Systematic study of the d = 5 Weinberg operator at one-loop order
Systematic study of the d = 5 Weinberg operator at one-loop order
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DOI：
10.1007/jhep07(2012)153
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发表时间：
2012-07
影响因子：
5.4
通讯作者：
F. Bonnet;M. Hirsch;T. Ota;W. Winter
中科院分区：
文献类型：
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作者：
F. Bonnet;M. Hirsch;T. Ota;W. Winter
我们在单圈水平上对d= 5的温伯格算子进行了系统的研究。我们确定了三种不同类型的中微子质量产生：（1）有限不可约图;（2）通常的跷跷板机制在单圈的有限扩展和（3）跷跷板的发散圈实现。所有辐射单圈中微子质量模型都必须属于这一类。情况（1）自然地给出了中微子质量的主要贡献，这类的一个经典例子是Zee模型。我们证明，为了防止树级贡献占主导地位的情况下（2），马约拉纳费米子运行在循环和额外的对称性是需要一个真正的领先的单圈贡献。在II型环扩展中，汤川耦合将在一个环处产生，而I/III型扩展可以被解释为环诱导的逆或线性跷跷板机制。对于类别（3）中的发散图，树级贡献是不可避免的，实际上需要作为反项来吸收发散。
We perform a systematic study of the d= 5 Weinberg operator at the one-loop level. We identify three different categories of neutrino mass generation:(1) finite irreducible diagrams;(2) finite extensions of the usual seesaw mechanisms at one-loop and (3) divergent loop realizations of the seesaws. All radiative one-loop neutrino mass models must fall into one of these classes. Case (1) gives the leading contribution to neutrino mass naturally and a classic example of this class is the Zee model. We demonstrate that in order to prevent that a tree level contribution dominates in case (2), Majorana fermions running in the loop and an additionalsymmetry are needed for a genuinely leading one-loop contribution. In the type-II loop extensions, the Yukawa coupling will be generated at one loop, whereas the type-I/III extensions can be interpreted as loop-induced inverse or linear seesaw mechanisms. For the divergent diagrams in category (3), the tree level contribution cannot be avoided and is in fact needed as counter term to absorb the divergence.