Abstract
We revisit the electroweak precision tests for Higgsless models of strong EWSB. We use the Vector Meson Dominance approach and express S and T via couplings characterizing vector and axial spin-1 resonances of the strong sector. These couplings are constrained by the elastic unitarity and by requiring a good UV behavior of various form- factors. We pay particular attention to the one-loop contribution of resonances to T (beyond the chiral log), and to how it can improve the fit. We also make contact with the recent studies of Conformal Technicolor. We explain why the second Weinberg sum rule never converges in these models, and formulate a condition necessary for preserving the custodial symmetry in the IR.
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G. Giudice, C. Grojean, A. Pomarol and R. Rattazzi, The Strongly-Interacting Light Higgs, JHEP 06 (2007) 045 [hep-ph/0703164] [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].
G. Ecker, J. Gasser, A. Pich and E. de Rafael, The Role of Resonances in Chiral Perturbation Theory, Nucl. Phys. B 321 (1989) 311 [INSPIRE].
J. Bagger et al., The Strongly interacting W W system: Gold plated modes, Phys. Rev. D 49 (1994)1246 [hep-ph/9306256] [INSPIRE].
R. Chivukula, D.A. Dicus and H.-J. He, Unitarity of compactified five dimensional Yang-Mills theory, Phys. Lett. B 525 (2002) 175 [hep-ph/0111016] [INSPIRE].
C. Csáki, C. Grojean, H. Murayama, L. Pilo and J. Terning, Gauge theories on an interval: Unitarity without a Higgs, Phys. Rev. D 69 (2004) 055006 [hep-ph/0305237] [INSPIRE].
R. Barbieri, G. Isidori, V.S. Rychkov and E. Trincherini, Heavy Vectors in Higgs-less models, Phys. Rev. D 78 (2008) 036012 [arXiv:0806.1624] [INSPIRE].
S. Weinberg, Implications of Dynamical Symmetry Breaking: An Addendum, Phys. Rev. D 19 (1979)1277 [INSPIRE].
L. Susskind, Dynamics of Spontaneous Symmetry Breaking in the Weinberg-Salam Theory, Phys. Rev. D 20 (1979) 2619 [INSPIRE].
B. Holdom, Techniodor, Phys. Lett. B 150 (1985) 301 [INSPIRE].
T.W. Appelquist, D. Karabali and L. Wijewardhana, Chiral Hierarchies and the Flavor Changing Neutral Current Problem in Technicolor, Phys. Rev. Lett. 57 (1986) 957 [INSPIRE].
M.A. Luty and T. Okui, Conformal technicolor, JHEP 09 (2006) 070 [hep-ph/0409274] [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].
R. Rattazzi, S. Rychkov and A. Vichi, Bounds in 4D Conformal Field Theories with Global Symmetry, J. Phys. A 44 (2011) 035402 [arXiv:1009.5985] [INSPIRE].
A. Vichi, Improved bounds for CFT’s with global symmetries, JHEP 01 (2012) 162 [arXiv:1106.4037] [INSPIRE].
D. Poland, D. Simmons-Duffin and A. Vichi, Carving Out the Space of 4D CFTs, arXiv:1109.5176 [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].
G. Cacciapaglia, C. Csáki, C. Grojean and J. Terning, Curing the Ills of Higgsless models: The S parameter and unitarity, Phys. Rev. D 71 (2005) 035015 [hep-ph/0409126] [INSPIRE].
R. Chivukula, E.H. Simmons, H.-J. He, M. Kurachi and M. Tanabashi, Deconstructed Higgsless models with one-site delocalization, Phys. Rev. D 71 (2005) 115001 [hep-ph/0502162] [INSPIRE].
G. Altarelli and R. Barbieri, Vacuum polarization effects of new physics on electroweak processes, Phys. Lett. B 253 (1991) 161 [INSPIRE].
G. Altarelli, R. Barbieri and S. Jadach, Toward a model independent analysis of electroweak data, Nucl. Phys. B 369 (1992) 3 [Erratum ibid. B 376 (1992) 444] [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].
V. Novikov, L. Okun and M. Vysotsky, On the Electroweak one loop corrections, Nucl. Phys. B 397 (1993) 35 [INSPIRE].
M.E. Peskin and T. Takeuchi, Estimation of oblique electroweak corrections, Phys. Rev. D 46 (1992)381 [INSPIRE].
A. Falkowski, C. Grojean, A. Kaminska, S. Pokorski and A. Weiler, If no Higgs then what?, JHEP 11 (2011) 028 [arXiv:1108.1183] [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].
G. Ecker, J. Gasser, H. Leutwyler, A. Pich and E. de Rafael, Chiral Lagrangians for Massive Spin 1 Fields, Phys. Lett. B 223 (1989) 425 [INSPIRE].
R. Barbieri, A. Carcamo Hernandez, G. Corcella, R. Torre and E. Trincherini, Composite Vectors at the Large Hadron Collider, JHEP 03 (2010) 068 [arXiv:0911.1942] [INSPIRE].
G. Panico and A. Wulzer, The Discrete Composite Higgs Model, JHEP 09 (2011) 135 [arXiv:1106.2719] [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. Bando, T. Kugo and K. Yamawaki, Nonlinear Realization and Hidden Local Symmetries, Phys. Rept. 164 (1988) 217 [INSPIRE].
D.T. Son and M.A. Stephanov, QCD and dimensional deconstruction, Phys. Rev. D 69 (2004)065020 [hep-ph/0304182] [INSPIRE].
E. Accomando, S. De Curtis, D. Dominici and L. Fedeli, Drell-Yan production at the LHC in a four site Higgsless model, Phys. Rev. D 79 (2009) 055020 [arXiv:0807.5051] [INSPIRE].
S. De Curtis, M. Redi and A. Tesi, The 4D Composite Higgs, arXiv:1110.1613 [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].
M. Bando, T. Kugo and K. Yamawaki, Nonlinear Realization and Hidden Local Symmetries, Phys. Rept. 164 (1988) 217 [INSPIRE].
B.W. Lee, C. Quigg and H. Thacker, Weak Interactions at Very High-Energies: The Role of the Higgs Boson Mass, Phys. Rev. D 16 (1977) 1519 [INSPIRE].
M. Papucci, NDA and perturbativity in Higgsless models, hep-ph/0408058 [INSPIRE].
J. Nieves, A. Pich and E. Ruiz Arriola, Large-Nc Properties of the rho and f0(600) Mesons from Unitary Resonance Chiral Dynamics, Phys. Rev. D 84 (2011) 096002 [arXiv:1107.3247] [INSPIRE].
O. Catà and J.F. Kamenik, ElectroWeak Precision Observables at One-Loop in Higgsless models, Phys. Rev. D 83 (2011) 053010 [arXiv:1010.2226] [INSPIRE].
E. Witten, Some Inequalities Among Hadron Masses, Phys. Rev. Lett. 51 (1983) 2351 [INSPIRE].
R. Sundrum and S.D. Hsu, Walking technicolor and electroweak radiative corrections, Nucl. Phys. B 391 (1993) 127 [hep-ph/9206225] [INSPIRE].
T. Appelquist and F. Sannino, The Physical spectrum of conformal SU(N ) gauge theories, Phys. Rev. D 59 (1999) 067702 [hep-ph/9806409] [INSPIRE].
S. Weinberg, Precise relations between the spectra of vector and axial vector mesons, Phys. Rev. Lett. 18 (1967) 507 [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].
M.S. Carena, E. Ponton, J. Santiago and C. Wagner, Electroweak constraints on warped models with custodial symmetry, Phys. Rev. D 76 (2007) 035006 [hep-ph/0701055] [INSPIRE].
P. Lodone, Vector-like quarks in a composite Higgs model, JHEP 12 (2008) 029 [arXiv:0806.1472] [INSPIRE].
M. Gillioz, A Light composite Higgs boson facing electroweak precision tests, Phys. Rev. D 80 (2009)055003 [arXiv:0806.3450] [INSPIRE].
C. Anastasiou, E. Furlan and J. Santiago, Realistic Composite Higgs Models, Phys. Rev. D 79 (2009)075003 [arXiv:0901.2117] [INSPIRE].
A. Pomarol and J. Serra, Top Quark Compositeness: Feasibility and Implications, Phys. Rev. D 78 (2008) 074026 [arXiv:0806.3247] [INSPIRE].
R. Barbieri, G. Isidori and D. Pappadopulo, Composite fermions in Electroweak Symmetry Breaking, JHEP 02 (2009) 029 [arXiv:0811.2888] [INSPIRE].
R. Chivukula, R. Foadi and E.H. Simmons, Patterns of Custodial Isospin Violation from a Composite Top, Phys. Rev. D 84 (2011) 035026 [arXiv:1105.5437] [INSPIRE].
S. Matsuzaki, R. Chivukula, E.H. Simmons and M. Tanabashi, One-Loop Corrections to the S and T Parameters in a Three Site Higgsless Model, Phys. Rev. D 75 (2007) 073002 [hep-ph/0607191] [INSPIRE].
R. Chivukula, E.H. Simmons, S. Matsuzaki and M. Tanabashi, The Three Site Model at One-Loop, Phys. Rev. D 75 (2007) 075012 [hep-ph/0702218] [INSPIRE].
T. Abe, S. Matsuzaki and M. Tanabashi, Does the three site Higgsless model survive the electroweak precision tests at loop?, Phys. Rev. D 78 (2008) 055020 [arXiv:0807.2298] [INSPIRE].
A.C. Longhitano, Heavy Higgs Bosons in the Weinberg-Salam Model, Phys. Rev. D 22 (1980)1166 [INSPIRE].
A.C. Longhitano, Low-Energy Impact of a Heavy Higgs Boson Sector, Nucl. Phys. B 188 (1981)118 [INSPIRE].
H. Georgi, Effective field theory and electroweak radiative corrections, Nucl. Phys. B 363 (1991)301 [INSPIRE].
R. Barbieri, Electroweak Precision Tests: What Do We Learn?, in Quantitative Particle Physics: Cargèse 1992, M. Lévy et al. eds., Plenum Press, New York U.S.A. (1993).
R. Barbieri, M. Beccaria, P. Ciafaloni, G. Curci and A. Vicere, Two loop heavy top effects in the Standard Model, Nucl. Phys. B 409 (1993) 105 [INSPIRE].
R. Barbieri, Ten Lectures on the ElectroWeak Interactions, arXiv:0706.0684 [INSPIRE].
T. Das, G. Guralnik, V. Mathur, F. Low and J. Young, Electromagnetic mass difference of pions, Phys. Rev. Lett. 18 (1967) 759 [INSPIRE].
J.F. Donoghue and E. Golowich, Chiral sum rules and their phenomenology, Phys. Rev. D 49 (1994)1513 [hep-ph/9307262] [INSPIRE].
R. Contino, The Higgs as a Composite Nambu-Goldstone Boson, arXiv:1005.4269 [INSPIRE].
D. NutBrown, Construction of three- and four-point functions of currents for arbitrary spin-one spectral functions, Phys. Rev. D 1 (1970) 2328 [INSPIRE].
K. Agashe, C. Csáki, C. Grojean and M. Reece, The S-parameter in holographic technicolor models, JHEP 12 (2007) 003 [arXiv:0704.1821] [INSPIRE].
LEP and SLC collaborations, Precision electroweak measurements on the Z resonance, Phys. Rept. 427 (2006) 257 [hep-ex/0509008] [INSPIRE].
www.cern.ch/LEPEWWG,
M. Baak et al., Updated Status of the Global Electroweak Fit and Constraints on New Physics, arXiv:1107.0975 [INSPIRE].
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Orgogozo, A., Rychkov, S. Exploring T and S parameters in Vector Meson Dominance models of strong electroweak symmetry breaking. J. High Energ. Phys. 2012, 46 (2012). https://doi.org/10.1007/JHEP03(2012)046
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DOI: https://doi.org/10.1007/JHEP03(2012)046