Abstract
Even though the Standard Model (SM) is weakly coupled at the Fermi scale, a new strong dynamics involving its degrees of freedom may conceivably lurk at slightly higher energies, in the multi TeV range. Approximate symmetries provide a structurally robust context where, within the low energy description, the dimensionless SM couplings are weak, while the new strong dynamics manifests itself exclusively through higher-derivative interactions. We present an exhaustive classification of such scenarios in the form of effective field theories, paying special attention to new classes of models where the strong dynamics involves, along with the Higgs boson, the SM gauge bosons and/or the fermions. The IR softness of the new dynamics suppresses its effects at LEP energies, but deviations are in principle detectable at the LHC, even at energies below the threshold for production of new states. We believe our construction provides the so far unique structurally robust context where to motivate several LHC searches in Higgs physics, diboson production, or W W scattering. Perhaps surprisingly, the interplay between weak coupling, strong coupling and derivatives, which is controlled by symmetries, can override the naive expansion in operator dimension, providing instances where dimension-8 dominates dimension-6, well within the domain of validity of the low energy effective theory. This result reveals the limitations of an analysis that is both ambitiously general and restricted to dimension-6 operators.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
D. Liu, A. Pomarol, R. Rattazzi and F. Riva, Exotic EFTs for weak scale physics, to appear.
R. Rattazzi, Precision searches in the high-energy era, talk given at Gearing up for LHC13, October 13-16, Florence, Italy (2015).
A. Biekötter, A. Knochel, M. Krämer, D. Liu and F. Riva, Vices and virtues of Higgs effective field theories at large energy, Phys. Rev. D 91 (2015) 055029 [arXiv:1406.7320] [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].
H. Georgi, D.B. Kaplan and P. Galison, Calculation of the composite Higgs mass, Phys. Lett. B 143 (1984) 152 [INSPIRE].
T. Banks, Constraints on SU(2) × U(1) breaking by vacuum misalignment, Nucl. Phys. B 243 (1984) 125 [INSPIRE].
H. Georgi and D.B. Kaplan, Composite Higgs and custodial SU(2), Phys. Lett. B 145 (1984) 216 [INSPIRE].
M.J. Dugan, H. Georgi and D.B. Kaplan, Anatomy of a composite Higgs model, Nucl. Phys. B 254 (1985) 299 [INSPIRE].
R. Contino, Y. Nomura and A. Pomarol, Higgs as a holographic pseudo-Goldstone boson, Nucl. Phys. B 671 (2003) 148 [hep-ph/0306259] [INSPIRE].
K. Agashe, R. Contino and A. Pomarol, The minimal composite Higgs model, Nucl. Phys. B 719 (2005) 165 [hep-ph/0412089] [INSPIRE].
G.F. Giudice, C. Grojean, A. Pomarol and R. Rattazzi, The strongly-interacting light Higgs, JHEP 06 (2007) 045 [hep-ph/0703164] [INSPIRE].
L. Randall and R. Sundrum, A large mass hierarchy from a small extra dimension, Phys. Rev. Lett. 83 (1999) 3370 [hep-ph/9905221] [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. Mrazek et al., The other natural two Higgs doublet model, Nucl. Phys. B 853 (2011) 1 [arXiv:1105.5403] [INSPIRE].
G. D’Ambrosio, G.F. Giudice, G. Isidori and A. Strumia, Minimal flavor violation: an effective field theory approach, Nucl. Phys. B 645 (2002) 155 [hep-ph/0207036] [INSPIRE].
M. Redi and A. Weiler, Flavor and CP invariant composite Higgs models, JHEP 11 (2011) 108 [arXiv:1106.6357] [INSPIRE].
T. Gherghetta and A. Pomarol, The standard model partly supersymmetric, Phys. Rev. D 67 (2003) 085018 [hep-ph/0302001] [INSPIRE].
R. Sundrum, SUSY splits, but then returns, JHEP 01 (2011) 062 [arXiv:0909.5430] [INSPIRE].
A. Manohar and H. Georgi, Chiral quarks and the nonrelativistic quark model, Nucl. Phys. B 234 (1984) 189 [INSPIRE].
D.B. Kaplan, Flavor at SSC energies: a new mechanism for dynamically generated fermion masses, Nucl. Phys. B 365 (1991) 259 [INSPIRE].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [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].
G. Panico and A. Wulzer, The composite Nambu-Goldstone Higgs, Lecture Notes in Physics volume 913, Springer, Germany (2016) [arXiv:1506.01961].
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].
C. Csáki, Y. Shirman and J. Terning, A Seiberg dual for the MSSM: partially composite W and Z, Phys. Rev. D 84 (2011) 095011 [arXiv:1106.3074] [INSPIRE].
N. Arkani-Hamed, L. Motl, A. Nicolis and C. Vafa, The string landscape, black holes and gravity as the weakest force, JHEP 06 (2007) 060 [hep-th/0601001] [INSPIRE].
E. İnönü and E.P. Wigner, On the contraction of groups and their represenations, Proc. Nat. Acad. Sci. 39 (1953) 510 [INSPIRE].
S. Samuel, Bosonic technicolor, Nucl. Phys. B 347 (1990) 625 [INSPIRE].
M. Dine, A. Kagan and S. Samuel, Naturalness in supersymmetry, or raising the supersymmetry breaking scale, Phys. Lett. B 243 (1990) 250 [INSPIRE].
A. Azatov, J. Galloway and M.A. Luty, Superconformal technicolor, Phys. Rev. Lett. 108 (2012) 041802 [arXiv:1106.3346] [INSPIRE].
T. Gherghetta and A. Pomarol, A distorted MSSM Higgs sector from low-scale strong dynamics, JHEP 12 (2011) 069 [arXiv:1107.4697] [INSPIRE].
S. Ferrara, R. Gatto and A.F. Grillo, Positivity restrictions on anomalous dimensions, Phys. Rev. D 9 (1974) 3564 [INSPIRE].
G. Mack, All unitary ray representations of the conformal group SU(2, 2) with positive energy, Commun. Math. Phys. 55 (1977) 1 [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].
B. Bellazzini, Softness and amplitudes’ positivity for spinning particles, arXiv:1605.06111 [INSPIRE].
J. Wess and J. Bagger, Supersymmetry and supergravity, Princeton University Press, Princeton U.S.A. (1992).
R. Casalbuoni, S. De Curtis, D. Dominici, F. Feruglio and R. Gatto, Nonlinear realization of supersymmetry algebra from supersymmetric constraint, Phys. Lett. B 220 (1989) 569 [INSPIRE].
T.E. Clark and S.T. Love, Goldstino couplings to matter, Phys. Rev. D 54 (1996) 5723 [hep-ph/9608243] [INSPIRE].
A. Brignole, F. Feruglio and F. Zwirner, Aspects of spontaneously broken N = 1 global supersymmetry in the presence of gauge interactions, Nucl. Phys. B 501 (1997) 332 [hep-ph/9703286] [INSPIRE].
Z. Komargodski and N. Seiberg, From linear SUSY to constrained superfields, JHEP 09 (2009) 066 [arXiv:0907.2441] [INSPIRE].
D.V. Volkov and V.P. Akulov, Is the neutrino a Goldstone particle?, Phys. Lett. B 46 (1973) 109 [INSPIRE].
W.A. Bardeen and V. Visnjic, Quarks and leptons as composite Goldstone fermions, Nucl. Phys. B 194 (1982) 422 [INSPIRE].
V.I. Ogievetsky, Nolinear realizations of internal and space-time symmetries, in the proceedings of the 10th Winter School of Theoretical Physics, February 19-March 4, Karpacz, Poland (1974).
[47]D.V. Volkov, Phenomenological lagrangians, Fiz. Elem. Chast. Atom. Yadra 4 (1973) 3.
L.V. Delacretaz, S. Endlich, A. Monin, R. Penco and F. Riva, (Re-)inventing the relativistic wheel: gravity, cosets and spinning objects, JHEP 11 (2014) 008 [arXiv:1405.7384] [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].
K. Hagiwara, R.D. Peccei, D. Zeppenfeld and K. Hikasa, Probing the weak boson sector in e + e − → W + W −, Nucl. Phys. B 282 (1987) 253 [INSPIRE].
DELPHI, OPAL, LEP Electroweak, ALEPH, L3 collaboration, S. Schael et al., Electroweak measurements in electron-positron collisions at W-boson-pair energies at LEP, Phys. Rept. 532 (2013) 119 [arXiv:1302.3415] [INSPIRE].
A. Falkowski and F. Riva, Model-independent precision constraints on dimension-6 operators, JHEP 02 (2015) 039 [arXiv:1411.0669] [INSPIRE].
L. Bian, J. Shu and Y. Zhang, Prospects for triple gauge coupling measurements at future lepton colliders and the 14 TeV LHC, JHEP 09 (2015) 206 [arXiv:1507.02238] [INSPIRE].
CMS collaboration, Evidence for exclusive gamma-gamma to W + W − production and constraints on anomalous quartic gauge couplings at \( \sqrt{s}=8 \) TeV, CMS-PAS-FSQ-13-008 (2013).
CMS collaboration, Evidence for the electroweak Zγ production in association with two jets and a search for anomalous quartic gauge couplings in pp collisions at \( \sqrt{s}=8 \) TeV, CMS-PAS-SMP-14-018 (2014).
ATLAS collaboration, Evidence for electroweak production of W ± W ± jj in pp collisions at \( \sqrt{s}=8 \) TeV with the ATLAS detector, Phys. Rev. Lett. 113 (2014) 141803 [arXiv:1405.6241] [INSPIRE].
A. Azatov, R. Contino, C. Machado and F. Riva, Helicity selection rules and non-interference for BSM amplitudes, arXiv:1607.05236 [INSPIRE].
R. Contino, C. Grojean, D. Pappadopulo, R. Rattazzi and A. Thamm, Strong Higgs interactions at a linear collider, JHEP 02 (2014) 006 [arXiv:1309.7038] [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].
S. Weinberg, The quantum theory of fields. Volume 2: modern applications, Cambridge University Press, Cambridge U.K. (2005).
M.E. Peskin and T. Takeuchi, A new constraint on a strongly interacting Higgs sector, Phys. Rev. Lett. 65 (1990) 964 [INSPIRE].
ATLAS and CMS collaborations, Measurements of the Higgs boson production and decay rates and constraints on its couplings from a combined ATLAS and CMS analysis of the LHC pp collision data at \( \sqrt{s}=7 \) and 8 TeV, ATLAS-CONF-2015-044 (2014).
O. Domenech, A. Pomarol and J. Serra, Probing the SM with dijets at the LHC, Phys. Rev. D 85 (2012) 074030 [arXiv:1201.6510] [INSPIRE].
A. Pomarol and F. Riva, Towards the ultimate SM fit to close in on Higgs physics, JHEP 01 (2014)151 [arXiv:1308.2803] [INSPIRE].
M. Redi, V. Sanz, M. de Vries and A. Weiler, Strong signatures of right-handed compositeness, JHEP 08 (2013) 008 [arXiv:1305.3818] [INSPIRE].
D.S.M. Alves, J. Galloway, J.T. Ruderman and J.R. Walsh, Running electroweak couplings as a probe of new physics, JHEP 02 (2015) 007 [arXiv:1410.6810] [INSPIRE].
J. de Blas, M. Chala and J. Santiago, Global constraints on lepton-quark contact interactions, Phys. Rev. D 88 (2013) 095011 [arXiv:1307.5068] [INSPIRE].
R.S. Gupta, A. Pomarol and F. Riva, BSM primary effects, Phys. Rev. D 91 (2015) 035001 [arXiv:1405.0181] [INSPIRE].
E.E. Jenkins, A.V. Manohar and M. Trott, On gauge invariance and minimal coupling, JHEP 09 (2013) 063 [arXiv:1305.0017] [INSPIRE].
S. Ferrara, M. Porrati and V.L. Telegdi, g = 2 as the natural value of the tree level gyromagnetic ratio of elementary particles, Phys. Rev. D 46 (1992) 3529 [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].
B. Henning, X. Lu, T. Melia and H. Murayama, Hilbert series and operator bases with derivatives in effective field theories, Commun. Math. Phys. 347 (2016) 363 [arXiv:1507.07240] [INSPIRE].
L. Lehman and A. Martin, Low-derivative operators of the standard model effective field theory via Hilbert series methods, JHEP 02 (2016) 081 [arXiv:1510.00372] [INSPIRE].
B. Henning, X. Lu, T. Melia and H. Murayama, 2, 84, 30, 993, 560, 15456, 11962, 261485, …: Higher dimension operators in the SM EFT,arXiv:1512.03433[INSPIRE].
B. Grzadkowski, M. Iskrzynski, M. Misiak and J. Rosiek, Dimension-six terms in the standard model lagrangian, JHEP 10 (2010) 085 [arXiv:1008.4884] [INSPIRE].
J. Elias-Miro, J.R. Espinosa, E. Masso and A. Pomarol, Higgs windows to new physics through D = 6 operators: constraints and one-loop anomalous dimensions, JHEP 11 (2013) 066 [arXiv:1308.1879] [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: 1603.03064
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
Liu, D., Pomarol, A., Rattazzi, R. et al. Patterns of strong coupling for LHC searches. J. High Energ. Phys. 2016, 141 (2016). https://doi.org/10.1007/JHEP11(2016)141
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2016)141