Abstract
Applying the three axiomatic criteria of Lorentz invariance, analyticity and unitarity to scattering amplitudes involving the Goldstone bosons and the Higgs boson, we derive a general sum rule for the Strongly Interacting Light Higgs Lagrangian. This sum rule connects the IR coefficient c H to the UV properties of the theory, and can be used, for instance, to capture the role of resonances in processes like V L V L → hh and V L V L → V L V L, with V = W ± , Z.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
F. Englert and R. Brout, Broken Symmetry and the Mass of Gauge Vector Mesons, Phys. Rev. Lett. 13 (1964) 321 [INSPIRE].
P.W. Higgs, Broken Symmetries and the Masses of Gauge Bosons, Phys. Rev. Lett. 13 (1964) 508 [INSPIRE].
P.W. Higgs, Broken symmetries, massless particles and gauge fields, Phys. Lett. 12 (1964) 132 [INSPIRE].
ATLAS collaboration, Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716 (2012) 1 [arXiv:1207.7214] [INSPIRE].
CMS collaboration, Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Phys. Lett. B 716 (2012) 30 [arXiv:1207.7235] [INSPIRE].
ATLAS collaboration, Higgs public results, https://twiki.cern.ch/twiki/bin/view/AtlasPublic/HiggsPublicResults.
CMS collaboration, Higgs public results, https://twiki.cern.ch/twiki/bin/view/CMSPublic/PhysicsResultsHIG.
ATLAS collaboration, Combined measurements of the mass and signal strength of the Higgs-like boson with the ATLAS detector using up to 25 fb −1 of proton-proton collision data, ATLAS-CONF-2013-014 (2013).
CMS collaboration, Combination of standard model Higgs boson searches and measurements of the properties of the new boson with a mass near 125 GeV, CMS-PAS-HIG-13-005.
D.B. Kaplan and H. Georgi, SU(2) × U(1) Breaking by Vacuum Misalignment, Phys. Lett. B 136 (1984) 183 [INSPIRE].
H. Georgi and D.B. Kaplan, Composite Higgs and Custodial SU(2), Phys. Lett. B 145 (1984) 216 [INSPIRE].
D.B. Kaplan, H. Georgi and S. Dimopoulos, Composite Higgs Scalars, Phys. Lett. B 136 (1984) 187 [INSPIRE].
M.J. Dugan, H. Georgi and D.B. Kaplan, Anatomy of a Composite Higgs Model, Nucl. Phys. B 254 (1985) 299 [INSPIRE].
R. Contino, Y. Nomura and A. Pomarol, Higgs as a holographic pseudo-Goldstone boson, Nucl. Phys. B 671 (2003) 148 [hep-ph/0306259] [INSPIRE].
K. Agashe, R. Contino and A. Pomarol, The Minimal composite Higgs model, Nucl. Phys. B 719 (2005) 165 [hep-ph/0412089] [INSPIRE].
ATLAS collaboration, Measurements of Higgs boson production and couplings in diboson final states with the ATLAS detector at the LHC, Phys. Lett. B 726 (2013) 88 [arXiv:1307.1427] [INSPIRE].
A. Falkowski, F. Riva and A. Urbano, Higgs at last, JHEP 11 (2013) 111 [arXiv:1303.1812] [INSPIRE].
P.P. Giardino, K. Kannike, I. Masina, M. Raidal and A. Strumia, The universal Higgs fit, JHEP 05 (2014) 046 [arXiv:1303.3570] [INSPIRE].
A. Pomarol and F. Riva, Towards the Ultimate SM Fit to Close in on Higgs Physics, JHEP 01 (2014) 151 [arXiv:1308.2803] [INSPIRE].
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] [INSPIRE].
J. Baglio, A. Djouadi, R. Gröber, M.M. Mühlleitner, J. Quevillon et al., The measurement of the Higgs self-coupling at the LHC: theoretical status, JHEP 04 (2013) 151 [arXiv:1212.5581] [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].
R.J. Eden, P.V. Landshoff, D.I. Olive and J.C. Polkinghorne, The analytic S-matrix, Cambridge University Press (2002).
V.N. Gribov, Y.L. Dokshitzer and J. Nyiri, Strong interactions of hadrons at high energies: Gribov lectures on theoretical physics, Cambridge University Press (2009).
M.S. Chanowitz and M.K. Gaillard, The TeV Physics of Strongly Interacting W’s and Z’s, Nucl. Phys. B 261 (1985) 379 [INSPIRE].
G.F. Giudice, C. Grojean, A. Pomarol and R. Rattazzi, The Strongly-Interacting Light Higgs, JHEP 06 (2007) 045 [hep-ph/0703164] [INSPIRE].
F. Caracciolo, A. Parolini and M. Serone, UV Completions of Composite Higgs Models with Partial Compositeness, JHEP 02 (2013) 066 [arXiv:1211.7290] [INSPIRE].
A. Adams, N. Arkani-Hamed, S. Dubovsky, A. Nicolis and R. Rattazzi, Causality, analyticity and an IR obstruction to UV completion, JHEP 10 (2006) 014 [hep-th/0602178] [INSPIRE].
I. Low, R. Rattazzi and A. Vichi, Theoretical Constraints on the Higgs Effective Couplings, JHEP 04 (2010) 126 [arXiv:0907.5413] [INSPIRE].
A. Nicolis, R. Rattazzi and E. Trincherini, Energy’s and amplitudes’ positivity, JHEP 05 (2010) 095 [Erratum ibid. 1111 (2011) 128] [arXiv:0912.4258] [INSPIRE].
I. Low, R. Rattazzi and A. Vichi, Theoretical Constraints on the Higgs Effective Couplings, JHEP 04 (2010) 126 [arXiv:0907.5413] [INSPIRE].
J. Distler, B. Grinstein, R.A. Porto and I.Z. Rothstein, Falsifying Models of New Physics via WW Scattering, Phys. Rev. Lett. 98 (2007) 041601 [hep-ph/0604255] [INSPIRE].
A.V. Manohar and V. Mateu, Dispersion Relation Bounds for ππ Scattering, Phys. Rev. D 77 (2008) 094019 [arXiv:0801.3222] [INSPIRE].
M.G. Olsson, Low-Energy p-Wave π-π Interaction, Phys. Rev. 162 (1967) 1338.
S.L. Adler, Sum rules for the axial vector coupling constant renormalization in β decay, Phys. Rev. 140 (1965) B736 [Erratum ibid. 149 (1966) 1294] [Erratum ibid. 175 (1968) 2224].
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].
M. Knecht, B. Moussallam, J. Stern and N.H. Fuchs, The Low-energy ππ amplitude to one and two loops, Nucl. Phys. B 457 (1995) 513 [hep-ph/9507319] [INSPIRE].
J. Bijnens, G. Colangelo, G. Ecker, J. Gasser and M.E. Sainio, Pion pion scattering at low-energy, Nucl. Phys. B 508 (1997) 263 [Erratum ibid. B 517 (1998) 639] [hep-ph/9707291] [INSPIRE].
V. Cirigliano, G. Ecker, M. Eidemuller, R. Kaiser, A. Pich et al., Towards a consistent estimate of the chiral low-energy constants, Nucl. Phys. B 753 (2006) 139 [hep-ph/0603205] [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].
D. Greynat and E. de Rafael, Froissart-Martin bound for ππ scattering in QCD, Phys. Rev. D 88 (2013) 034015 [arXiv:1305.7045] [INSPIRE].
B. Ananthanarayan, G. Colangelo, J. Gasser and H. Leutwyler, Roy equation analysis of ππ scattering, Phys. Rept. 353 (2001) 207 [hep-ph/0005297] [INSPIRE].
B. Ananthanarayan, D. Toublan and G. Wanders, Consistency of the chiral pion pion scattering amplitudes with axiomatic constraints, Phys. Rev. D 51 (1995) 1093 [hep-ph/9410302] [INSPIRE].
B. Ananthanarayan, P. Buettiker and B. Moussallam, πK sum rules and the SU(3) chiral expansion, Eur. Phys. J. C 22 (2001) 133 [hep-ph/0106230] [INSPIRE].
B. Ananthanarayan and P. Buettiker, Comparison of pion kaon scattering in SU(3) chiral perturbation theory and dispersion relations, Eur. Phys. J. C 19 (2001) 517 [hep-ph/0012023] [INSPIRE].
B. Ananthanarayan and P. Buettiker, Higher threshold parameters in ππ scattering, Phys. Lett. B 415 (1997) 402 [hep-ph/9707305] [INSPIRE].
K. Agashe, R. Contino, L. Da Rold and A. Pomarol, A Custodial symmetry for \( Zb\overline{b} \), Phys. Lett. B 641 (2006) 62 [hep-ph/0605341] [INSPIRE].
M. Froissart, Asymptotic behavior and subtractions in the Mandelstam representation, Phys. Rev. 123 (1961) 1053 [INSPIRE].
A. Martin, Unitarity and high-energy behavior of scattering amplitudes, Phys. Rev. 129 (1963) 1432 [INSPIRE].
A. Martin, Extension of the axiomatic analyticity domain of scattering amplitudes by unitarity. 1., Nuovo Cim. A 42 (1965) 930 [INSPIRE].
LHC Higgs Cross Section Working Group collaboration, A. David et al., LHC HXSWG interim recommendations to explore the coupling structure of a Higgs-like particle, arXiv:1209.0040 [INSPIRE].
S. Chang, A ‘Littlest Higgs’ model with custodial SU(2) symmetry, JHEP 12 (2003) 057 [hep-ph/0306034] [INSPIRE].
R. Rattazzi, A view on strongly coupled EWSB, talk at the Workshop on Strongly Coupled Physics Beyond the Standard Model, 25-27 January (2012), ICTP, Trieste, Italy, http://cdsagenda5.ictp.trieste.it/askArchive.php?base=agenda&categ=a11229&id=a11229s2t28/slides.
I. Low, A minimally symmetric Higgs boson, talk at the Workshop on Strongly Coupled Physics Beyond the Standard Model, 25-27 January (2012), ICTP, Trieste, Italy, http://cdsagenda5.ictp.trieste.it/askArchive.php?base=agenda&categ=a11229&id=a11229s1t14/slides.
A. Wulzer, An Equivalent Gauge and the Equivalence Theorem, arXiv:1309.6055 [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].
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].
G. Panico and A. Wulzer, The Discrete Composite Higgs Model, JHEP 09 (2011) 135 [arXiv:1106.2719] [INSPIRE].
O. Matsedonskyi, G. Panico and A. Wulzer, Light Top Partners for a Light Composite Higgs, JHEP 01 (2013) 164 [arXiv:1204.6333] [INSPIRE].
D. Marzocca, M. Serone and J. Shu, General Composite Higgs Models, JHEP 08 (2012) 013 [arXiv:1205.0770] [INSPIRE].
A. Pomarol and F. Riva, The Composite Higgs and Light Resonance Connection, JHEP 08 (2012) 135 [arXiv:1205.6434] [INSPIRE].
S. De Curtis, M. Redi and A. Tesi, The 4D Composite Higgs, JHEP 04 (2012) 042 [arXiv:1110.1613] [INSPIRE].
M. Redi and A. Tesi, Implications of a Light Higgs in Composite Models, JHEP 10 (2012) 166 [arXiv:1205.0232] [INSPIRE].
M. Ciafaloni, P. Ciafaloni and D. Comelli, Enhanced electroweak corrections to inclusive boson fusion processes at the TeV scale, Nucl. Phys. B 613 (2001) 382 [hep-ph/0103316] [INSPIRE].
P. Ciafaloni and A. Urbano, Infrared weak corrections to strongly interacting gauge bosons scattering, Phys. Rev. D 81 (2010) 085033 [arXiv:0902.1855] [INSPIRE].
A.A. Logunov, M.A. Mestvirishvili and O.A. Khrustalev, Restriction on the behaviour of the elastic and inelastic cross-sections at high energy. 1, Teor. Mat. Fiz. 9 (1971) 3 [INSPIRE].
A.A. Logunov, M.A. Mestvirishvili and O.A. Khrustalev, Restriction of the behaviour of the elastic and inelastic cross-sections at high energy. 2, Teor. Mat. Fiz. 9 (1971) 153 [INSPIRE].
F. Gursey and H.C. Tze, Complex and Quaternionic Analyticity in Chiral and Gauge Theories. Part 1, Annals Phys. 128 (1980) 29 [INSPIRE].
J. Gates, S. J., H. Nishino and E. Sezgin, Supergravity in d = 9 and Its Coupling to Noncompact σ Model, Class. Quant. Grav. 3 (1986) 21 [INSPIRE].
N.T. Yilmaz, The Non-split scalar coset in supergravity theories, Nucl. Phys. B 675 (2003) 122 [hep-th/0407006] [INSPIRE].
R. Bogdanovi and M.A. Whitehead, The representation of the SO(4,1) group in four-dimensional Euclidean and spinor space J. Math. Phys. 16 (1975) 400.
R. Contino, C. Grojean, D. Pappadopulo, R. Rattazzi and A. Thamm, Strong Higgs Interactions at a Linear Collider, JHEP 02 (2014) 006 [arXiv:1309.7038] [INSPIRE].
M.E. Peskin and T. Takeuchi, Estimation of oblique electroweak corrections, Phys. Rev. D 46 (1992) 381 [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].
M. Ciuchini, E. Franco, S. Mishima and L. Silvestrini, Electroweak Precision Observables, New Physics and the Nature of a 126 GeV Higgs Boson, JHEP 08 (2013) 106 [arXiv:1306.4644] [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].
R. Contino, The Higgs as a Composite Nambu-Goldstone Boson, arXiv:1005.4269 [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1310.5733
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Urbano, A. Remarks on analyticity and unitarity in the presence of a strongly interacting light Higgs. J. High Energ. Phys. 2014, 60 (2014). https://doi.org/10.1007/JHEP06(2014)060
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2014)060