SEESAW SCALES AND STEPS FROM THE STANDARD MODEL TOWARDS SUPERSTRING-INSPIRED FLIPPED E₆

Abstract

In the present paper we have investigated a number of available paths from the Standard Model (SM) to the Planck scale unification, considering a chain of flipped models following the seesaw scale extension of the SM:We have presented five cases including nonsupersymmetric and supersymmetric extensions of the SM and different contents of Higgs bosons providing the breaking of the flipped SO(10) and SU (5) down to the SM. It was shown that the final unification E 6 × U (1) or E 6 at the (Planck) GUT scale M SSG depends on the number of Higgs boson representations considered in theory. Only Higgses belonging to the vector and adjoint representations of SU (5) and SO(10) lead to the asymptotically free behaviour of nonabelian gauge coupling constants at large energies µ > ∼ 10 17 GeV. Asymptotically free models give the final unification E 6 × U (1) with the inversed E 6 fine structure constant α IntroductionNature is described by gauge theories and prefers to have the gauge groups with small rank, in comparison with the number N f of given fermion fields. For instance, the Standard Model (SM) contains 45 known fermion fields and could be described by the enormous global group SU(45) × U(1). Why does Nature choose only small subgroups of this enormous global group? The answer was given in Refs. [1][2][3][4]. The principles are simple: the resulting theory has to be (i) free from anomalies and (ii) free from bare masses. The largest simple subgroups of SU(N f ) × U(1) satisfying conditions (i) and (ii) are listed for a given N f in the Table 1 of Ref. [2] with N f going up to N f = 81. Examples taken from this Table show that we have SU(5) for N f = 15 and N f = 45, SO(10) for N f = 16 and N f = 48, E 6 for N f = 27, etc. If there exists one right-handed neutrino per family, in addition to the known SM fermions, then with one, two or three families we have the number of fermions 16, 32, 48, respectively.The insistence on the simple group is quite necessary. Otherwise, the largest semisimple groups also are possible:for N f = 78, etc., leading to the Family replicated gauge group models. The last 10 years Grand Unified Theories (GUTs) are inspired by superstring theories [5][6][7][8][9] showing a connection between superstrings and low energy particle physics phenomenology. The most realistic model based on the string theory is the heterotic string-derived flipped E 6 [10,11]. Compactification theory involving D-branes provides interesting features of the flipped models. Conventional GUT models, such as SU (5) and SO(10), have been investigated in details by a lot of authors, but none of them are not completely satisfactory. In Refs.[10] the gauge group SU(5) × U(1) ("flipped SU(5)") was suggested as a very economical candidate for unified theory: it may require only 10 + 10 Higgs representations to break the GUT symmetry, in contrast to other unified models which require large representations. There are many attractive experimentally testable results for flipped SU(5), including the prediction of α s (M Z )...

Cosmological constant in a model with superstring-inspired E 6 unification and shadow θ-particles

“…Among hundreds of papers devoted to the E 6 unification, we would like to single out Refs. [38][39][40][41][42][43][44][45].…”

Dyons Near the Planck Scale

“…Correspondingly, the flipped SO(10) (coming at the superGUT scale M SG ) contains 10 h + 10 h and 45 H + 45 H , 45-dimensional adjoint A and higher representations of Higgs bosons. As it was shown in [8], such Higgs boson contents lead to the flipped E 6 final unification at the supersuperGUT scale M SSG ∼ 10 18 GeV.…”

“…In Ref. [8] we have considered that only 'flipped' SU(5) unifies SU(3) C and SU(2) W of the Standard Model (SM) at the GUT scale M GU T ∼ 10 16 GeV. An explanation of the discrepancy between the unification scale M GU T and string scale M str ∼ 10 18 GeV was given by the assumption that there exists a chain of extra intermediate symmetries between M GU T and M P l :…”

Preon Model and Family Replicated E6 Unification

“…The paths (6)- (8) of the case 2) of Section 3 are presumably asymptotically free and do not give a minimum of the effective potential. As it was shown in [34], the E 6 -unification can give such a minimum for the chain (4), (5) if there exist symmetry breaking Higgs bosons belonging to the representations given in Section 3 by the Example 5 of [34]. This is a simplest example, because more complicated cases can be considered.…”

“…We have assumed as an Example 5 of [34] the breakdown of each supersymmetric 'flipped' i (x) near the Planck scale predicted by the case 1) of our model in the one-loop approximation of the above-mentioned Example 5 of [34]. Here for α i = g 2 i /4π index i corresponds to the groups (4) and (5): i = 1, 2, 3, X, Z, X1, Z1, 5, 10; x = log 10 µ(GeV), and µ is the energy scale.…”