Scattering Amplitudes

  • Rafael Delgado LópezEmail author
Part of the Springer Theses book series (Springer Theses)


In this chapter, the scattering amplitudes VV->VV (\(V=W_L^\pm , Z_L\)), VV->hh, hh->hh, and VV, hh->gamma gamma, ttbar are computed at the NLO level in perturbation theory by means of the Electroweak Chiral Lagrangian exposed in Chap.  2. For the scattering processes involving 2-gamma and ttbar states, a detailed helicity study is performed.


Scat Tering Amplitude Scattering Amplitudes Partial Wave Isospin Singlet State Isospin Basis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    B.R. Martin, D. Morgan, G. Shaw, Pion–Pion Interactions in Particle Physics (Academic Press, London, 1976)Google Scholar
  2. 2.
    M.E. Peskin, D.V. Schroeder, An Introduction to Quantum Field Theory, 1995th edn. (Westview, Boulder, CO, 1995)Google Scholar
  3. 3.
    M.E. Rose, Elementary Theory of Angular Momentum (Wiley, New York, 1957). (Also as a reprint ed.: New York, Dover, 1995)zbMATHGoogle Scholar
  4. 4.
    J.R. Taylor, Scattering Theory: The Quantum Theory of Nonrelativistic Collisions, Dover Books on Engineering (Dover Publications, Newburyport, MA, 2012)Google Scholar
  5. 5.
    R.J. Eden, P.V. Landshoff, D.I. Olive, J.C. Polkinghorne, The Analytic S-Matrix (Cambridge University Press, Cambridge, 1966)zbMATHGoogle Scholar
  6. 6.
    A. Dobado, A. Gómez-Nicola, A.L. Maroto, J.R. Peláez, Effective Lagrangians for the Standard Model, Texts and Monographs in Physics (Springer, Berlin, 1997)CrossRefzbMATHGoogle Scholar
  7. 7.
    K. Olive et al., Review of particle physics. Chin. Phys. C 38, 090001 (2014)ADSCrossRefGoogle Scholar
  8. 8.
    R.L. Delgado, A. Dobado, F.J. Llanes-Estrada, Light ‘Higgs’, yet strong interactions. J. Phys. G41, 025002 (2014)ADSCrossRefGoogle Scholar
  9. 9.
    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)ADSCrossRefGoogle Scholar
  10. 10.
    A. Dobado, R.L. Delgado, F.J. Llanes-Estrada, Strongly interacting electroweak symmetry breaking sector with a Higgs-like light scalar. AIP Conf. Proc. 1606, 151–158 (2014)ADSCrossRefGoogle Scholar
  11. 11.
    R.L. Delgado, A. Dobado, F.J. Llanes-Estrada, Possible new resonance from \(W_LW_L-hh\) interchannel coupling. Phys. Rev. Lett. 114, 221803 (2015)ADSCrossRefGoogle Scholar
  12. 12.
    R.L. Delgado, A. Dobado, F.J. Llanes-Estrada, Strongly interacting \(W_LW_L, Z_LZ_L\) and \(hh\) from unitarized one-loop computations. Nucl. Part. Phys. Proc. 273–275, 2436–2438 (2016)CrossRefGoogle Scholar
  13. 13.
    R.L. Delgado, A. Dobado, F.J. Llanes-Estrada, A strongly interacting electroweak symmetry breaking sector with a Higgs-like light scalar. AIP Conf. Proc. 1701, 090003 (2016)CrossRefGoogle Scholar
  14. 14.
    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)ADSCrossRefGoogle Scholar
  15. 15.
    A. Dobado, R.L. Delgado, F.J. Llanes-Estrada, Resonances in \(W_LW_L,Z_LZ_L\) and \(hh\) scattering from dispersive analysis of the non-linear Electroweak+Higgs Effective Theory, PoS EPS-HEP2015, 173 (2015)Google Scholar
  16. 16.
    F.J. Llanes-Estrada, A. Dobado, R.L. Delgado, Describing 2-TeV scale \(W_LW_L\) resonances with Unitarized Effective Theory, in 18th Workshop on What Comes Beyond the Standard Models? Bled, Slovenia, July 11–19, 2015 (2015). arXiv:1509.00441 [hep-ph]
  17. 17.
    D. Espriu, F. Mescia, B. Yencho, Radiative corrections to WL WL scattering in composite Higgs models. Phys. Rev. D 88, 055002 (2013)ADSCrossRefGoogle Scholar
  18. 18.
    A. Alloul, N.D. Christensen, C. Degrande, C. Duhr, B. Fuks, FeynRules 2.0—A complete toolbox for tree-level phenomenology. Comput. Phys. Commun. 185, 2250–2300 (2014)ADSCrossRefGoogle Scholar
  19. 19.
    T. Hahn, Generating Feynman diagrams and amplitudes with FeynArts 3. Comput. Phys. Commun. 140, 418–431 (2001)ADSCrossRefzbMATHGoogle Scholar
  20. 20.
    T. Hahn, M. Perez-Victoria, Automatized one loop calculations in four-dimensions and D-dimensions. Comput. Phys. Commun. 118, 153–165 (1999)ADSCrossRefGoogle Scholar
  21. 21.
    J.A.M. Vermaseren, New features of FORM (2000), arXiv:math - ph / 0010025 [math-ph]
  22. 22.
    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)ADSCrossRefGoogle Scholar
  23. 23.
    J. Elias-Miro, J.R. Espinosa, A. Pomarol, One-loop non-renormalization results in EFTs. Phys. Lett. B 747, 272–280 (2015)ADSCrossRefGoogle Scholar
  24. 24.
    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)ADSCrossRefGoogle Scholar
  25. 25.
    The ATLAS collaboration, Updated coupling measurements of the Higgs boson with the ATLAS detector using up to \(25\,\text{fb}^{-1}\) of proton-proton collision data, ATLASCONF- 2014-009 (2014)Google Scholar
  26. 26.
    A. Castillo, R.L. Delgado, A. Dobado, F.J. Llanes-Estrada, Top-antitop production from \(W^+_L W^-_L\) and \(Z_LZ_L\) scattering under a strongly-interacting symmetrybreaking sector, (2016), arXiv:1607.01158 [hep-ph]
  27. 27.
    E.T. Whittaker, G.N. Watson, A Course of Modern Analysis, 4th edn. (Cambridge Mathematical Library (Cambridge University Press), Cambridge, 1996)CrossRefzbMATHGoogle Scholar
  28. 28.
    G.E. Andrews, R.A. Askey, R. Roy, Special Functions Encyclopaedia of Mathematics and Its Applications, 2nd edn. (Cambridge University Press, Cambridge, 2001)Google Scholar
  29. 29.
    M. Jacob, G.C. Wick, On the general theory of collisions for particles with spin. Ann. Phys. 7, 404–428 (1959)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    A. Alboteanu, W. Kilian, J. Reuter, Resonances and unitarity in weak boson scattering at the LHC. JHEP 11, 010 (2008)ADSCrossRefGoogle Scholar
  31. 31.
    S. Weinberg, Phenomenological Lagrangians. Phys. A 96, 327 (1979)CrossRefGoogle Scholar
  32. 32.
    G. Buchalla, O. Cata, Effective theory of a dynamically broken electroweak standard model at NLO. JHEP 07, 101 (2012)ADSCrossRefGoogle Scholar
  33. 33.
    G. Buchalla, O. Catá, C. Krause, On the power counting in effective field theories. Phys. Lett. B 731, 80–86 (2014)ADSMathSciNetCrossRefGoogle Scholar
  34. 34.
    R.L. Delgado, A. Dobado, F.J. Llanes-Estrada, Coupling WW, ZZ unitarized amplitudes to \(\gamma \gamma \) in the TeV region. Eur. Phys. J. C 77, 205 (2017)ADSCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Facultad de Ciencias Físicas, Theoretical Physics I DepartmentComplutense University of MadridMadridSpain

Personalised recommendations