论文标题
mellin转换方法以重新出现不变性
A Mellin Transform Approach to Rephasing Invariants
论文作者
论文摘要
在中微子的低能量有效理论中，单位矩阵的HAAR度量很可能会引起观察到的PMN矩阵。假设采用HAAR度量，我们确定所有二次，四分之一的主要和四分之一的狄拉克的概率密度函数，用于任意数量的中微子世代的不变性。我们表明，对于固定数量的中微子，同一类型的所有不变性都具有相同的概率密度函数，在HAAR度量下。然后，我们计算重新不变的矩，以在梅林变换的帮助下确定三个概率密度函数。我们最终研究了结果在中微子数量功能方面的物理意义。
In the low-energy effective theory of neutrinos, the Haar measure for unitary matrices is very likely to give rise to the observed PMNS matrix. Assuming the Haar measure, we determine the probability density functions for all quadratic, quartic Majorana, and quartic Dirac rephasing invariants for an arbitrary number of neutrino generations. We show that for a fixed number of neutrinos, all rephasing invariants of the same type have the same probability density function under the Haar measure. We then compute the moments of the rephasing invariants to determine, with the help of the Mellin transform, the three probability density functions. We finally investigate the physical implications of our results in function of the number of neutrinos.
