跷跷板模型中三阶中微子混合矩阵的幺正性破坏(英文)

Why is the 3×3 Neutrino Mixing Matrix Almost Unitary in Realistic Seesaw Models?

对标准模型的一种简单扩充就是引入n个重的右手中微子且保持其SU(2)_L×U(1)_Y规范对称性．通过对角化(3+n)×(3+n)阶中微子质量矩阵,得到关于v_e,v_μ和v_τ的有效质量矩阵的精确的解析表达式．结果表明,在轻子带电弱流中出现的3×3中微子混合矩阵V必须不是严格幺正的．如果通过跷跷板机制产生正确的轻的中微子的质量标度,那么V的幺正性破坏的程度非常小,几乎可以忽略．类似的结论同样可以在第二类跷跷板模型中得到．

A simple extension of the standard model is to introduce n heavy right-handed Majorana neutrinos and preserve its SU（2）L × U（1）Y gauge symmetry. Diagonalizing the （3 ＋ n） × （3 ＋ n） neutrino mass matrix, we obtain an exact analytical expression for the effective mass matrix of ve, vμ and vτ. It turns out that the 3 × 3 neutrino mixing matrix V, which appears in the leptonic charged-current weak interactions, must not be exactly unitary. The unitarity violation of V is negligibly tiny, however, if the canonical seesaw mechanism works to reproduce the correct mass scale of light Majorana neutrinos. A similar conclusion can be drawn in the realistic Type-Ⅱ seesaw models.