Genjituteki na SO(10) GUT no kousei to soreniyoru quak-lepton no gensyouron no kaiseki (The Construction of realistic SO(10) GUT and its application to quark-lepton phenomenology)

本文特别关注可重整最小SO（10）模型，其中两个希格斯多重态${{bf10} + {bf overline{126}}}$用于与物质${bf16}_i ~ (i=mbox{generation})$的汤川耦合。该模型的一个显著特点是对中微子振荡参数具有较高的预测能力，并能再现带电费米子的质量和混合角。我们指出汤川扇区的cp相对再现中微子振荡数据起着重要的作用。Fukuyama-Okada在MSSM背景下结合重整化群（renormization group， RG）效应的详细分析明确表明，该模型与当时的中微子振荡数据是一致的。之后，这个最小SO（10）被许多与精确测量相对应的作者修改，使用ii型跷跷板机制和/或考虑除了${bf overline{126}}$希格斯之外的${bf 120}$希格斯耦合到物质。人们一直期望在最小SO（10）模型中建立一个具体的希格斯扇区。我们明确地构造了一个最简单的、可重整的希格斯超极，并展示了SO（10）规范对称破缺到标准模型的模式。这个结构给出了中间能量尺度的细节。这样我们的理论就进入了精密计算阶段，这也给规范耦合统一带来了麻烦。为了解决这一问题，我们提出了以自然的方式提供GUT尺度作为有效场理论的截止尺度的场景。出于我们的目的，我们将最小的SO（10）模型嵌入到一个扭曲的额外维度中。我们可以提出一个简单的设置，自然地在中等尺度上产生右手中微子质量，即使是在大尺度上的希格斯场vev。因此，规范耦合统一仍然存在于MSSM中。因此，SO(10) GUT进入了一个新的阶段，并有望进一步增长。

The renormalizable minimal SO(10) model has been paid a particular attention, where two Higgs multiplets ${{bf 10} oplus {bf overline{126}}}$ are utilized for the Yukawa couplings with matters ${bf16}_i〜(i=mbox{generation})$. A remarkable feature of the model is its high predictive power of the neutrino oscillation parameters as well as reproducing charged fermion masses and mixing angles. We pointed out that CP-phases in the Yukawa sector play an important role to reproduce the neutrino oscillation data. The detailed analysis incorporating the renormalization group (RG) effects in the context of MSSM has explicitly shown by Fukuyama-Okada that the model is consistent with the neutrino oscillation data at that time. Afterward this minimal SO(10) was modified by many authors corresponding the precision measurements, using the type-II see-saw mechanism and/or considering a ${bf 120}$ Higgs coupling to the matter in addition to the ${bf overline{126}}$ Higgs. It has been long expected to construct a concrete Higgs sector of the minimal SO(10) model. A simplest and renormalizable Higgs superpolential was constructed explicitly and the patterns of the SO(10) gauge symmetry breaking to the standard model one was shown by us. This construction gives the detail of the intermediate energy scale. Thus our theory goes to the precision calculation phase, which also give rise to a trouble in the gauge coupling unification. In order to solve the problem, we proposed the scenario to provide the GUT scale as the cutoff scale of effective filed theory in a natural way. For our purpose, we embed the minimal SO(10) model into a warped extra dimension). We can propose a simple setup that naturally generates right-handed neutrino masses at intermediate scale even with Higgs field VEVs at the GUT scale. Thus, the gauge coupling unification remains in the MSSM. Thus SO(10) GUT enters into new phase and is expected to grow further.