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Chiral EW Lagrangian

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Study of the Electroweak Symmetry Breaking Sector for the LHC

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Abstract

The ATLAS and CMS collaborations at LHC have found a new boson compatible with the SM Higgs, with a mass of nearly \(M_h\simeq 125\,\mathrm{GeV}\). Furthermore, the most probable \(J^P\) quantum numbers are \(0^+\), and couplings with other particles are in agreement with the SM Higgs, although with moderate precision. Moreover, there is a mass gap for the presence of new physics until an energy of about 600-700 GeV, or even higher for the presence of new vector resonances. However, the data is still compatible with either an elementary or a composite Higgs: this last possibility will be considered in this work. The mass gap between the \(M_W\), \(M_Z\) and \(M_h\) masses, all of \(\mathcal {O}(100\,\mathrm{GeV})\), and the new physics scale (if there is one within reach), suggests that the Higgs boson and the would-be Goldstone bosons \(\omega ^\pm \) and z could be (pseudo) Goldstone Boson, related with a global spontaneous symmetry breaking extending the \(SU(2)_L\times SU(2)_R\rightarrow SU(2)_{L+R}\) global symmetry breaking of the SM. There are several models with specific implementations for the relevant global symmetry breaking pattern: the (Minimal) Composite Higgs Model based on the coset SO(5)/SO(4), dilaton models and others. In this chapter, the old electroweak chiral Lagrangian (ECL) is extended to include the new Higgs-like particle found at the LHC. The non-linear Electroweak Chiral Lagrangian (EWChPT) is considered as a low-energy parameterization of the new physics at the TeV scale, within the limits of the Equivalence Theorem: \(M_W,M_h\ll \sqrt{s}\ll 3\,\mathrm{TeV}\). Couplings to \(\gamma \gamma \) and \(t\bar{t}\) states are also providen.

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Notes

  1. 1.

    \(M_h^\mathrm{ATLAS} = 125.5\,\pm \,0.6\,\mathrm{GeV}\) and \(M_h^\mathrm{CMS}=125.7\,\pm \,0.4\,\mathrm{GeV}\), according to [3] and [4], respectively.

  2. 2.

    See app. D.5 for a brief historical review about the discussion concerning the hypothesis of the ET.

  3. 3.

    See, for instance, Ref. [65] or [61].

  4. 4.

    Also called \(\varphi \) in some early works like [66].

  5. 5.

    Einstein’s sum convention will be used unless otherwise stated.

  6. 6.

    This regime verifies the Equivalence Theorem. See Sect. 2.1.

References

  1. ATLAS Collaboration, Observation and study of the Higgs boson candidate in the two photon decay channel with the ATLAS detector at the LHC, ATLAS-CONF-2012-168, ATLAS-COM-CONF-2012-203 (2012)

    Google Scholar 

  2. CMS Collaboration, Evidence for a new state decaying into two photons in the search for the standard model Higgs boson in pp collisions, CMS-PAS-HIG-12-015 (2012)

    Google Scholar 

  3. G. Aad et al., Measurements of Higgs boson production and couplings in diboson final states with the ATLAS detector at the LHC. Phys. Lett. B726, [Erratum: Phys. Lett. B734, 406 (2014)], 88–119 (2013)

    Google Scholar 

  4. S. Chatrchyan et al., Observation of a new boson with mass near 125 GeV in pp collisions at \(\sqrt{s}=7\) and 8 TeV. JHEP 06, 081 (2013)

    Article  ADS  Google Scholar 

  5. G. Aad et al., Search for heavy vector-like quarks coupling to light quarks in protonproton collisions at \(\sqrt{s}=7\) TeV with the ATLAS detector. Phys. Lett. B 712, 22–39 (2012)

    Article  ADS  Google Scholar 

  6. G. Aad et al., Search for long-lived, multi-charged particles in pp collisions at \(\sqrt{s}=7\) TeV using the ATLAS detector. Phys. Lett. B 722, 305–323 (2013)

    Article  ADS  Google Scholar 

  7. S. Chatrchyan et al., Search for resonances in the dijet mass spectrum from 7 TeV pp collisions at CMS. Phys. Lett. B 704, 123–142 (2011)

    Article  ADS  Google Scholar 

  8. D.B. Kaplan, H. Georgi, \(\text{ SU }(2) \times U(1)\) breaking by vacuum misalignment. Phys. Lett. B 136, 183 (1984)

    Article  ADS  Google Scholar 

  9. S. Dimopoulos, J. Preskill, Massless composites with massive constituents. Nucl. Phys. B 199, 206 (1982)

    Article  ADS  Google Scholar 

  10. T. Banks, Nucl. Phys. B 243, 125 (1984)

    Article  ADS  Google Scholar 

  11. D.B. Kaplan, H. Georgi, S. Dimopoulos, Composite Higgs scalars. Phys. Lett. B 136, 187 (1984)

    Article  ADS  Google Scholar 

  12. H. Georgi, D.B. Kaplan, P. Galison, Calculation of the composite Higgs mass. Phys. Lett. B 143, 152 (1984)

    Article  ADS  Google Scholar 

  13. H. Georgi, D.B. Kaplan, Composite Higgs and custodial SU(2). Phys. Lett. B 145, 216 (1984)

    Article  ADS  Google Scholar 

  14. M.J. Dugan, H. Georgi, D.B. Kaplan, Anatomy of a composite Higgs model. Nucl. Phys. B 254, 299 (1985)

    Article  ADS  Google Scholar 

  15. G.F. Giudice, C. Grojean, A. Pomarol, R. Rattazzi, The strongly-interacting light Higgs. JHEP 06, 045 (2007)

    Article  ADS  Google Scholar 

  16. K. Agashe, R. Contino, A. Pomarol, The minimal composite Higgs model. Nucl. Phys. B 719, 165–187 (2005)

    Article  ADS  Google Scholar 

  17. R. Contino, L. Da Rold, A. Pomarol, Light custodians in natural composite Higgs models. Phys. Rev. D 75, 055014 (2007)

    Article  ADS  Google Scholar 

  18. R. Contino, D. Marzocca, D. Pappadopulo, R. Rattazzi, On the effect of resonances in composite Higgs phenomenology. JHEP 10, 081 (2011)

    Article  ADS  MATH  Google Scholar 

  19. D. Barducci, A. Belyaev, M.S. Brown, S. De Curtis, S. Moretti, G.M. Pruna, The 4-dimensional composite higgs model (4DCHM) and the 125 GeV Higgs-like signals at the LHC. JHEP 09, 047 (2013)

    Article  ADS  Google Scholar 

  20. E. Halyo, Technidilaton or Higgs? Mod. Phys. Lett. A 8, 275–284 (1993)

    Article  ADS  Google Scholar 

  21. W.D. Goldberger, B. Grinstein, W. Skiba, Distinguishing the Higgs boson from the dilaton at the Large Hadron Collider. Phys. Rev. Lett. 100, 111802 (2008)

    Article  ADS  Google Scholar 

  22. 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, USA, 1–26 June 2009 (2011), pp. 235–306, arXiv:1005.4269 [hep-ph]

  23. T. Appelquist, C.W. Bernard, Strongly interacting Higgs bosons. Phys. Rev. D 22, 200 (1980)

    Article  ADS  Google Scholar 

  24. T. Appelquist, M.J. Bowick, E. Cohler, A.I. Hauser, The breaking of isospin symmetry in theories with a dynamical Higgs mechanism. Phys. Rev. D 31, 1676 (1985)

    Article  ADS  Google Scholar 

  25. A.C. Longhitano, Low-energy impact of a heavy Higgs boson sector. Nucl. Phys. B 188, 118 (1981)

    Article  ADS  Google Scholar 

  26. A.C. Longhitano, Heavy Higgs bosons in the weinberg-salam model. Phys. Rev. D 22, 1166 (1980)

    Article  ADS  Google Scholar 

  27. G. Cvetic, R. Kogerler, Fermionic couplings in an electroweak theory with nonlinear spontaneous symmetry breaking. Nucl. Phys. B 328, 342 (1989)

    Article  ADS  Google Scholar 

  28. A. Dobado, M.J. Herrero, Phenomenological lagrangian approach to the symmetry breaking sector of the standard model. Phys. Lett. B 228, 495 (1989)

    Article  ADS  Google Scholar 

  29. A. Dobado, M.J. Herrero, Testing the hypothesis of strongly interacting longitudinal weak bosons in electron–positron collisions at Tev energies. Phys. Lett. B 233, 505 (1989)

    Article  ADS  Google Scholar 

  30. A. Dobado, M.J. Herrero, T.N. Truong, Study of the strongly interacting higgs sector. Phys. Lett. B 235, 129 (1990)

    Article  ADS  Google Scholar 

  31. A. Dobado, M.J. Herrero, J. Terron, The role of chiral Lagrangians in strongly interacting \(W(\)l\() W(\)l\()\) signals at \(pp\) supercolliders. Z. Phys. C 50, 205–220 (1991)

    Google Scholar 

  32. A. Dobado, D. Espriu, M.J. Herrero, Chiral Lagrangians as a tool to probe the symmetry breaking sector of the SM at LEP. Phys. Lett. B 255, 405–414 (1991)

    Article  ADS  Google Scholar 

  33. A. Dobado, M.J. Herrero, J.R. Pelaez, E. Ruiz Morales, M.T. Urdiales, Learning about the strongly interacting symmetry breaking sector at LHC. Phys. Lett. B352, 400–410 (1995)

    Google Scholar 

  34. A. Dobado, M.J. Herrero, J.R. Pelaez, E. Ruiz Morales, CERN LHC sensitivity to the resonance spectrum of a minimal strongly interacting electroweak symmetry breaking sector. Phys. Rev. D 62, 055011 (2000)

    Article  ADS  Google Scholar 

  35. B. Holdom, J. Terning, Large corrections to electroweak parameters in technicolor theories. Phys. Lett. B 247, 88–92 (1990)

    Article  ADS  Google Scholar 

  36. M. Golden, L. Randall, Radiative corrections to electroweak parameters in technicolor theories. Nucl. Phys. B 361, 3–23 (1991)

    Article  ADS  Google Scholar 

  37. D. Espriu, J. Manzano, CP violation and family mixing in the effective electroweak Lagrangian. Phys. Rev. D 63, 073008 (2001)

    Article  ADS  Google Scholar 

  38. G. Buchalla, O. Cata, Effective theory of a dynamically broken electroweak standard model at NLO. JHEP 07, 101 (2012)

    Article  ADS  Google Scholar 

  39. G. Buchalla, O. Cata, R. Rahn, M. Schlaffer, Effective field theory analysis of new physics in \(\text{ e }+\text{ e }- \rightarrow \text{ W }+\text{ W }-\) at a Linear Collider. Eur. Phys. J. C 73, 2589 (2013)

    Article  ADS  Google Scholar 

  40. R. Alonso, M.B. Gavela, L. Merlo, S. Rigolin, J. Yepes, Minimal flavour violation with strong Higgs dynamics. JHEP 06, 076 (2012)

    Article  ADS  Google Scholar 

  41. S. Weinberg, Phenomenological lagrangians. Phys. A 96, 327 (1979)

    Article  Google Scholar 

  42. J. Gasser, H. Leutwyler, Chiral perturbation theory to one loop. Ann. Phys. 158, 142 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  43. J. Gasser, H. Leutwyler, Chiral perturbation theory: expansions in the mass of the strange quark. Nucl. Phys. B 250, 465 (1985)

    Article  ADS  Google Scholar 

  44. J. Gasser, H. Leutwyler, Low-energy expansion of meson form-factors. Nucl. Phys. B 250, 517–538 (1985)

    Article  ADS  Google Scholar 

  45. F. Feruglio, The chiral approach to the electroweak interactions. Int. J. Mod. Phys. A 8, 4937–4972 (1993)

    Article  ADS  Google Scholar 

  46. J. Bagger, V.D. Barger, K.-M. Cheung, J.F. Gunion, T. Han, G.A. Ladinsky, R. Rosenfeld, C.P. Yuan, The strongly interacting W W system: gold plated modes. Phys. Rev. D 49, 1246–1264 (1994)

    Article  ADS  Google Scholar 

  47. V. Koulovassilopoulos, R.S. Chivukula, The phenomenology of a nonstandard Higgs boson in W(L) W(L) scattering. Phys. Rev. D 50, 3218–3234 (1994)

    Article  ADS  Google Scholar 

  48. C.P. Burgess, J. Matias, M. Pospelov, A Higgs or not a Higgs? What to do if you discover a new scalar particle. Int. J. Mod. Phys. A 17, 1841–1918 (2002)

    Article  ADS  MATH  Google Scholar 

  49. L.-M. Wang, Q. Wang, Electroweak chiral Lagrangian for neutral Higgs boson. Chin. Phys. Lett. 25, 1984 (2008)

    Article  ADS  Google Scholar 

  50. B. Grinstein, M. Trott, A Higgs–Higgs bound state due to new physics at a TeV. Phys. Rev. D 76, 073002 (2007)

    Article  ADS  Google Scholar 

  51. R. Alonso, M.B. Gavela, L. Merlo, S. Rigolin, J. Yepes, The effective Chiral Lagrangian for a light dynamical Higgs Particle. Phys. Lett. B722 [Erratum: Phys. Lett. B726, 926 (2013)], 330–335 (2013)

    Google Scholar 

  52. G. Buchalla, O. Catà, C. Krause, Complete electroweak chiral Lagrangian with a light Higgs at NLO. Nucl. Phys. B 880, 552–573 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  53. G. Buchalla, O. Catà, C. Krause, On the power counting in effective field theories. Phys. Lett. B 731, 80–86 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  54. R. Contino, M. Ghezzi, C. Grojean, M. Muhlleitner, M. Spira, Effective lagrangian for a light Higgs-like scalar. JHEP 07, 035 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  55. I. Brivio, O.J.P. Éboli, M.B. Gavela, M.C. Gonzalez-Garcia, L. Merlo, S. Rigolin, Higgs ultraviolet softening. JHEP 12, 004 (2014)

    Article  ADS  Google Scholar 

  56. M.B. Gavela, J. Gonzalez-Fraile, M.C. Gonzalez-Garcia, L. Merlo, S. Rigolin, J. Yepes, CP violation with a dynamical Higgs. JHEP 10, 44 (2014)

    ADS  Google Scholar 

  57. J.M. Cornwall, D.N. Levin, G. Tiktopoulos, Derivation of gauge invariance from high-energy unitarity bounds on the s matrix. Phys. Rev. D10 [Erratum: Phys. Rev. D11, 972 (1975)], 1145 (1974)

    Google Scholar 

  58. C.E. Vayonakis, Born helicity amplitudes and cross-sections in nonabelian gauge theories. Lett. Nuovo Cim. 17, 383 (1976)

    Article  Google Scholar 

  59. B.W. Lee, C. Quigg, H.B. Thacker, Weak interactions at very high-energies: the role of the Higgs Boson Mass. Phys. Rev. D 16, 1519 (1977)

    Article  ADS  Google Scholar 

  60. M.S. Chanowitz, M.K. Gaillard, The TeV physics of strongly interacting W’s and Z’s. Nucl. Phys. B 261, 379 (1985)

    Article  ADS  Google Scholar 

  61. M.E. Peskin, D.V. Schroeder, An Introduction to Quantum Field Theory, 1995th edn. (Westview, Boulder, CO, 1995)

    Google Scholar 

  62. P.B. Pal, What is the equivalence theorem really? (1994), arXiv:hep-ph/9405362 [hep-ph]

  63. D. Espriu, J. Matias, Renormalization and the equivalence theorem: on-shell scheme. Phys. Rev. D 52, 6530–6552 (1995)

    Article  ADS  Google Scholar 

  64. J. Alwall et al., The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations. JHEP 07, 079 (2014)

    Article  ADS  Google Scholar 

  65. K. Olive et al., Review of particle physics. Chin. Phys. C 38, 090001 (2014)

    Article  ADS  Google Scholar 

  66. R.L. Delgado, A. Dobado, F.J. Llanes-Estrada, Light ‘Higgs’, yet strong interactions. J. Phys. G41, 025002 (2014)

    Article  ADS  Google Scholar 

  67. R. Delgado, A. Dobado, M. Herrero, J. Sanz-Cillero, One-loop \(\gamma \gamma \rightarrow W^+_L W^{-}_L\) and \(\gamma \gamma \rightarrow Z_L Z_L\) from the electroweak Chiral Lagrangian with a light Higgs-like scalar. JHEP 1407, 149 (2014)

    Article  ADS  Google Scholar 

  68. R.L. Delgado, A. Dobado, F.J. Llanes-Estrada, Possible new resonance from \(W_{L}W_{L}-hh\) interchannel coupling. Phys. Rev. Lett. 114, 221803 (2015)

    Google Scholar 

  69. The ATLAS collaboration, Updated coupling measurements of the Higgs boson with the ATLAS detector using up to 25 fb\(^{1}\) of proton-proton collision data, ATLASCONF-2014-009 (2014)

    Google Scholar 

  70. V. Khachatryan et al., Precise determination of the mass of the Higgs boson and tests of compatibility of its couplings with the standard model predictions using proton collisions at 7 and 8 TeV. Eur. Phys. J. C 75, 212 (2015)

    Article  ADS  Google Scholar 

  71. G. Buchalla, O. Cata, A. Celis, C. Krause, Fitting Higgs data with nonlinear effective theory. Eur. Phys. J. C 76, 233 (2016)

    Article  ADS  Google Scholar 

  72. J. Bernon, B. Dumont, Lilith: a tool for constraining new physics from Higgs measurements. Eur. Phys. J. C 75, 440 (2015)

    Article  ADS  Google Scholar 

  73. P.P. Giardino, Aspects of LHC phenomenology, PhD thesis (Pisa U., 2013)

    Google Scholar 

  74. R.L. Delgado, A. Dobado, F.J. Llanes-Estrada, One-loop \(W_LW_L\) and \(Z_LZ_L\) scattering from the electroweak Chiral Lagrangian with a light Higgs-like scalar. JHEP 1402, 121 (2014)

    Article  ADS  Google Scholar 

  75. R.L. Delgado, A. Dobado, F.J. Llanes-Estrada, Unitarity, analyticity, dispersion relations, and resonances in strongly interacting \(W_LW_L\), \(Z_LZ_L\), and \(hh\) scattering. Phys. Rev. D 91, 075017 (2015)

    Article  ADS  Google Scholar 

  76. G. Aad et al., Evidence for electroweak production of \(W^{\pm }W^{\pm } jj\) in \(pp\) Collisions at \(\sqrt{s} = 8\, \text{ TeV }\) with the ATLAS detector. Phys. Rev. Lett. 113, 141803 (2014)

    Article  ADS  Google Scholar 

  77. V. Khachatryan et al., Study of vector boson scattering and search for new physics in events with two same-sign leptons and two jets. Phys. Rev. Lett. 114, 051801 (2015)

    Article  ADS  Google Scholar 

  78. M. Baak et al., Working group report: precision study of electroweak interactions, in Community Summer Study 2013: Snowmass on the Mississippi (CSS2013), Minneapolis, MN, USA, July 29-August 6, 2013 (2013), arXiv:1310.6708 [hep-ph]

  79. M. Fabbrichesi, M. Pinamonti, A. Tonero, A. Urbano, Vector boson scattering at the LHC: a study of the \(\text{ WW } \rightarrow \text{ WW }\) channels with the Warsaw cut. Phys. Rev. D 93, 015004 (2016)

    Article  ADS  Google Scholar 

  80. A. Castillo, R.L. Delgado, A. Dobado, F.J. Llanes-Estrada, Top-antitop production from \(W^{+}_LW^{-}_L\) and \(Z_LZ_L\) scattering under a strongly-interacting symmetrybreaking sector, (2016), arXiv:1607.01158 [hep-ph]

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  1. Facultad de Ciencias Físicas, Theoretical Physics I Department, Complutense University of Madrid, Madrid, Spain

    Rafael Delgado López

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Delgado López, R. (2017). Chiral EW Lagrangian. In: Study of the Electroweak Symmetry Breaking Sector for the LHC. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-60498-5_2

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