Leptonic Dirac CP violation predictions from residual discrete symmetries

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• 作者：I. Girardi^a ; S.T. Petcov^a ; ^b ; ¹ ; Alexander J. Stuart^a ; A.V. Titov^a ; ^{atitov@sissa.it" class="auth_mail" title="E-mail the corresponding author}
• 刊名：Nuclear Physics B
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：902
• 期：Complete
• 页码：1-57
• 全文大小：1006 K

文摘

Assuming that the observed pattern of 3-neutrino mixing is related to the existence of a (lepton) flavour symmetry, corresponding to a non-Abelian discrete symmetry group G_f$G_f$, and that G_f$G_f$ is broken to specific residual symmetries ecbca44749fb4c" title="Click to view the MathML source">G_e$G_e$ and G_ν$G_{\nu }$ of the charged lepton and neutrino mass terms, we derive sum rules for the cosine of the Dirac phase δ of the neutrino mixing matrix U  . The residual symmetries considered are: i) G_e=Z₂$G_e=Z_2$ and G_ν=Z_n$G_{\nu }=Z_n$, n>2$n>2$ or Z_n×Z_m$Z_n\times Z_m$, n,m≥2$n,m\ge 2$; ii) G_e=Z_n$G_e=Z_n$, n>2$n>2$ or Z_n×Z_m$Z_n\times Z_m$, n,m≥2$n,m\ge 2$ and G_ν=Z₂$G_{\nu }=Z_2$; iii) G_e=Z₂$G_e=Z_2$ and G_ν=Z₂$G_{\nu }=Z_2$; iv) ecbca44749fb4c" title="Click to view the MathML source">G_e$G_e$ is fully broken and G_ν=Z_n$G_{\nu }=Z_n$, n>2$n>2$ or Z_n×Z_m$Z_n\times Z_m$, n,m≥2$n,m\ge 2$; and v) G_e=Z_n$G_e=Z_n$, n>2$n>2$ or Z_n×Z_m$Z_n\times Z_m$, n,m≥2$n,m\ge 2$ and G_ν$G_{\nu }$ is fully broken. For given ecbca44749fb4c" title="Click to view the MathML source">G_e$G_e$ and G_ν$G_{\nu }$, the sum rules for cos⁡δ$\cos \delta$ thus derived are exact, within the approach employed, and are valid, in particular, for any G_f$G_f$ containing ecbca44749fb4c" title="Click to view the MathML source">G_e$G_e$ and G_ν$G_{\nu }$ as subgroups. We identify the cases when the value of cos⁡δ$\cos \delta$ cannot be determined, or cannot be uniquely determined, without making additional assumptions on unconstrained parameters. In a large class of cases considered the value of cos⁡δ$\cos \delta$ can be unambiguously predicted once the flavour symmetry G_f$G_f$ is fixed. We present predictions for cos⁡δ$\cos \delta$ in these cases for the flavour symmetry groups G_f=S₄$G_f=S_4$, A₄$A_4$, T^′$T^{\prime }$ and A₅$A_5$, requiring that the measured values of the 3-neutrino mixing parameters sin²⁡θ₁₂${\sin }^2{\theta }_{12}$, sin²⁡θ₁₃${\sin }^2{\theta }_{13}$ and sin²⁡θ₂₃${\sin }^2{\theta }_{23}$, taking into account their respective 3σ uncertainties, are successfully reproduced.