Text says that, the essence of the seesaw mechanism demands the lepton number violation at a high energy scale. As a result left handed neutrinos get tiny masses through the formula m_{\nu} = v_{w}^2 / \Lambda, where, v_{w} is the elctroweak cutoff scale and \Lambda is associated to the lepton number violation scale. While working in type I seesaw for \Lambda = 10^14 GeV, we get the neutrino masses in sub-eV scale. The Inverse seesaw scheme offers the Right handed neutrino mass scale at a much lower level (around TeV) to get the light neutrino mass in sub-eV scale . In that picture what will be the high energy scale where the Lepton number symmetry will be explicitly violated (if any)?
In this type of models there is an additional singlet fermion. The mass matrix is written in a basis ν, NR, S. It is a 3x3 matrix having three mass eigenvalues.
0 md 0
md 0 ms
0 ms μ
Heavy right handed neutrino mixes with the singlet which has a diagonal mass term (μ) that violates lepton number by two units. For a parameter range md = 10 GeV, ms= 1 TeV and μ =1 keV one gets light neutrinos in the correct mass range, as calculated (for example) by Aoki et al http://arxiv.org/abs/1506.06946
An easy way to understand the result is as following. Consider a see-saw in lower 2x2 block. Then effective value of 22 element is ms2/μ. After this consider the upper 2x2 matrix where 22 element is replaced by meff = m2s/μ. Consequently the light neutrino mass eigenvalue now becomes, md2/meff = md2 μ / m2s= 102 10-6 / 106 = 10-10 GeV =0.1 eV
In three generation case md is a 3x3 matrix ms is a 3x1 column vector and μ is a number. In total the mass matrix is 7x7. This will have seven mass eigenvalues which you can count. Three light, three heavy and one for the extra singlet fermion.
Singlet fermion S couples to right handed neutrino NR. They have opposite lepton numbers. Then the (cross) mass term mS is lepton number conserving. Whereas μ term violates lepton number. You have some freedom of choice while choosing the lepton number violating energy scale. As long as the combination md2 μ / ms2 is kept in the right range of order O(0.1) eV. For example you can also have an alternative choice which is different from that of Aoki et. al. Take μ= 1 GeV, then ms= 106 GeV will give you the right answer.
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