关于Schechter-Valle定理的定量影响
On the Quantitative Impact of the Schechter-Valle Theorem
摘要：
本文通过考虑无中微子双β衰变中最一般的由点状算符组成的Lorentz不变拉格朗日量，对Schechter-Valle（黑箱）定理作了定量的评价.众所周知，黑箱算符在四圈水平上诱导出Majorana中微子质量。这证明了这样一种说法，即对无中微子双β衰变的观测保证了中微子的马约拉纳性质。我们计算了这些辐射产生的质量，发现它们比观测到的中微子质量和分裂小很多个数量级。因此，某些轻子数违反了新物理学（在树水平上可能与中微子质量无关），可能会导致黑箱算符，而黑箱算符可以解释观测到的无中微子双β衰变速率。虽然这些算子保证了有限的马约拉纳中微子质量，但黑箱贡献的微小性意味着其他中微子质量项（狄拉克或马约拉纳）必须存在。如果中微子质量有一个显着的马约拉纳贡献，那么这将成为黑箱算子的主要部分。然而，中微子也可能主要是狄拉克粒子，而其他违反新物理学的轻子数主导着无中微子的双β衰变。如果把观测到的无中微子双β衰变的速率转换成中微子质量，那将是完全错误的。虽然Schechter-Valle定理的主要陈述仍然有效，但我们得出结论，黑盒图本身只产生辐射质量项，其数量级太小，无法解释中微子质量。因此，其他算符必须对中微子质量做出主要贡献，这可能是狄拉克或马约拉纳性质的。
英文摘要：
We evaluate the Schechter-Valle (Black Box) theorem quantitatively by considering the most general Lorentz invariant Lagrangian consisting of point-like operators for neutrinoless double beta decay. It is well known that the Black Box operators induce Majorana neutrino masses at four-loop level. This warrants the statement that an observation of neutrinoless double beta decay guarantees the Majorana nature of neutrinos. We calculate these radiatively generated masses and find that they are many orders of magnitude smaller than the observed neutrino masses and splittings. Thus, some lepton number violating New Physics (which may at tree-level not be related to neutrino masses) may induce Black Box operators which can explain an observed rate of neutrinoless double beta decay. Although these operators guarantee finite Majorana neutrino masses, the smallness of the Black Box contributions implies that other neutrino mass terms (Dirac or Majorana) must exist. If neutrino masses have a significant Majorana contribution then this will become the dominant part of the Black Box operator. However, neutrinos might also be predominantly Dirac particles, while other lepton number violating New Physics dominates neutrinoless double beta decay. Translating an observed rate of neutrinoless double beta decay into neutrino masses would then be completely misleading. Although the principal statement of the Schechter-Valle theorem remains valid, we conclude that the Black Box diagram itself generates radiatively only mass terms which are many orders of magnitude too small to explain neutrino masses. Therefore, other operators must give the leading contributions to neutrino masses, which could be of Dirac or Majorana nature.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
