标题： 与Weinberg算符相关的物种尺度和Majorana中微子质量的界限 显示英文标题

标题： Species scale associated with Weinberg operator and bound on Majorana neutrino mass

摘要： 当类似卡鲁扎-克莱因或弦理论塔中的状态通过相同类型的无关算符与另一个状态耦合时，它们对相关或边缘算符的圈修正贡献不可忽略，这威胁到了微扰性。 只要截止尺度低于与无关算符相关的物种尺度，就可以避免这种情况。 我们将此应用于与中微子相关的状态塔，这些状态通过魏因伯格算符（生成 Majorana 中微子质量的维度-5无关算符）与希格斯场耦合。 要求“Majorana 物种尺度”——与魏因伯格算符相关的物种尺度——低于引力物种尺度，则可以由物种数量确定 Majorana 中微子质量的下限。 Festina-Lente 约束也给出了 Majorana 中微子质量的下限，但并不那么严格。 同时，即使在可重整化层次上中微子质量为 Dirac 类型，只要魏因伯格算符未被禁止，仍然可以在有效场论作用量中写出 Majorana 质量项。 即使 Majorana 中微子质量大于 Dirac 质量，只要存在足够多的质量小于宇宙学常数尺度的自由度，中微子的 Majorana 性质的观测可能不会与排除完全由 Majorana 类型给出中微子质量的量子引力约束相矛盾。 显示英文摘要

摘要： When states in a tower like the Kaluza-Klein or the string tower couple to another state through the irrelevant operators of the same type, their contributions to the loop corrections of the relevant or the marginal operators are not negligible, threatening the perturbativity. This can be avoided provided the cutoff scale is lower than the species scale associated with the irrelevant operator. We apply this to towers of states associated with the neutrino which couple to the Higgs through the Weinberg operator, the dimension-5 irrelevant operator generating the Majorana neutrino mass. Requiring the `Majorana species scale', the species scale associated with the Weinberg operator, to be below the gravitational species scale, one finds the lower bound on the Majorana neutrino mass determined by the species number. The Festina-Lente bound also gives the lower bound on the Majorana neutrino mass, but it is not so stringent. Meanwhile, even if the neutrino mass is of the Dirac type at the renormalizable level, the Majorana mass term still can be written in the effective field theory action so far as the Weinberg operator is not forbidden. Even if the Majorana neutrino mass is larger than the Dirac one, so far as there are sufficient degrees of freedom with mass smaller than the scale of the cosmological constant, the observation of the Majorana nature of the neutrino may not contradict to quantum gravity constraints which rules out the neutrino mass purely given by the Majorana type.