Abstract
Composite Higgs and neutral-naturalness models are popular scenarios in which the Higgs boson is a pseudo Nambu-Goldstone boson (PNGB), and naturalness problem is addressed by composite top partners. Since the standard model effective field theory (SMEFT) with dimension-six operators cannot fully retain the information of Higgs nonlinearity due to its PNGB nature, we systematically construct low energy Lagrangian in which the information of compositeness and Higgs nonlinearity are encoded in the form factors, the two-point functions in the top sector. We classify naturalness conditions in various scenarios, and first present these form factors in composite neutral naturalness models. After extracting out Higgs effective couplings from these form factors and performing the global fit, we find the value of Higgs top coupling could still be larger than the standard model one if the top quark is embedded in the higher dimensional representations. Also we find the impact of Higgs nonlinearity is enhanced by the large mass splitting between composite states. In this case, pattern of the correlation between the t\( \overline{t} \)h and t\( \overline{t} \)hh couplings is quite different for the linear and nonlinear Higgs descriptions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
M.J. Dugan, H. Georgi and D.B. Kaplan, Anatomy of a Composite Higgs Model, Nucl. Phys.B 254 (1985) 299 [INSPIRE].
S.R. Coleman, J. Wess and B. Zumino, Structure of phenomenological Lagrangians. 1, Phys. Rev.177 (1969) 2239 [INSPIRE].
C.G. Callan Jr., S.R. Coleman, J. Wess and B. Zumino, Structure of phenomenological Lagrangians. 2, Phys. Rev.177 (1969) 2247 [INSPIRE].
R. Alonso, E.E. Jenkins and A.V. Manohar, σ-models with Negative Curvature, Phys. Lett.B 756 (2016) 358 [arXiv:1602.00706] [INSPIRE].
R. Alonso, E.E. Jenkins and A.V. Manohar, Geometry of the Scalar Sector, JHEP08 (2016) 101 [arXiv:1605.03602] [INSPIRE].
B. Henning, X. Lu and H. Murayama, How to use the Standard Model effective field theory, JHEP01 (2016) 023 [arXiv:1412.1837] [INSPIRE].
W. Buchmüller and D. Wyler, Effective Lagrangian Analysis of New Interactions and Flavor Conservation, Nucl. Phys.B 268 (1986) 621 [INSPIRE].
B. Grzadkowski, M. Iskrzynski, M. Misiak and J. Rosiek, Dimension-Six Terms in the Standard Model Lagrangian, JHEP10 (2010) 085 [arXiv:1008.4884] [INSPIRE].
G.F. Giudice, C. Grojean, A. Pomarol and R. Rattazzi, The Strongly-Interacting Light Higgs, JHEP06 (2007) 045 [hep-ph/0703164] [INSPIRE].
R. Contino, D. Marzocca, D. Pappadopulo and R. Rattazzi, On the effect of resonances in composite Higgs phenomenology, JHEP10 (2011) 081 [arXiv:1109.1570] [INSPIRE].
R. Alonso, I. Brivio, B. Gavela, L. Merlo and S. Rigolin, Sigma Decomposition, JHEP12 (2014) 034 [arXiv:1409.1589] [INSPIRE].
D. Liu, I. Low and Z. Yin, Universal Imprints of a Pseudo-Nambu-Goldstone Higgs Boson, Phys. Rev. Lett.121 (2018) 261802 [arXiv:1805.00489] [INSPIRE].
D. Liu, I. Low and Z. Yin, Universal Relations in Composite Higgs Models, JHEP05 (2019) 170 [arXiv:1809.09126] [INSPIRE].
H. Terazawa, K. Akama and Y. Chikashige, Unified Model of the Nambu-Jona-Lasinio Type for All Elementary Particle Forces, Phys. Rev.D 15 (1977) 480 [INSPIRE].
K. Agashe, R. Contino and A. Pomarol, The Minimal composite Higgs model, Nucl. Phys.B 719 (2005) 165 [hep-ph/0412089] [INSPIRE].
H. Terazawa, Subquark Model of Leptons and Quarks, Phys. Rev.D 22 (1980) 184 [INSPIRE].
Z. Chacko, H.-S. Goh and R. Harnik, The Twin Higgs: Natural electroweak breaking from mirror symmetry, Phys. Rev. Lett.96 (2006) 231802 [hep-ph/0506256] [INSPIRE].
N. Craig, A. Katz, M. Strassler and R. Sundrum, Naturalness in the Dark at the LHC, JHEP07 (2015) 105 [arXiv:1501.05310] [INSPIRE].
T. Appelquist and C.W. Bernard, Strongly Interacting Higgs Bosons, Phys. Rev.D 22 (1980) 200 [INSPIRE].
A.C. Longhitano, Heavy Higgs Bosons in the Weinberg-Salam Model, Phys. Rev.D 22 (1980) 1166 [INSPIRE].
F. Feruglio, The Chiral approach to the electroweak interactions, Int. J. Mod. Phys.A 8 (1993) 4937 [hep-ph/9301281] [INSPIRE].
V. Koulovassilopoulos and R.S. Chivukula, The Phenomenology of a nonstandard Higgs boson in W(L) W(L) scattering, Phys. Rev.D 50 (1994) 3218 [hep-ph/9312317] [INSPIRE].
B. Grinstein and M. Trott, A Higgs-Higgs bound state due to new physics at a TeV, Phys. Rev.D 76 (2007) 073002 [arXiv:0704.1505] [INSPIRE].
R. Contino, C. Grojean, M. Moretti, F. Piccinini and R. Rattazzi, Strong Double Higgs Production at the LHC, JHEP05 (2010) 089 [arXiv:1002.1011] [INSPIRE].
R. Alonso, M.B. Gavela, L. Merlo, S. Rigolin and J. Yepes, The Effective Chiral Lagrangian for a Light Dynamical “Higgs Particle”, Phys. Lett.B 722 (2013) 330 [Erratum ibid.B 726 (2013) 926] [arXiv:1212.3305] [INSPIRE].
G. Buchalla, O. Catà and C. Krause, Complete Electroweak Chiral Lagrangian with a Light Higgs at NLO, Nucl. Phys.B 880 (2014) 552 [Erratum ibid.B 913 (2016) 475] [arXiv:1307.5017] [INSPIRE].
G. Buchalla, O. Catá and C. Krause, On the Power Counting in Effective Field Theories, Phys. Lett.B 731 (2014) 80 [arXiv:1312.5624] [INSPIRE].
G. Buchalla, O. Catà and C. Krause, A Systematic Approach to the SILH Lagrangian, Nucl. Phys.B 894 (2015) 602 [arXiv:1412.6356] [INSPIRE].
D.B. Kaplan, Flavor at SSC energies: A New mechanism for dynamically generated fermion masses, Nucl. Phys.B 365 (1991) 259 [INSPIRE].
R. Contino, T. Kramer, M. Son and R. Sundrum, Warped/composite phenomenology simplified, JHEP05 (2007) 074 [hep-ph/0612180] [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 U.S.A. (2009), pg. 235 [arXiv:1005.4269] [INSPIRE].
A. Pomarol and F. Riva, The Composite Higgs and Light Resonance Connection, JHEP08 (2012) 135 [arXiv:1205.6434] [INSPIRE].
D. Marzocca, M. Serone and J. Shu, General Composite Higgs Models, JHEP08 (2012) 013 [arXiv:1205.0770] [INSPIRE].
R. Contino, L. Da Rold and A. Pomarol, Light custodians in natural composite Higgs models, Phys. Rev.D 75 (2007) 055014 [hep-ph/0612048] [INSPIRE].
M. Geller and O. Telem, Holographic Twin Higgs Model, Phys. Rev. Lett.114 (2015) 191801 [arXiv:1411.2974] [INSPIRE].
R. Barbieri, D. Greco, R. Rattazzi and A. Wulzer, The Composite Twin Higgs scenario, JHEP08 (2015) 161 [arXiv:1501.07803] [INSPIRE].
M. Low, A. Tesi and L.-T. Wang, Twin Higgs mechanism and a composite Higgs boson, Phys. Rev.D 91 (2015) 095012 [arXiv:1501.07890] [INSPIRE].
L.-X. Xu, J.-H. Yu and S.-H. Zhu, Minimal Neutral Naturalness Model, arXiv:1810.01882 [INSPIRE].
N. Arkani-Hamed, A.G. Cohen and H. Georgi, (De)constructing dimensions, Phys. Rev. Lett.86 (2001) 4757 [hep-th/0104005] [INSPIRE].
N. Arkani-Hamed, A.G. Cohen and H. Georgi, Electroweak symmetry breaking from dimensional deconstruction, Phys. Lett.B 513 (2001) 232 [hep-ph/0105239] [INSPIRE].
A. Azatov and J. Galloway, Light Custodians and Higgs Physics in Composite Models, Phys. Rev.D 85 (2012) 055013 [arXiv:1110.5646] [INSPIRE].
M. Gillioz, R. Grober, C. Grojean, M. Muhlleitner and E. Salvioni, Higgs Low-Energy Theorem (and its corrections) in Composite Models, JHEP10 (2012) 004 [arXiv:1206.7120] [INSPIRE].
M. Montull, F. Riva, E. Salvioni and R. Torre, Higgs Couplings in Composite Models, Phys. Rev.D 88 (2013) 095006 [arXiv:1308.0559] [INSPIRE].
D. Pappadopulo, A. Thamm and R. Torre, A minimally tuned composite Higgs model from an extra dimension, JHEP07 (2013) 058 [arXiv:1303.3062] [INSPIRE].
M. Carena, L. Da Rold and E. Pontón, Minimal Composite Higgs Models at the LHC, JHEP06 (2014) 159 [arXiv:1402.2987] [INSPIRE].
S. Kanemura, K. Kaneta, N. Machida and T. Shindou, New resonance scale and fingerprint identification in minimal composite Higgs models, Phys. Rev.D 91 (2015) 115016 [arXiv:1410.8413] [INSPIRE].
S. Kanemura, K. Kaneta, N. Machida, S. Odori and T. Shindou, Single and double production of the Higgs boson at hadron and lepton colliders in minimal composite Higgs models, Phys. Rev.D 94 (2016) 015028 [arXiv:1603.05588] [INSPIRE].
D. Liu, I. Low and C.E.M. Wagner, Modification of Higgs Couplings in Minimal Composite Models, Phys. Rev.D 96 (2017) 035013 [arXiv:1703.07791] [INSPIRE].
A. Banerjee, G. Bhattacharyya, N. Kumar and T.S. Ray, Constraining Composite Higgs Models using LHC data, JHEP03 (2018) 062 [arXiv:1712.07494] [INSPIRE].
R. Foadi, J.T. Laverty, C.R. Schmidt and J.-H. Yu, Radiative Electroweak Symmetry Breaking in a Little Higgs Model, JHEP06 (2010) 026 [arXiv:1001.0584] [INSPIRE].
G. Panico and A. Wulzer, The Discrete Composite Higgs Model, JHEP09 (2011) 135 [arXiv:1106.2719] [INSPIRE].
C. Csáki, T. Ma, J. Shu and J.-H. Yu, Emergence of Maximal Symmetry, arXiv:1810.07704 [INSPIRE].
J. Serra and R. Torre, Neutral naturalness from the brother-Higgs model, Phys. Rev.D 97 (2018) 035017 [arXiv:1709.05399] [INSPIRE].
C. Csáki, T. Ma and J. Shu, Trigonometric Parity for Composite Higgs Models, Phys. Rev. Lett.121 (2018) 231801 [arXiv:1709.08636] [INSPIRE].
G. Burdman, Z. Chacko, R. Harnik, L. de Lima and C.B. Verhaaren, Colorless Top Partners, a 125 GeV Higgs and the Limits on Naturalness, Phys. Rev.D 91 (2015) 055007 [arXiv:1411.3310] [INSPIRE].
J.R. Ellis, M.K. Gaillard and D.V. Nanopoulos, A Phenomenological Profile of the Higgs Boson, Nucl. Phys.B 106 (1976) 292 [INSPIRE].
M.A. Shifman, A.I. Vainshtein, M.B. Voloshin and V.I. Zakharov, Low-Energy Theorems for Higgs Boson Couplings to Photons, Sov. J. Nucl. Phys.30 (1979) 711 [INSPIRE].
B.A. Kniehl and M. Spira, Low-energy theorems in Higgs physics, Z. Phys.C 69 (1995) 77 [hep-ph/9505225] [INSPIRE].
Q.-H. Cao, L.-X. Xu, B. Yan and S.-H. Zhu, Signature of pseudo Nambu-Goldstone Higgs boson in its decay, Phys. Lett.B 789 (2019) 233 [arXiv:1810.07661] [INSPIRE].
ATLAS collaboration, Measurements of Higgs boson properties in the diphoton decay channel with 36 fb −1of pp collision data at \( \sqrt{s} \) = 13 TeV with the ATLAS detector, Phys. Rev.D 98 (2018) 052005 [arXiv:1802.04146] [INSPIRE].
ATLAS collaboration, Cross-section measurements of the Higgs boson decaying into a pair of τ -leptons in proton-proton collisions at \( \sqrt{s} \) = 13 TeV with the ATLAS detector, Phys. Rev.D 99 (2019) 072001 [arXiv:1811.08856] [INSPIRE].
ATLAS collaboration, Measurements of gluon-gluon fusion and vector-boson fusion Higgs boson production cross-sections in the H → W W ∗ → eνμν decay channel in pp collisions at \( \sqrt{s} \) = 13 TeV with the ATLAS detector, Phys. Lett.B 789 (2019) 508 [arXiv:1808.09054] [INSPIRE].
ATLAS collaboration, Measurement of the Higgs boson coupling properties in the H →ZZ ∗ →4ℓ decay channel at \( \sqrt{s} \) = 13 TeV with the ATLAS detector, JHEP03 (2018) 095 [arXiv:1712.02304] [INSPIRE].
ATLAS collaboration, Observation of H → b \( \overline{b} \)decays and V H production with the ATLAS detector, Phys. Lett.B 786 (2018) 59 [arXiv:1808.08238] [INSPIRE].
ATLAS collaboration, Observation of Higgs boson production in association with a top quark pair at the LHC with the ATLAS detector, Phys. Lett.B 784 (2018) 173 [arXiv:1806.00425] [INSPIRE].
CMS collaboration, Combined measurements of Higgs boson couplings in proton-proton collisions at \( \sqrt{s} \) = 13 TeV, Eur. Phys. J.C 79 (2019) 421 [arXiv:1809.10733] [INSPIRE].
J. Bernon and B. Dumont, Lilith: a tool for constraining new physics from Higgs measurements, Eur. Phys. J.C 75 (2015) 440 [arXiv:1502.04138] [INSPIRE].
R. Barbieri, A. Pomarol, R. Rattazzi and A. Strumia, Electroweak symmetry breaking after LEP-1 and LEP-2, Nucl. Phys.B 703 (2004) 127 [hep-ph/0405040] [INSPIRE].
M.E. Peskin and T. Takeuchi, Estimation of oblique electroweak corrections, Phys. Rev.D 46 (1992)381 [INSPIRE].
C. Grojean, O. Matsedonskyi and G. Panico, Light top partners and precision physics, JHEP10 (2013)160 [arXiv:1306.4655] [INSPIRE].
R. Barbieri, B. Bellazzini, V.S. Rychkov and A. Varagnolo, The Higgs boson from an extended symmetry, Phys. Rev.D 76 (2007) 115008 [arXiv:0706.0432] [INSPIRE].
R. Contino, D. Greco, R. Mahbubani, R. Rattazzi and R. Torre, Precision Tests and Fine Tuning in Twin Higgs Models, Phys. Rev.D 96 (2017) 095036 [arXiv:1702.00797] [INSPIRE].
CMS collaboration, Search for Pair Production of Vector-Like Quarks in the Fully Hadronic Channel, CMS-PAS-B2G-18-005 (2019) [arXiv:1906.11903] [INSPIRE].
ATLAS collaboration, Combination of the searches for pair-produced vector-like partners of the third-generation quarks at \( \sqrt{s} \) = 13 TeV with the ATLAS detector, Phys. Rev. Lett.121 (2018) 211801 [arXiv:1808.02343] [INSPIRE].
C. Csáki, M. Geller, O. Telem and A. Weiler, The Flavor of the Composite Twin Higgs, JHEP09 (2016) 146 [arXiv:1512.03427] [INSPIRE].
Gfitter Group collaboration, The global electroweak fit at NNLO and prospects for the LHC and ILC, Eur. Phys. J.C 74 (2014) 3046 [arXiv:1407.3792] [INSPIRE].
T. Corbett, A. Joglekar, H.-L. Li and J.-H. Yu, Exploring Extended Scalar Sectors with Di-Higgs Signals: A Higgs EFT Perspective, JHEP05 (2018) 061 [arXiv:1705.02551] [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: 1904.05359
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
Li, HL., Xu, LX., Yu, JH. et al. EFTs meet Higgs nonlinearity, compositeness and (neutral) naturalness. J. High Energ. Phys. 2019, 10 (2019). https://doi.org/10.1007/JHEP09(2019)010
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2019)010