The classically conformal B-L extended standard model 古典的なコンフォーマル対称性を持ったB-L拡張模型
The classically conformal B-L extended standard model
To understand the dynamics of the electroweak symmetry breaking is one of the most important issues in particle physics. In particular, the hierarchy problem, i.e. the stability of the electroweak scale against a higher energy scale (e.g. GUT scale or Planck scale) is the most mysterious. Low energy supersymmetry provides a natural solution, and predicts new particles around the TeV scale. We pay a special attention to the (almost) classical conformal invariance of the SM. Because of the chiral nature, the SM Lagrangian at the classical level cannot possess dimensionful parameters except for the Higgs mass term closely related to the gauge hierarchy problem. Even if the SM Lagrangian possesses the classical conformal invariance, the Higgs mass term is radiatively induced by matter fields with quadratically divergent coefficients, and hence we cannot be free from the gauge hierarchy problem. Bardeen has argued that once the classical conformal invariance and its minimal violation by quantum anomalies are imposed on the SM, it may be free from the quadratic divergences and hence the gauge hierarchy problem. It seems difficult to realize such a mechanism in ordinary field theories based on the Wilsonian renormalization group, but we cannot either deny a possibility of an yet unknown mechanism to forbid the quadratic (and possibly the quartic) divergences in field theories based on the Planck scale physics. Such a mechanism inevitably requires the absence of intermediate mass scales between the electroweak and the Planck scales. In other words, physics at the Planck scale is directly connected with the electroweak physics. In this thesis, we do not discuss the mechanism itself, but investigate its phenomenological implications. If the quadratic divergences are absent in classically conformal theories, the conformal symmetry is broken only by the logarithmic running of the coupling constants. As a result, the electroweak symmetry breaking is realized not by the negative mass squared term of the Higgs doublet, but the radiative breaking, called Coleman-Weinberg (CW) mechanism. However it is well-recognized that the CW scenario is already excluded for the SM because of the large top-Yukawa coupling. In the original paper by Coleman and Weinberg, they predicted the Higgs boson mass at 10 GeV assuming a small top-quark mass, but at present, the heavy top-quark is known to destabilize the Higgs potential, and the CW mechanism does not work. Hence we should extend the SM so that the CW mechanism works with phenomenologically viable parameters. We have proposed a minimal phenomenologically viable model that the electroweak symmetry can be radiatively broken. It is the minimal B-L model. The electroweak as well as the B-L symmetries should be broken radiatively by the CW mechanism because of the classical conformal invariance. The condition that the theory is stable up to the Planck scale gives a strong constraint on the parameter space of the model. The stability of the electroweak scale against radiative corrections gives upper bounds for the masses of the B-L gauge boson and the right-handed neutrinos, and in this way we are led to the minimal B-L gauged model naturally realized at the TeV scale. In this thesis, we further study the theoretical and phenomenological properties of the model. Because of the theoretical requirements, Z' gauge boson mass is predicted to be around a few TeV, and will be soon discovered at the LHC. Our model can generate baryon asymmetry and dark matter density in the universe. First, the baryogenesis is realized thorough the resonant leptogenesis. In this thesis we investigate the resonant leptogenesis scenario in the minimal B-L extended SM with the B-L symmetry breaking at the TeV scale. Through detailed analysis of the Boltzmann equations, we show how much the resultant baryon asymmetry via leptogenesis is enhanced or suppressed, depending on the model parameters, in particular, the neutrino Dirac Yukawa couplings and the TeV-scale Majorana masses of heavy degenerate neutrinos. In order to consider a realistic case, we impose a simple ansatz for the model parameters and analyze the neutrino oscillation parameters and the baryon asymmetry via leptogenesis as a function of only a single CP-phase. We find that for a fixed CP-phase all neutrino oscillation data and the observed baryon asymmetry of the present universe can be simultaneously reproduced. We propose a very simple idea to introduce the DM candidate in our model. We introduce the Z2 parity into the model and impose one of three right-handed neutrinos to be odd, while the others even. In this way, the parity odd right-handed neutrino becomes stable and the DM candidate. We demonstrated that the dark matter relic abundance with an enhanced annihilation cross section by the Higgs bosons and the B-L gauge boson resonances is in accord with the current observations.