arXiv subjects
Publications and source records attributed to J. Kubo.
These are the proceedings of the 2nd Workshop on Flavor Symmetries and Consequences in Accelerators and Cosmology, held 30 June 2012 - 4 July 2012, Dortmund, Germany.
Assuming that the lepton, quark and Higgs fields belong to the three-dimensional reducible representation of the permutation group S_3, we suggest a minimal S_3 invariant extension of the standard model. We find that in the leptonic sector, the exact S_3 x Z_2 symmetry, which allows 6 real independent parameters with two CP-violating phases, is consistent with experimental data and predicts a maximal mixing of the atmospheric neutrinos, and that the third neutrino is the lightest neutrino. With the exact S_3 only, there are 10 real parameters and five phases in the quark sector. A set of values of these parameters that are consistent with experimental observations is given.
Gauge-Yukawa unified theories, and in particular those which are finite beyond the unification scale, have been extended to include a soft supersymmetry breaking (SSB) sector. In the case of the Finite Unified Theories a new solution to the condition of two-loop finiteness of the SSB parameters is found, which requires a sum rule for the relevant scalar masses. The sum rule permits violations of the universality of the scalar masses which is found to lead to phenomenological problems. The minimal supersymmetric SU(5) Gauge-Yukawa model and two Finite-Gauge-Yukawa models have been examined using the sum rule. The characteristic features of these models are: a) the old agreement of the top quark mass prediction persists using the new data, b) the lightest Higgs boson is predicted to be around 120 GeV, c) the s-spectrum starts above 200 GeV.
Requiring the soft supersymmetry-breaking (SSB) parameters in finite gauge-Yukawa unified models to be finite up to and including two-loop order, we derive a two-loop sum rule for the soft scalar-masses. It is shown that this sum rule coincides with that of a certain class of string models in which the massive string states are organized into N=4 supermultiplets. We investigate the SSB sector of two finite SU(5) models. Using the sum rule which allows the non-universality of the SSB terms and requiring that the lightest superparticle particleis neutral, we constrain the parameter space of the SSB sector in each model.
Reduction of couplings in supersymmetric GUTs is achieved by searching for renormalization group invariant (RGI) relations among couplings which hold beyond the unification scale. Finiteness is due to the fact that there exist RGI relations among couplings that guarantee the vanishing of the beta-functions of a N=1 supersymmetric GUT even to all orders in perturbation theory. Of particular interest are the relations among gauge and Yukawa couplings which lead to very interesting predictions of the top quark mass
Gauge-Yukawa Unification (GYU) is a renormalization group invariant functional relation among gauge and Yukawa couplings which holds beyond the unification point in Grand Unified Theories (GUTs). We present here various models where GYU is obtained by requiring the principles of finiteness and reduction of couplings. We examine the consequences of these requirements for the low energy parameters, especially for the top quark mass. The predictions are such that they clearly distinguish already GYU from ordinary GUTs. It is expected that it will be possible to discriminate among the various GYUs when more accurate measurements of the top quark mass are available.
Gauge-Yukawa Unification (GYU) is obtained in GUTs by searching for renormalization group invariant relations among gauge and Yukawa couplings beyond the unification scale. Of particular interest are two supersymmetric GUTs, the finite and the minimal SU(5) models. Both models provided us,among others,with predictions of the top quark mass which so far have passed successfully the tests of progressively more accurate measurements.
Two-dimensional quantum gravity is identified as a second-class system which we convert into a first-class system via the Batalin-Fradkin (BF) procedure. Using the extended phase space method, we then formulate the theory in most general class of gauges. The conformal gauge action suggested by David, Distler and Kawai is derived from a first principle. We find a local, light-cone gauge action whose Becchi-Rouet-Stora-Tyutin invariance implies Polyakov's curvature equation $\partial_{-}R=\partial_{-}^{3}g_{++}=0$, revealing the origin of the $SL(2,R)$ Kac-Moody symmetry. The BF degree of freedom turns out be dynamically active as the Liouville mode in the conformal gauge, while in the light-cone gauge the conformal degree of freedom plays that r{ô}le. The inclusion of the cosmological constant term in both gauges and the harmonic gauge-fixing are also considered.
The classical 2D cosmological model of Callan, Giddings, Harvey and Strominger possesses a global symmetry that is responsible for decoupling of matter fields. The model is quantized on the basis of the extended phase space method to allow an exhaustive, algebraic analysis to find potential anomalies. Under a certain set of reasonable assumptions we show that neither the BRST symmetry of the theory nor the global symmetry suffers from an anomaly. From this we conclude that there is nothing to recognize the existence of black hole and therefore nothing to radiate in their cosmological model.
The extended phase space method of Batalin, Fradkin and Vilkovisky is applied to formulate two dimensional gravity in a general class of gauges. A BRST formulation of the light-cone gauge is presented to reveal the relationship between the BRST symmetry and the origin of $SL(2,R)$ current algebra. From the same principle we derive the conformal gauge action suggested by David, Distler and Kawai.
Using the generalized hamiltonian method of Batalin, Fradkin and Vilkovisky, we investigate the algebraic structure of anomalies in the Polyakov string theory that appear as the Schwinger terms in super-commutation relations between BRST charge and total hamiltonian. We obtain the most general form of the anomalies in the extended phase space, without any reference to a two dimensional metric. This pregeometri- cal result, refered to as the genelarized Virasoro anomaly, independent of the gauge and the regularization under a minor assumption, is a non-perturbative result, and valid for any space-time dimension. In a configuration space, in which the two dimensional metric can be identified, we can geometrize the result without assuming the weak gravitational field, showing that the most general anomaly exactly exhibits the Weyl anomaly.