Wing Sheung Chan

The Standard Model and lepton flavour violation 21 The actual masses of the neutrinos are then result of the diagonalisation of M ν . Disregarding the multiple flavours and treating the entries of the mass matrix as plain numbers, one can immediately show that the eigenvalues of the matrix are m ± = M R ± p M 2 R + 4 m 2 D 2 . (1.29) In the regime of M R m D , m + ≈ M R and m − ≈ − m 2 D M R . (1.30) This can be interpreted as the right-handed neutrino retaining its heavy Majorana mass, while the left-handed neutrino acquires a very small mass that is inversely proportional to the right-handed neutrino mass. The same argument still holds when multiple flavours are considered if the condition q Tr( | m D M − 1 R | 2 ) 1 is met. By this, the model naturally explains the smallness of the left-handed neutrino masses without fine-tuning the neutrino- Higgs Yukawa coupling. This is known as the (type-I) seesaw mechanism. The name “seesaw” refers to the feature that the larger the right-handed neutrino masses are, the smaller the left-handed neutrino masses will be. There are also some more sophisticated and complete models that make use of similar mechanisms (type-II and type-III seesaw mechanisms), but the basic working principle is the same. Models with heavy Majorana neutrinos are certainly attractive since they could “com- plete” the SM with the “missing” right-handed neutrinos and explain the smallness of the SM neutrino masses at the same time. But there is another reason for them to be favoured. That is the possibility for these models to fit with leptogenesis models in cosmology. Leptogenesis models are models constructed to explain the matter-antimatter asymmetry problem (see Section 1.2.6) . As mentioned earlier, CP violation in the SM is not enough to explain the observed abundance of matter in the universe. An attempt to resolve this problem is to introduce conjectured physical processes that generate leptons and antileptons asymmetrically in the early universe. These processes are collectively referred to as leptogenesis. Since heavy neutrinos with Majorana mass origins clearly violate CP at a high energy scale, their interactions could also contribute to leptogenesis. Although the interactions of heavy neutrinos are new physics at high energy scale, their existence could still induce observable effects at low energy scale. These effects include the possible enhancement of LFV processes. There have been theoretical studies that calculated the expected branching fraction of LFV Z decays assuming the existence of Majorana neutrinos [39, 40] . These studies built their models in a way that incorporates or averts existing experimental constraints, such as the stringent µ – e transition constraint from µ → eγ experiments. The calculations show that, with heavy neutrinos at the TeV scale, the branching fractions B ( Z → eτ ) and B ( Z → µτ ) could be as large as 10 − 8 – 10 − 7 .