arXiv 1409.86002014-09-30hep-ph

$μ$ - $τ$反射对称性和辐射修正

$μ$-$τ$ reflection symmetry and radiative corrections

Ye-Ling Zhou

备注：: 16 pages, 1 figure

摘要：

$μ$ - $τ$反射对称性与当前中微子振荡数据一致，并且在族对称性下易于实现.我们证明了这种对称性保持了$θ_{23}=45^\circ$，$δ=\pm90^\circ$，$ρ,σ=0,90^\circ$，并且可以嵌入到跷跷板机制中.在高能标度$Λ_\text{FS}$下保持的$μ$-$τ$反射对称性将被辐射修正打破，并导致在电弱标度下$θ_{23}$与$45^\circ$以及$δ$与$\pm90^\circ$的偏差。我们发展了一种分析方法来推导所有混合参数的修正。我们进行了数值分析，在MSSM $Λ_\text{FS}$的$δ=-90^\circ$，并观察到，$θ_{23}>45^\circ$在正常的质量排序，$θ_{23}<45^\circ$在颠倒的质量排序，和相当大的修正$δ$喜欢一个负号。这些偏差有明确的方向，可以在未来的中微子振荡实验中得到检验。

英文摘要：

The $μ$-$τ$ reflection symmetry is compatible with current neutrino oscillation data and easily realized under family symmetries. We prove that this symmetry preserves $θ_{23}=45^\circ$, $δ=\pm90^\circ$, $ρ,σ=0,90^\circ$, and can be embedded into the seesaw mechanism. The $μ$-$τ$ reflection symmetry preserved at a high energy scale $Λ_\text{FS}$ will be broken by radiative corrections and result in deviations of $θ_{23}$ from $45^\circ$ and $δ$ from $\pm90^\circ$ at the electroweak scale. We develop an analytical method to derive the corrections to all the mixing parameters. We perform a numerical analysis in the MSSM for $δ=-90^\circ$ at $Λ_\text{FS}$, and observe that $θ_{23}>45^\circ$ in the normal mass ordering, $θ_{23}<45^\circ$ in the inverted mass ordering, and the sizable correction to $δ$ prefers a negative sign. These deviations have definite directions and can be tested in the future neutrino oscillation experiments.

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