Mass Hierarchy from SU(1,1) Horizontal Symmetry

Abstract

The new mechanism for the generation of the chiral generations is proposed based on the SU(1,1) horizontal gauge symmetry. The appearance of the chiral generations is controlled by the coupling constant s of the model. This is crucial in the grand unification scheme. The resulting chiral generations naturally acquire the hierarchal Yukawa coupli ng matrices. Propriety of the model to the observed hierarchical structure is discussed nume rically under the minimal parameter set.Comment: 12 pages, 5 figure

Dynamical generation of fermion mass hierarchy in an extra dimension

“…5 As we discussed in [26], if the warped scalar VEV is provided in the Higgs doublet, a serious violation in the gauge universality is expected. Thereby, in the previous works [26][27][28], we introduced an additional singlet scalar with the warped VEV, while the Higgs doublet has the ordinary constant VEV, and considered "higher-dimensional" Yukawa terms where both the Higgs doublet and the singlet scalar appear.…”

“…Another problem is on the fermion mass hierarchy. Each generation of the quarks and the charged leptons has exactly the same quantum numbers though their masses have an exponential hierarchy around 10 5 . In the SM, the masses are generated by the Higgs mechanism and are determined by the dimensionless Yukawa couplings; however, there is no explanation to the question of why so large a hierarchy appears in the dimensionless parameters.…”

“…One possibility in the context of four-dimensional (4d) gauge theory is a scenario with noncompact gauge symmetry, which can naturally produce the fermion mass hierarchy and three generations [4][5][6][7][8]. Another way is achieved by using extra dimensions.…”

A supersymmetric grand unified model with noncompact horizontal symmetry

“…The number of chiral generations of matter fields, such as quarks, leptons and higgses are determined by the spontaneous symmetry breaking of the horizontal symmetry SU (1, 1), called the spontaneous generation of generations [80]. Through the mechanism, the doublet-triplet splitting of higgses can be realized without fine-tuning and also unreasonably suppressed tiny mass parameters [83,85]. When the horizontal symmetry is unbroken, the original Yukawa coupling matrices of matter fields are completely determined by SU (1, 1) symmetry.…”

“…The correction for the Kähler potential of matter fields and the gauge kinetic function of the SU (5) gauge fields is negligible. After the chiral fields are generated via the spontaneous generation of generations [80,83,85,87], the effect from the SU (1, 1) gauge bosons and the structure fields is negligible for the chiral matter fields at low energy. Only the structure fields have large VEVs and the matter fields have smaller VEVs compared to those of the structure fields because of maintaining the structures of the horizontal symmetry; e.g., the VEVs of the structure fields are GUT-scale mass M GUT ≃ O(10 16 ) GeV and the VEVs of the matter fields are m SUSY ≃ O(10 3 ) GeV.…”