Finite Grand Unified Theories and Inflation

A class of finite GUTs in curved spacetime is considered in connection with the cosmological inflation scenario. It is confirmed that the use of the running scalar-gravitational coupling constant in these models helps realizing a successful chaotic inflation. The analyses are made for some different sets of the models.Comment: 10 pages, latex, 4 figures, epic.sty and eepic.sty are use

The sigma meson from QCD sum rules for large-NcN_c Regge spectra

The QCD sum rules in the large-$N_c$ limit for the light non-strange vector, axial and scalar mesons are considered assuming a string-like linear spectrum for the radially excited states. We propose a improved method for combined analysis of these channels that gives a reasonable description of the observed spectrum. In the vector-axial case, fixing the pion decay constant and the gluon condensate we obtain more or less physical values for the masses of ground states and the quark condensate. Thus a typical need for this method to fix the mass of some ground state is overcome. Using in the scalar channel the values of presumably universal slope of radial trajectories and the quark condensate obtained in the vector-axial channel, we find that, in contrast to some strong claims in the literature, a prediction of light scalar state with a mass close to the mass of $f_0(500)$ seems to be natural in the considered approach and may follow in a natural way from the Regge phenomenology.Comment: Many new discussions concerning the origin of sigma-meson mass, its angular Regge trajectory, comparison with other results etc. are added to Sections 5 and 6. The new text corresponds to the version published in Eur. Phys. J.

The linear radial spectrum of scalar mesons within the QCD sum rules in the planar limit

We discuss the radial spectrum of light scalar mesons in the framework of spectral sum rules in the large-Nc (planar) limit of QCD. Two methods based on the use of linear radial Regge trajectories are presented. A special emphasis is placed on the appearance of scalar isoscalar state near 0.5 GeV. Within the considered sum rules, the existence of this meson (which could be a large-Nc counterpart to the sigma-meson) is closely related with existence of resonances in the vector channels and on the radial scalar trajectory.Comment: 8 pages, 2 figures, presented at QUARKS-2018. arXiv admin note: substantial text overlap with arXiv:1805.0672

Quantization of U_q[so(2n+1)] with deformed para-Fermi operators

The observation that n pairs of para-Fermi (pF) operators generate the universal enveloping algebra of the orthogonal Lie algebra so(2n+1) is used in order to define deformed pF operators. It is shown that these operators are an alternative to the Chevalley generators. On this background Uq[so(2n+1)] and its "Cartan-Weyl" generators are written down entirely in terms of deformed pB operators.Comment: plain TeX, Preprint INRNE-TH-93/7, 6