Next, two variants are possible depending on whether we want the neutrino to be Majorana or Dirac particles. In the case of the Dirac neutrino we should identify NlR with the right-handed component of the ordinary neutrino, that is, NlR = νlR. After the SSB we

Particle and

may already disregard those Higgs degrees of freedom that have been spent on giving the masses to gauge bosons and use the following expressions for the Higgs doublets

ϕ(x) = 1√ 2

( 0

H(x) + v

) , ϕc(x) =

1√ 2

( H(x) + v

) . (14.2)

To substitute (14.2) into LY brings into existence the mass term in the free neutrino Lagrangian L0(x), which have the form now

L0(x) = i 2

∑ l

[νlL(x)γ λ∂λνlL(x) + νlR(x)γ

λ∂λνlR(x)] − 1 2


+νl′L(x)Ml′lνlR(x)], (14.3)

where the neutrino mass matrix M in the flavor basis is defined by the expression:

M = 1√ 2

  h′eev h′eµv h′eτvh′µev h′µµv h′µτv h′τev h

′ τµv h

  . (14.4)

In what follows we shall assume h′ll′ to be equal to h ′ l′l to provide M = M

T . As we can see, the mass matrix in the flavor basis is not diagonal. The responsibility for this rests with those Yukawa constants that lead to the lepton flavor (LF) violation at the tree level because of the interaction

Lηint(x) = − 1√ 2

hll′νlL(x)Nl′R(x)H(x) + h.c.. (14.5)

The matrix M could be diagonalized using the unitary transformation

UMU−1 = diag(m1,m2,m3).