Geodesic
Of Higgs, unitarity and other questions
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Problems of modern theoretical and mathematical physics: Gauge theories and superstrings, Tome 272 (2011), pp. 29-45.

Voir la notice de l'article provenant de la source Math-Net.Ru

On the verge of conclusive checks on the Standard Model by the LHC, we discuss some of the basic assumptions. The reason for this analysis stems from arecent proposal of an electroweak model based on a nonlinearly realized gauge group $\mathrm{SU}(2)\otimes\mathrm U(1)$, where, in the perturbative approximation, there is no Higgs boson. The model enjoys the Slavnov–Taylor identities and therefore the perturbative unitarity. On the other hand, it is commonly believed that the existence of the Higgs boson is entangled with the property of unitarity, when high energy processes are considered. The argument is based mostly on the Froissart bound and on the equivalence theorem. In this paper we briefly review some of our objections to the validity of such arguments. Some open questions are pointed out, in particular on the limit of zero mass for the vector mesons and on the fate of the longitudinal polarizations. 
@article{TM_2011_272_a3,
     author = {D. Bettinelli and R. Ferrari and A. Quadri},
     title = {Of {Higgs,} unitarity and other questions},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {29--45},
     publisher = {mathdoc},
     volume = {272},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2011_272_a3/}
}
TY  - JOUR
AU  - D. Bettinelli
AU  - R. Ferrari
AU  - A. Quadri
TI  - Of Higgs, unitarity and other questions
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2011
SP  - 29
EP  - 45
VL  - 272
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2011_272_a3/
LA  - en
ID  - TM_2011_272_a3
ER  - 
%0 Journal Article
%A D. Bettinelli
%A R. Ferrari
%A A. Quadri
%T Of Higgs, unitarity and other questions
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2011
%P 29-45
%V 272
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2011_272_a3/
%G en
%F TM_2011_272_a3
D. Bettinelli; R. Ferrari; A. Quadri. Of Higgs, unitarity and other questions. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Problems of modern theoretical and mathematical physics: Gauge theories and superstrings, Tome 272 (2011), pp. 29-45. http://geodesic.mathdoc.fr/item/TM_2011_272_a3/

[1] Cornwall J.M., Levin D.N., Tiktopoulos G., “Derivation of gauge invariance from high-energy unitarity bounds on the $S$ matrix”, Phys. Rev. D, 10 (1974), 1145 ; 11 (1975), 972 | DOI | DOI

[2] Lee B.W., Quigg C., Thacker H.B., “Weak interactions at very high energies: The role of the Higgs-boson mass”, Phys. Rev. D, 16 (1977), 1519 | DOI

[3] Weldon H.A., “Effects of multiple Higgs bosons on tree unitarity”, Phys. Rev. D, 30 (1984), 1547 | DOI

[4] Chanowitz M.S., Gaillard M.K., “The TeV physics of strongly interacting W's and Z's”, Nucl. Phys. B, 261 (1985), 379 | DOI

[5] Gounaris G.J., Kögerler R., Neufeld H., “Relationship between longitudinally polarized vector bosons and their unphysical scalar partners”, Phys. Rev. D, 34 (1986), 3257 | DOI

[6] Denner A., Dittmaier S., Hahn T., “Radiative corrections to $ZZ\to ZZ$ in the electroweak standard model”, Phys. Rev. D, 56 (1997), 117 | DOI

[7] Denner A., Hahn T., “Radiative corrections to $\mathrm W^+\mathrm W^-\to \mathrm W^+\mathrm W^-$ in the electroweak standard model”, Nucl. Phys. B, 525 (1998), 27 | DOI

[8] Ferrari R., “Endowing the nonlinear sigma model with a flat connection structure: A way to renormalization”, J. High Energy Phys., 2005, no. 8, 048 | DOI | MR

[9] Ferrari R., Quadri A., “Weak power-counting theorem for the renormalization of the nonlinear sigma model in four dimensions”, Intern. J. Theor. Phys., 45 (2006), 2497 | DOI | Zbl

[10] Ferrari R., Quadri A., “Renormalization of the non-linear sigma model in four dimensions: A two-loop example”, J. High Energy Phys., 2006, no. 1, 003 | DOI | MR | Zbl

[11] Bettinelli D., Ferrari R., Quadri A., “The hierarchy principle and the large mass limit of the linear sigma model”, Intern. J. Theor. Phys., 46 (2007), 2560 | DOI | Zbl

[12] Bettinelli D., Ferrari R., Quadri A., “Further comments on the symmetric subtraction of the nonlinear sigma model”, Intern. J. Mod. Phys. A, 23 (2008), 211 | DOI | MR | Zbl

[13] Bettinelli D., Ferrari R., Quadri A., “Path-integral over non-linearly realized groups and hierarchy solutions”, J. High Energy Phys., 2007, no. 3, 065 | DOI | MR

[14] Bettinelli D., Ferrari R., Quadri A., “Massive Yang–Mills theory based on the nonlinearly realized gauge group”, Phys. Rev. D, 77 (2008), 045021 | DOI | MR

[15] Bettinelli D., Ferrari R., Quadri A., “One-loop self-energy and counterterms in a massive Yang–Mills theory based on the nonlinearly realized gauge group”, Phys. Rev. D, 77 (2008), 105012 | DOI | MR

[16] Bettinelli D., Ferrari R., Quadri A., “The $\mathrm {SU}(2)\otimes \mathrm U(1)$ electroweak model based on the nonlinearly realized gauge group”, Intern. J. Mod. Phys. A, 24 (2009), 2639 | DOI | Zbl

[17] Bettinelli D., Ferrari R., Quadri A., “The $\mathrm {SU}(2)\otimes \mathrm {U}(1)$ electroweak model based on the nonlinearly realized gauge group. II: Functional equations and the weak power-counting”, Acta phys. Pol. B, 41 (2010), 597

[18] Bettinelli D., Ferrari R., Quadri A., “One-loop self-energies in the electroweak model with a nonlinearly realized gauge group”, Phys. Rev. D, 79 (2009), 125028 | DOI

[19] Ferrari R., “On the renormalization of the complex scalar free field theory”, J. Math. Phys., 51 (2010), 032305 | DOI | MR