, Phys. Rev. D 97 (2018) 115046 [arXiv:1712.07646] [INSPIRE].
T. Alanne, N. Bizot, G. Cacciapaglia and F. Sannino, Classification of NLO operators for composite Higgs models, Phys. Rev. D 97 (2018) 075028 [arXiv:1801.05444] [INSPIRE].
G. Ferretti and D. Karateev, Fermionic UV completions of Composite Higgs models, JHEP 03 (2014) 077 [arXiv:1312.5330] [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].
A. Belyaev, G. Cacciapaglia, H. Cai, T. Flacke, A. Parolini and H. Serôdio, Singlets in composite Higgs models in light of the LHC 750 GeV diphoton excess, Phys. Rev. D 94 (2016) 015004 [arXiv:1512.07242] [INSPIRE].
A. Belyaev et al., Di-boson signatures as Standard Candles for Partial Compositeness, JHEP 01 (2017) 094 [Erratum ibid. 12 (2017) 088] [arXiv:1610.06591] [INSPIRE].
E. Bennett et al., Sp(4) gauge theory on the lattice: towards SU(4)/Sp(4) composite Higgs (and beyond), JHEP 03 (2018) 185 [arXiv:1712.04220] [INSPIRE].
F. Sannino, Conformal Windows of Sp(2N) and SO(N) Gauge Theories, Phys. Rev. D 79 (2009) 096007 [arXiv:0902.3494] [INSPIRE].
T.A. Ryttov and F. Sannino, Conformal House, Int. J. Mod. Phys. A 25 (2010) 4603 [arXiv:0906.0307] [INSPIRE].
G. Ferretti, Gauge theories of Partial Compositeness: Scenarios for Run-II of the LHC, JHEP 06 (2016) 107 [arXiv:1604.06467] [INSPIRE].
C. Csáki, T. Ma and J. Shu, Maximally Symmetric Composite Higgs Models, Phys. Rev. Lett. 119 (2017) 131803 [arXiv:1702.00405] [INSPIRE].
O. Matsedonskyi, G. Panico and A. Wulzer, Light Top Partners for a Light Composite Higgs, JHEP 01 (2013) 164 [arXiv:1204.6333] [INSPIRE].
D. Marzocca, M. Serone and J. Shu, General Composite Higgs Models, JHEP 08 (2012) 013 [arXiv:1205.0770] [INSPIRE].
R. Contino, D. Marzocca, D. Pappadopulo and R. Rattazzi, On the effect of resonances in composite Higgs phenomenology, JHEP 10 (2011) 081 [arXiv:1109.1570] [INSPIRE].
M. Golterman and Y. Shamir, Effective potential in ultraviolet completions for composite Higgs models, Phys. Rev. D 97 (2018) 095005 [arXiv:1707.06033] [INSPIRE].
A. Arbey, G. Cacciapaglia, H. Cai, A. Deandrea, S. Le Corre and F. Sannino, Fundamental Composite Electroweak Dynamics: Status at the LHC, Phys. Rev. D 95 (2017) 015028 [arXiv:1502.04718] [INSPIRE].
T. Hambye, F.S. Ling, L. Lopez Honorez and J. Rocher, Scalar Multiplet Dark Matter, JHEP 07 (2009) 090 [Erratum ibid. 05 (2010) 066] [arXiv:0903.4010] [INSPIRE].
Z.-H. Yu, J.-M. Zheng, X.-J. Bi, Z. Li, D.-X. Yao and H.-H. Zhang, Constraining the interaction strength between dark matter and visible matter: II. scalar, vector and spin-3/2 dark matter, Nucl. Phys. B 860 (2012) 115 [arXiv:1112.6052] [INSPIRE].
XENON collaboration, Dark Matter Search Results from a One Ton-Year Exposure of XENON1T, Phys. Rev. Lett. 121 (2018) 111302 [arXiv:1805.12562] [INSPIRE].
LUX collaboration, Results from a search for dark matter in the complete LUX exposure, Phys. Rev. Lett. 118 (2017) 021303 [arXiv:1608.07648] [INSPIRE].
PandaX-II collaboration, Dark Matter Results From 54-Ton-Day Exposure of PandaX-II Experiment, Phys. Rev. Lett. 119 (2017) 181302 [arXiv:1708.06917] [INSPIRE].
MAGIC and Fermi-LAT collaborations, Limits to Dark Matter Annihilation Cross-Section from a Combined Analysis of MAGIC and Fermi-LAT Observations of Dwarf Satellite Galaxies, JCAP 02 (2016) 039 [arXiv:1601.06590] [INSPIRE].
J. Serra, Beyond the Minimal Top Partner Decay, JHEP 09 (2015) 176 [arXiv:1506.05110] [INSPIRE].
A. Banerjee, G. Bhattacharyya and T.S. Ray, Improving Fine-tuning in Composite Higgs Models, Phys. Rev. D 96 (2017) 035040 [arXiv:1703.08011] [INSPIRE].
J. Wess and B. Zumino, Consequences of anomalous Ward identities, Phys. Lett. B 37 (1971) 95 [INSPIRE].
E. Witten, Global Aspects of Current Algebra, Nucl. Phys. B 223 (1983) 422 [INSPIRE].
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Cai, C., Zhang, HH. & Cacciapaglia, G. Vacuum alignment in a composite 2HDM. J. High Energ. Phys. 2019, 130 (2019). https://doi.org/10.1007/JHEP01(2019)130
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DOI: https://doi.org/10.1007/JHEP01(2019)130