Abstract
The Abelian Higgs model forms an essential part of the electroweak standard model: it is the sector containing only Z0 and Higgs bosons. We present a diagram-based proof of the tree-level unitarity of this model inside the unitary gauge, where only physical degrees of freedom occur. We derive combinatorial recursion relations for off-shell amplitudes in the massless approximation, which allows us to prove the cancellation of the first two orders in energy of unitarity-violating high-energy behaviour for any tree-level amplitude in this model. We describe a deformation of the amplitudes by extending the physical phase space to at least 7 spacetime dimensions, which leads to on-shell recursion relations à la BCFW. These lead to a simple proof that all on-shell tree amplitudes obey partial-wave unitarity.
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References
P.W. Anderson, Plasmons, gauge invariance and mass, Phys. Rev. 130 (1963) 439 [INSPIRE].
G. ’t Hooft and M.J.G. Veltman, Regularization and renormalization of gauge fields, Nucl. Phys. B 44 (1972) 189 [INSPIRE].
C. Becchi, A. Rouet and R. Stora, The Abelian Higgs-Kibble model. Unitarity of the S operator, Phys. Lett. B 52 (1974) 344 [INSPIRE].
H.G.J. Veltman, The equivalence theorem, Phys. Rev. D 41 (1990) 2294 [INSPIRE].
C. Grosse-Knetter and R. Kögerler, Unitary gauge, Stuckelberg formalism and gauge invariant models for effective lagrangians, Phys. Rev. D 48 (1993) 2865 [hep-ph/9212268] [INSPIRE].
H. Elvang and Y.-T. Huang, Scattering amplitudes, arXiv:1308.1697 [INSPIRE].
S. Weinzierl, Tales of 1001 gluons, Phys. Rept. 676 (2017) 1 [arXiv:1610.05318] [INSPIRE].
C. Itzykson and J.-B. Zuber, Quantum field theory, McGraw-Hill, New York U.S.A., (1980) [INSPIRE].
M.E. Peskin and D.V. Schroeder, An introduction to quantum field theory, Addison-Wesley, Reading U.S.A., (1995) [INSPIRE].
D. Bailin and A. Love, Introduction to gauge field theory, IOP and Adam Hilger, U.K., (1986) [INSPIRE].
R. Kleiss, P4 lecture notes “paths, pictures, particles, processes”, Radboud University, Nijmegen The Netherlands, (2017).
J.M. Cornwall, D.N. Levin and G. Tiktopoulos, Uniqueness of spontaneously broken gauge theories, Phys. Rev. Lett. 30 (1973) 1268 [Erratum ibid. 31 (1973) 572] [INSPIRE].
J.M. Cornwall, D.N. Levin and G. Tiktopoulos, Derivation of gauge invariance from high-energy unitarity bounds on the S matrix, Phys. Rev. D 10 (1974) 1145 [Erratum ibid. D 11 (1975) 972] [INSPIRE].
E.N. Argyres, C.G. Papadopoulos and R.H.P. Kleiss, On amplitude zeros at threshold, Phys. Lett. B 302 (1993) 70 [hep-ph/9212280] [INSPIRE].
E.N. Argyres, R.H.P. Kleiss and C.G. Papadopoulos, Nullification of multi-Higgs threshold amplitudes in the Standard Model, Phys. Lett. B 308 (1993) 315 [Addendum ibid. B 319 (1993) 544] [hep-ph/9303322] [INSPIRE].
L.S. Brown, Summing tree graphs at threshold, Phys. Rev. D 46 (1992) R4125 [hep-ph/9209203] [INSPIRE].
V.V. Khoze and M. Spannowsky, Higgsplosion: solving the hierarchy problem via rapid decays of heavy states into multiple Higgs bosons, Nucl. Phys. B 926 (2018) 95 [arXiv:1704.03447] [INSPIRE].
R. Britto, F. Cachazo, B. Feng and E. Witten, Direct proof of tree-level recursion relation in Yang-Mills theory, Phys. Rev. Lett. 94 (2005) 181602 [hep-th/0501052] [INSPIRE].
N. Arkani-Hamed and J. Kaplan, On tree amplitudes in gauge theory and gravity, JHEP 04 (2008) 076 [arXiv:0801.2385] [INSPIRE].
H. Elvang, D.Z. Freedman and M. Kiermaier, Proof of the MHV vertex expansion for all tree amplitudes in N = 4 SYM theory, JHEP 06 (2009) 068 [arXiv:0811.3624] [INSPIRE].
T. Cohen, H. Elvang and M. Kiermaier, On-shell constructibility of tree amplitudes in general field theories, JHEP 04 (2011) 053 [arXiv:1010.0257] [INSPIRE].
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ArXiv ePrint: 1705.04859
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Kleiss, R., Luna, O.B. Amplitudes, recursion relations and unitarity in the Abelian Higgs model. J. High Energ. Phys. 2017, 2 (2017). https://doi.org/10.1007/JHEP12(2017)002
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DOI: https://doi.org/10.1007/JHEP12(2017)002