One-loop calculation of the oblique S parameter in higgsless electroweak models

Journal of High Energy Physics

Volumn 2012, Issue 8, 2012, Pages

  Pich, A ^a   Rosell, I ^a,b   Sanz Cillero, J J ^c  

^a UNIVERSITY OF VALENCIA   (Spain)

^b UNIVERSIDAD CEU CARDENAL HERRERA   (Spain)

^c INFN SEZIONE DI BARI   (Italy)

Author keywords

Beyond Standard Model; Chiral Lagrangians; Higgs Physics; Technicolor and Composite Models

Indexed keywords

EID: 84865737769     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP08(2012)106     Document Type: Article

References (141)

1. A. Pich, The standard model of electroweak interactions, arXiv:1201.0537
2. F. Englert and R. Brout, Broken symmetry and the mass of gauge vector mesons, Phys. Rev. Lett. 13 (1964) 321
3. P.W. Higgs, Spontaneous symmetry breakdown without massless bosons, Phys. Rev. 145 (1966) 1156
4. P.W. Higgs, Broken symmetries and the masses of gauge bosons, Phys. Rev. Lett. 13 (1964) 508
5. G. Guralnik, C. Hagen and T. Kibble, Global conservation laws and massless particles, Phys. Rev. Lett. 13 (1964) 585
6. T. Kibble, Symmetry breaking in nonAbelian gauge theories, Phys. Rev. 155 (1967) 1554
7. -1 of pp collision data at √s = 7 TeV with the ATLAS detector at the LHC, Phys. Lett. B 710 (2012) 49 [arXiv:1202.1408]
8. -1 of pp collision data at s = 7TeV with ATLAS, Phys. Lett. B 710 (2012) 383 [arXiv:1202.1415]
9. 1 of pp collisions at fs = 7 TeVwith ATLAS, Phys. Rev. Lett. 108 (2012) 111803 [arXiv: 1202.1414]
10. ATLAS collaboration, G. Aad et al., Search for the Higgs boson in the H -+ WW -+ ℓνℓν decay channel inpp collisions at fs = 7 TeV with the ATLAS detector, Phys. Rev. Lett. 108 (2012) 111802 [arXiv: 1112.2577]
11. CMS collaboration, S. Chatrchyan et al., Combined results of searches for the standard model Higgs boson in pp collisions at = 7 TeV, Phys. Lett. B 710 (2012) 26 [arXiv : 1202.1488]
12. CMS collaboration, S. Chatrchyan et al., Search for the standard model Higgs boson decaying to a W pair in the fully leptonic final state in pp collisions at = 7 TeV, Phys. Lett. B 710 (2012) 91 [arXiv: 1202.1489]
13. CMS collaboration, S. Chatrchyan et al., Search for the standard model Higgs boson decaying to bottom quarks in pp collisions at = 7 TeV, Phys. Lett. B 710 (2012) 284 [arXiv: 1202.4195]
14. CMS collaboration, S. Chatrchyan et al., Search for the standard model Higgs boson decaying into two photons in pp collisions at = 7 TeV, Phys. Lett. B 710 (2012) 403 [arXiv : 1202.1487]
15. CMS collaboration, S. Chatrchyan et al., Search for the standard model Higgs boson in the decay channel H ZZ -4 leptons in pp collisions at s = 7 TeV, Phys. Rev. Lett. 108, 111804 (2012) [arXiv: 1202.1997]
16. * -> qq̄ℓ-ℓ+ inpp collisions at ys = 7 TeV, JHEP 04 (2012) 036 [arXiv: 1202.1416]
17. CMS collaboration, S. Chatrchyan et al., Search for the standard model Higgs boson in the H -> ZZ -> 2ℓ2ν channel in pp collisions at s = 7 TeV, JHEP 03 (2012) 040 [arXiv: 1202.3478]
18. CMS collaboration, S. Chatrchyan et al., Search for the standard model Higgs boson in the H ZZ -+ ℓℓττ decay channel inpp collisions at s = 7 TeV, JHEP 03 (2012) 081 [arXiv: 1202.3617]
19. CMS collaboration, S. Chatrchyan et al., Search for neutral Higgs bosons decaying to τ pairs inpp collisions at = 7 TeV, Phys. Lett. B 713 (2012) 68 [arXiv: 1202.4083]
20. CMS collaboration, Combination of SM, SM4, FP Higgs boson searches, CMS-PAS-HIG-12-008 (2012).
21. 1 of pp collision data at js = 7 TeV, ATLAS-CONF-2012-019 (2012).
22. 1 of data, arXiv: 1203.3774
23. M. Baak et al., Updated status of the global electroweak fit and constraints on new physics, Eur. Phys. J. C 72 (2012) 2003 [arXiv: 1107.0975]
24. H. Flacher et al., Revisiting the global electroweak fit of the standard model and beyond with Gfitter, Eur. Phys. J. C 60 (2009) 543 [Erratum ibid. C 71 (2011) 1718] [arXiv: 0811. 0009]
25. Gfitter, http://gfitter.desy.de/.
26. LEP Electroweak Working Group, http://lepewwg.web.cern.ch/LEPEWWG/.
27. - annihilation, Comput. Phys. Commun. 133 (2001) 229 [hep-ph/9908433]
28. - annihilation, from version 6.21 to version 6.42, Comput. Phys. Commun. 174 (2006) 728 [hep-ph/0507146]
29. A. Pich, Chiral perturbation theory, Rept. Prog. Phys. 58 (1995) 563 [hep-ph/9502366]
30. A. Pich, Effective field theory: course, in Probing the standard model of particle interactions, R. Gupta et al. eds., North-Holland, The Netherlands (1999), hep-ph/9806303
31. T. Appelquist and C.W. Bernard, Strongly interacting Higgs bosons, Phys. Rev. D 22 (1980) 200
32. P. Sikivie, L. Susskind, M.B. Voloshin and V.I. Zakharov, Isospin breaking in technicolor models, Nucl. Phys. B 173 (1980) 189
33. S. Weinberg, Phenomenological lagrangians, Physica A 96 (1979) 327
34. J. Gasser and H. Leutwyler, Chiral perturbation theory to one loop, Annals Phys. 158 (1984) 142
35. J. Gasser and H. Leutwyler, Chiral perturbation theory: expansions in the mass of the strange quark, Nucl. Phys. B 250 (1985) 465
36. J. Gasser and H. Leutwyler, Low-energy expansion of meson form-factors, Nucl. Phys. B 250 (1985) 517
37. G. Ecker, Chiral perturbation theory, Prog. Part. Nucl. Phys. 35 (1995) 1 [hep-ph/9501357]
38. T. Appelquist, Broken gauge theories and effective lagrangians, in Gauge theories and experiments at high energies, Scottish Universities Summer School in Physics, U.K. (1981).
39. A.C. Longhitano, Heavy Higgs bosons in the Weinberg-Salam model, Phys. Rev. D 22 (1980) 1166
40. A.C. Longhitano, Low-energy impact of a heavy Higgs boson sector, Nucl. Phys. B 188 (1981) 118
41. A. Dobado, D. Espriu and M.J. Herrero, Chiral lagrangians as a tool to probe the symmetry breaking sector of the SM at LEP, Phys. Lett. B 255 (1991) 405
42. D. Espriu and M.J. Herrero, Chiral lagrangians and precision tests of the symmetry breaking sector of the Standard Model, Nucl. Phys. B 373 (1992) 117
43. M.J. Herrero and E. Ruiz Morales, The electroweak chiral lagrangian for the standard model with a heavy Higgs, Nucl. Phys. B 418 (1994) 431 [hep-ph/9308276]
44. D. Espriu and J. Matias, Renormalization and the equivalence theorem: on-shell scheme, Phys. Rev. D 52 (1995) 6530 [hep-ph/9501279]
45. D. Espriu and J. Matias, Some remarks on the matching conditions, Phys. Lett. B 341 (1995) 332 [hep-ph/9407292]
46. A. Dobado, M. Herrero, J.R. Pelaez, E. Ruiz Morales and M. Urdiales, Learning about the strongly interacting symmetry breaking sector at LHC, Phys. Lett. B 352 (1995) 400 [hep-ph/9502309]
47. A. Dobado, M. Herrero, J.R. Pelaez and E. Ruiz Morales, CERN LHC sensitivity to the resonance spectrum of a minimal strongly interacting electroweak symmetry breaking sector, Phys. Rev. D 62 (2000) 055011 [hep-ph/9912224]
48. A. Dobado, A. Gomez-Nicola, A.L. Maroto and J.R. Pelaez, Effective lagrangians for the standard model, Texts and Monographs in Physics, Springer, U.S.A. (1997).
49. R.S. Chivukula, Models of electroweak symmetry breaking: course, in Probing the standard model of particle interactions, R. Gupta et al. eds., North-Holland, The Netherlands (1999), hep-ph/9803219
50. A. Pomarol, Beyond the standard model, arXiv:1202.1391
51. J. Andersenet al., Discovering technicolor, Eur. Phys. J. Plus 126 (2011) 81 [arXiv:1104.1255]
52. S. Weinberg, Implications of dynamical symmetry breaking: an addendum, Phys. Rev. D 19 (1979) 1277
53. S. Weinberg, Implications of dynamical symmetry breaking, Phys. Rev. D 13 (1976) 974
54. L. Susskind, Dynamics of spontaneous symmetry breaking in the Weinberg-Salam theory, Phys. Rev. D 20 (1979) 2619
55. B. Holdom, Techniodor, Phys. Lett. B 150 (1985) 301
56. 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
57. K. Yamawaki, M. Bando and K.-i. Matumoto, Scale invariant technicolor model and a technidilaton, Phys. Rev. Lett. 56 (1986) 1335
58. M.A. Luty and T. Okui, Conformal technicolor, JHEP 09 (2006) 070 [hep-ph/0409274]
59. 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]
60. R. Rattazzi, V.S. Rychkov, E. Tonni and A. Vichi, Bounding scalar operator dimensions in 4D CFT, JHEP 12 (2008) 031 [arXiv:0807.0004]
61. R. Foadi and F. Sannino, WW scattering in walking technicolor: No discovery scenarios at the CERN LHC and ILC, Phys. Rev. D 78 (2008) 037701 [arXiv:0801.0663]
62. F. Sannino, Mass deformed exact S-parameter in conformal theories, Phys. Rev. D 82 (2010) 081701 [arXiv:1006.0207]
63. F. Sannino, Magnetic S-parameter, Phys. Rev. Lett. 105 (2010) 232002 [arXiv:1007.0254]
64. S. Di Chiara, C. Pica and F. Sannino, Flavor dependence of the S-parameter, Phys. Lett. B 700 (2011) 229 [arXiv:1008.1267]
65. L. Randall and R. Sundrum, A large mass hierarchy from a small extra dimension, Phys. Rev. Lett. 83 (1999) 3370 [hep-ph/9905221]
66. N. Arkani-Hamed, A.G. Cohen and H. Georgi, (De)constructing dimensions, Phys. Rev. Lett. 86 (2001) 4757 [hep-th/0104005]
67. H. Georgi, Fun with Higgsless theories, Phys. Rev. D 71 (2005) 015016 [hep-ph/0408067]
68. C.T. Hill, S. Pokorski and J. Wang, Gauge invariant effective lagrangian for Kaluza-Klein modes, Phys. Rev. D 64 (2001) 105005 [hep-th/0104035]
69. C. Cśaki, C. Grojean, L. Pilo and J. Terning, Towards a realistic model of Higgsless electroweak symmetry breaking, Phys. Rev. Lett. 92 (2004) 101802 [hep-ph/0308038]
70. C. Cśaki, 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]
71. G. Cacciapaglia, C. Cśaki, C. Grojean and J. Terning, Oblique corrections from Higgsless models in warped space, Phys. Rev. D 70 (2004) 075014 [hep-ph/0401160]
72. G. Cacciapaglia, C. Cśaki, 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]
73. R.S. 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]
74. R.S. Chivukula and H.-J. He, Unitarity of deconstructed five-dimensional Yang-Mills theory, Phys. Lett. B 532 (2002) 121 [hep-ph/0201164]
75. R.S. Chivukula, D.A. Dicus, H.-J. He and S. Nandi, Unitarity of the higher dimensional standard model, Phys. Lett. B 562 (2003) 109 [hep-ph/0302263]
76. R.S. Chivukula, E.H. Simmons, H.-J. He, M. Kurachi and M. Tanabashi, The structure of corrections to electroweak interactions in Higgsless models, Phys. Rev. D 70 (2004) 075008 [hep-ph/0406077]
77. R.S. Chivukula, E.H. Simmons, H.-J. He, M. Kurachi and M. Tanabashi, Electroweak corrections and unitarity in linear moose models, Phys. Rev. D 71 (2005) 035007 [hep-ph/0410154]
78. K. Agashe, A. Delgado, M.J. May and R. Sundrum, RS1, custodial isospin and precision tests, JHEP 08 (2003) 050 [hep-ph/0308036]
79. G. Burdman and Y. Nomura, Holographic theories of electroweak symmetry breaking without a Higgs boson, Phys. Rev. D 69 (2004) 115013 [hep-ph/0312247]
80. R. Contino, L. Da Rold and A. Pomarol, Light custodians in natural composite Higgs models, Phys. Rev. D 75 (2007) 055014 [hep-ph/0612048]
81. K. Agashe, R. Contino and A. Pomarol, The minimal composite Higgs model, Nucl. Phys. B 719 (2005) 165 [hep-ph/0412089]
82. R. Foadi, S. Gopalakrishna and C. Schmidt, Higgsless electroweak symmetry breaking from theory space, JHEP 03 (2004) 042 [hep-ph/0312324]
83. J. Hirn and J. Stern, The role of spurions in Higgsless electroweak effective theories, Eur. Phys. J. C 34 (2004) 447 [hep-ph/0401032]
84. R. Casalbuoni, S. De Curtis and D. Dominici, Moose models with vanishing S parameter, Phys. Rev. D 70 (2004) 055010 [hep-ph/0405188]
85. M. Perelstein, Gauge-assisted technicolor?, JHEP 10 (2004) 010 [hep-ph/0408072]
86. M.E. Peskin and T. Takeuchi, Estimation of oblique electroweak corrections, Phys. Rev. D 46 (1992) 381
87. M.E. Peskin and T. Takeuchi, A new constraint on a strongly interacting Higgs sector, Phys. Rev. Lett. 65 (1990) 964
88. G. Ecker, J. Gasser, A. Pich and E. de Rafael, The role of resonances in chiral perturbation theory, Nucl. Phys. B 321 (1989) 311
89. 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
90. V. Cirigliano et al., Towards a consistent estimate of the chiral low-energy constants, Nucl. Phys. B 753 (2006) 139 [hep-ph/0603205]
91. A. Pich, Colorless mesons in a polychromatic world, hep-ph/0205030
92. O. Cat̀a and S. Peris, An example of resonance saturation at one loop, Phys. Rev. D 65 (2002) 056014 [hep-ph/0107062]
93. I. Rosell, J. Sanz-Cillero and A. Pich, Quantum loops in the resonance chiral theory: the vector form-factor, JHEP 08 (2004) 042 [hep-ph/0407240]
94. 38(μ) , JHEP 01 (2007) 039 [hep-ph/0610290]
95. C, JHEP 07 (2008) 014 [arXiv:0803.1567]
96. 90(μ), JHEP 02 (2011) 109 [arXiv: 1011. 5771]
97. I. Rosell, Quantum corrections in the resonance chiral theory, hep-ph/0701248
98. I. Rosell, P. Ruiz-Femenia and J. Portoles, One-loop renormalization of resonance chiral theory: Scalar and pseudoscalar resonances, JHEP 12 (2005) 020 [hep-ph/0510041]
99. c, Phys. Lett. B 649 (2007) 180 [hep-ph/0702217]
100. L. Xiao and J. Sanz-Cillero, Renormalizable sectors in resonance chiral theory: S → ππ decay amplitude, Phys. Lett. B 659 (2008) 452 [arXiv: 0705. 3899]
101. S. Matsuzaki, R.S. 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]
102. R.S. 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]
103. 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]
104. O. Cat̀a and J.F. Kamenik, Electroweak precision observables at one-loop in Higgsless models, Phys. Rev. D 83 (2011) 053010 [Erratum ibid. D 85 (2012) 059902] [arXiv: 1010. 2226]
105. A. Orgogozo and S. Rychkov, Exploring T and S parameters in vector meson dominance models of strong electroweak symmetry breaking, JHEP 03 (2012) 046 [arXiv: 1111.3534]
106. D. Kennedy and P. Langacker, Precision electroweak experiments and heavy physics: a global analysis, Phys. Rev. Lett. 65 (1990) 2967 [Erratum ibid. 66 (1991) 395]
107. D. Kennedy and P. Langacker, Precision electroweak experiments and heavy physics: an update, Phys. Rev. D 44 (1991) 1591
108. G. Altarelli and R. Barbieri, Vacuum polarization effects of new physics on electroweak processes, Phys. Lett. B 253 (1991) 161
109. 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]
110. M. Davier, L. Girlanda, A. Hocker and J. Stern, Finite energy chiral sum rules and τ spectral functions, Phys. Rev. D 58 (1998) 096014 [hep-ph/9802447]
111. 87 from semileptonic τ decays, Phys. Rev. D 78 (2008) 116012 [arXiv: 0810. 0760]
112. G. Buchalla and O. Cat̀a, Effective theory of a dynamically broken electroweak standard model at NLO, arXiv: 1203. 6510
113. S.R. Coleman, J. Wess and B. Zumino, Structure of phenomenological lagrangians. 1, Phys. Rev. 177 (1969) 2239
114. CG. Callan Jr., S.R. Coleman, J. Wess and B. Zumino, Structure of phenomenological lagrangians. 2, Phys. Rev. 177 (1969) 2247
115. J. Bagger et al., The strongly interacting WW system: gold plated modes, Phys. Rev. D 49 (1994) 1246 [hep-ph/9306256]
116. R. Contino, C. Grojean, M. Moretti, F. Piccinini and R. Rattazzi, Strong double Higgs production at the LHC, JHEP 05 (2010) 089 [arXiv: 1002.1011]
117. G. Giudice, C. Grojean, A. Pomarol and R. Rattazzi, The strongly-interacting light Higgs, JHEP 06 (2007) 045 [hep-ph/0703164]
118. R. Contino, The Higgs as a composite Nambu-Goldstone boson, arXiv: 1005.4269
119. D.B. Kaplan and H. Georgi, SU(2) x U(1) breaking by vacuum misalignment, Phys. Lett. B 136 (1984) 183
120. H. Georgi and D.B. Kaplan, Composite Higgs and custodial SU(2), Phys. Lett. B 145 (1984) 216.
121. D.B. Kaplan, H. Georgi and S. Dimopoulos, Composite Higgs scalars, Phys. Lett. B 136 (1984) 187
122. H. Georgi, D.B. Kaplan and P. Galison, Calculation of the composite Higgs mass, Phys. Lett. B 143 (1984) 152
123. M.J. Dugan, H. Georgi and D.B. Kaplan, Anatomy of a composite Higgs model, Nucl. Phys. B 254 (1985) 299
124. S. Dimopoulos and J. Preskill, Massless composites with massive constituents, Nucl. Phys. B 199 (1982) 206
125. T. Banks, Constraints on SU(2) x U(1) breaking by vacuum misalignment, Nucl. Phys. B 243 (1984) 125
126. R. Grober and M. Muhlleitner, Composite Higgs boson pair production at the LHC, JHEP 06 (2011) 020 [arXiv: 1012.1562]
127. A. Azatov, R. Contino and J. Galloway, Model-independent bounds on a light Higgs, JHEP 04 (2012) 127 [arXiv: 1202.3415]
128. J. Espinosa, C. Grojean, M. Muhlleitner and M. Trott, Fingerprinting Higgs suspects at the LHC, JHEP 05 (2012) 097 [arXiv: 1202.3697]
129. J. Espinosa, C. Grojean and M. Muhlleitner, Composite Higgs under LHC experimental scrutiny, EPJ Web Conf. 28 (2012) 08004 [arXiv: 1202.1286]
130. C.W. Bernard, A. Duncan, J. LoSecco and S. Weinberg, Exact spectral function sum rules, Phys. Rev. D 12 (1975) 792
131. S. Weinberg, Precise relations between the spectra of vector and axial vector mesons, Phys. Rev. Lett. 18 (1967) 507
132. T. Appelquist and F. Sannino, The physical spectrum of conformal SU(N) gauge theories, Phys. Rev. D 59 (1999) 067702 [hep-ph/9806409]
133. c, Phys. Rev. D 81 (2010) 056005 [arXiv: 0912. 0495]
134. 6) revisited, Phys. Rev. D 79 (2009) 096006 [arXiv: 0903. 0782]
135. 0(600) mesons from unitary resonance chiral dynamics, Phys. Rev. D 84 (2011) 096002 [arXiv : 1107. 3247]
136. Particle Data Group collaboration, K. Nakamura et al., Review of particle physics, J. Phys. G 37 (2010) 075021
137. c limit of QCD-like theories, Phys. Lett. B 424 (1998) 335 [hep-ph/9712457]
138. c QCD, JHEP 05 (1998) 011 [hep-ph/9805442]
139. c QCD, JHEP 05 (2007) 040 [arXiv: 0704.1247]
140. 6) low-energy constant, Phys. Lett. B 663 (2008) 61 [arXiv: 0801.3558]
141. R. Foadi and F. Sannino, S and T parameters from a light nonstandard Higgs versus near conformal dynamics, arXiv: 1207.1541