arXiv 0903.21612009-03-12hep-ph

$μ$ - $τ$对称SO中的费米子质量和混合（10）

Fermion Masses and Mixings in a $μ$-$τ$ symmetric SO(10)

Anjan S. Joshipura, Bhavik P. Kodrani, Ketan M. Patel

备注：: 22 pages, six postscript figures
发表信息：: Phys.Rev.D79:115017,2009
DOI：: 10.1103/PhysRevD.79.115017

摘要：

$μ$ - $τ$对称性强加在味基中的中微子质量矩阵上，已知是相当有预测性的。我们将这个非常特殊的中微子对称性整合到一个更一般的框架，基于超对称SO（10）大统一理论。和其他几个模型一样，费米子的质量谱是由厄米质量矩阵决定的，厄米质量矩阵是由费米子的16重态与希格斯场的可重整化汤川耦合转化为SO（10）群的$10, \bar{126},120$表示而得到的。$μ$ - $τ$对称性通过120重态自发破缺。这个计划的后果被认为是费米子质量使用I型和II型跷跷板机制。如果汤川耦合在$μ$ - $τ$对称性下是不变的，则这种情况会导致质量矩阵的广义CP不变性和CP破坏相消失。小的明确破缺的$μ$ - $τ$对称性，然后显示提供了一个很好的理解所有的费米子质量和混合。费米子谱的详细拟合在几种情况下。人们得到了一个非常好的适合所有的可观测的上下文中的第一型跷跷板机制，但第二型跷跷板模型也提供了一个很好的描述，除了中微子质量的整体规模。在I型跷跷板情形下，轻子混合参数的三个主要预言是：（1）大气混合角$θ_{23}^{l}$接近最大值，（2）$θ_{13}^{l}$接近目前的上界，（3）中微子振荡中的狄拉克CP破坏相位为负但很小.

英文摘要：

$μ$-$τ$ symmetry imposed on the neutrino mass matrix in the flavour basis is known to be quite predictive. We integrate this very specific neutrino symmetry into a more general framework based on the supersymmetric SO(10) grand unified theory. As in several other models, the fermion mass spectrum is determined by Hermitian mass matrices resulting from the renormalizable Yukawa couplings of the 16-plet of fermions with the Higgs fields transforming as $10, \bar{126},120$ representations of the SO(10) group. The $μ$-$τ$ symmetry is spontaneously broken through the 120-plet. Consequences of this scheme are considered for fermion masses using both type-I and type-II seesaw mechanism. This scenario is shown to lead to a generalized CP invariance of the mass matrices and vanishing CP violating phases if the Yukawa couplings are invariant under the $μ$-$τ$ symmetry. Small explicit breaking of the $μ$-$τ$ symmetry is then shown to provide a very good understanding of all the fermion masses and mixing. Detailed fits to the fermion spectrum are presented in several scenarios. One obtains a very good fit to all observables in the context of the type-I seesaw mechanism but type-II seesaw model also provides a good description except for the overall scale of the neutrino masses. Three major predictions on the leptonic mixing parameters in the type-I seesaw case are (1) the atmospheric mixing angle $θ_{23}^{l}$ close to maximal, (2) $θ_{13}^{l}$ close to the present upper bound and (3) negative but very small Dirac CP violating phase in the neutrino oscillations.

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