Operator regularization beyond lowest order

McKeon, D. G. C.; Samant, S.S.; Sherry, T. N.

doi:10.1139/p88-041

Cited by 9 publications

(8 citation statements)

References 2 publications

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“…Contrary to the approach of the mentioned above papers on the top -quark condensation models we do not use the conventional cutoff regularization. We use zeta regularization [15,16]. It allows to construct the effective theory without any ultraviolet divergencies.The 1/N c expansion is a good approximation within our effective theory.…”

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confidence: 99%

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Strong dynamics behind the formation of the 125 GeV Higgs boson

Zubkov

2014

Phys. Rev. D

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We consider the scenario, in which the new strong dynamics is responsible for the formation of the 125 GeV Higgs boson. The Higgs boson appears as composed of all known quarks and leptons of the Standard Model. The description of the mentioned strong dynamics is given using the ζ -regularization. It allows to construct the effective theory without ultraviolet divergences, in which the 1/Nc expansion works naturally. It is shown, that in the leading order of the 1/Nc expansion the mass of the composite h -boson is given by M h = mt/ √ 2 ≈ 125 GeV, where mt is the top -quark mass.PACS numbers: I. INTRODUCTIONIn the present paper we suggest the scenario, in which the recently discovered 125 GeV h -boson [1, 2] is composite. According to the suggested model it is composed of all fermions of the Standard Model (SM). The scale of the hidden strong dynamics is supposed to be of the order of several TeV. We suppose, that the W and Z boson masses are determined by the condensate of the 125 GeV h -boson according to the Higgs mechanism [3,4]. All Dirac fermion masses are determined by the h -boson as well. In the present paper we do not consider the Majorana masses at all and assume, that neutrinos have extremely small Dirac masses [5]. The low energy effective theory contains the fourfermion interaction [8] between all SM fermions. Our model differs from the conventional models with four -fermion interactions [6], in which the top quark is condensed. The model of top -quark condensation was first suggested in [7] (and developed later in [9][10][11][12][13]). The idea, that the Higgs boson may be composed of the known SM fermions was discussed even earlier, in [14], together with the certain preon models (however, in [14] there was no emphasis in the dominating role of the top quark and the compositeness of the Higgs boson was considered together with the compositeness of quarks and leptons). There are two main aspects, in which the model discussed in the present paper differs from the conventional models of top -quark condensation:1. The four -fermion interaction is non -local. It contains the form -factors G that correspond to the interaction between the composite Higgs boson and the pair fermion -antifermion. The formfactors depend on three scalar parameters of the dimension of mass squared: q 2 , p 2 , k 2 , where p and k are the 4 -momenta of the fermion and anti -fermion while q = p − k is the 4 -momentum of the composite scalar boson. G(p, k) = g(q 2 , p 2 , k 2 ) are different for different fermions at large distances (both time -like and space -like), i.e. if at least one of the quantities |q 2 |, |p 2 |, |k 2 | is much smaller, than the Electroweak scale M Z ≈ 90 GeV. However, at small space -like and time -like distances (i.e. for |q 2 | ∼ |p 2 | ∼ |k 2 | ∼ M 2 Z ) those form -factors become equal for all SM fermions. Unlike for the other fermions the mentioned form -factor for the top -quark is assumed to be independent of momenta. 2. Our model with the four -fermion interaction is not renormalizable. Therefo...

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confidence: 99%

“…Zeta regularization [15,16] provides the natural mechanism of cancelling the unphysical divergent contributions to various physical quantities in the field theories. For example, being applied to quantum hydrodynamics it provides the absence of the unphysical divergent contributions to vacuum energy due to the phonon loops.…”

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confidence: 99%

Strong dynamics behind the formation of the 125 GeV Higgs boson

Zubkov

2014

Phys. Rev. D

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“…Here we use the method for the calculation of various Green functions using zeta -regularization developed in. [56][57][58] In order to calculate the fermion determinant we perform the rotation to Euclidean space -time. It corresponds to the change:…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Dynamical torsion as the microscopic origin of the neutrino seesaw

Zubkov

2014

Mod. Phys. Lett. A

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It is assumed, that there are two scales in quantum gravity. Metric fluctuates at the scales of the order of the Plank mass. The second scale M T is related to the fluctuations of torsion. We suppose, that it may be as low as M T ∼ 1 TeV. Due to the non -minimal coupling to torsion the attractive interaction between the fermions appears. The non -minimal coupling admits the appearance of different coupling constants for different fermions. This opens the possibility that the interaction with torsion gives the Majorana masses for the right -handed neutrinos (that are assumed to be of the order of M T ). We suppose, that the Dirac masses for the neutrino are all close to the mass of electron. This gives the light neutrino masses ≤ 0.25 eV. In addition, the model predicts the appearance of Majorons that may contribute to the dark matter as well as to the invisible decay of the 125 GeV Higgs boson.

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“…Having discussed this approach within the context of traditional renormalization; it is intriguing to note that the use of analytic continuation [Bollini at al., 1964;Speer, 1968;Salam and Strathdee, 1975;Hawking, 1975;Dowker and Critchley, 1976] and the more recent method of operator regularization McKeon et al, 1988;Mann, 1988;Mann et al, 1989;Shiekh, 1990], implements the above scheme in a much cleaner way.…”

Section: Viable Formulationmentioning

confidence: 99%