arXiv 0912.49762009-12-25hep-ph

关于Neutrino Masses

Playing with Neutrino Masses

Sheldon L. Glashow

备注：: 6 pages

摘要：

关于中微子质量和混合的大部分知识都来自于对振荡现象的研究。我们重点研究那些不适合于此类研究的中微子性质：$Σ$，中微子质量绝对值之和; $m_β$，电子中微子的有效质量;以及$m_{ββ} $，控制无中微子双β衰变的参数。这些都是正在进行的实验或观察研究的主题。在这里我们推导出由六个涉及三个复质量参数$m_i$的{ \it ad hoc\}假设中的任何一个对这些可观测量的约束：（1）它们的乘积或（2）和为零;（3）它们的绝对值，像带电轻子或带电夸克的绝对值一样，不形成三角形;（4）中微子质量矩阵的$e$ - $e$项为零;（5）$μ$ - $μ$和$τ$ - $τ$项都消失;（6）所有三个对角线项的大小相等。本说明的标题反映出，这些简单的断言缺乏任何理论基础。

英文摘要：

Most of what is known about neutrino masses and mixings results from studies of oscillation phenomena. We focus on those neutrino properties that are not amenable to such studies: $Σ$, the sum of the absolute values of the neutrino masses; $m_β$, the effective mass of the electron neutrino; and $m_{ββ} $, the parameter governing neutrinoless double beta decay. Each of these is the subject of ongoing experimental or observational studies. Here we deduce constraints on these observables resulting from any one of six {\it ad hoc\} hypotheses that involve the three complex mass parameters $m_i$: (1) Their product or (2) sum vanishes; (3) Their absolute values, like those of charged leptons or quarks of either charge, do not form a triangle; (4) The $e$-$e$ entry of the neutrino mass matrix vanishes; (5) Both the $μ$-$μ$ and $τ$-$τ$ entries vanish; (6) All three diagonal entries are equal in magnitude. The title of this note reflects the lack of any theoretical basis for any of these simple assertions.

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