Vacuum expectation value Higgs field

The second Higgs field acts in such a way that if the vacuum expectation value is zero, ( ) = 0, then the symmetry breaking mechanism effectively collapses to the Higgs mechanism of the standard SU(2) x U(l) electroweak theory. The result is a vector electromagnetic gauge theory 0(3)/> and a broken chiral SU(2) weak interaction theory. The mass of the vector boson sector is in the A(3) boson plus the W and Z° particles. 

Recall that, in the SM, a natural scale is set by the vacuum expectation value of the Higgs field v, related to the parameters of the Higgs potential, and it has a rather precise value (4.2.38)... 

The gauge potentials and are 2x2 Hermitian traceless matrices, and the Higgs fields and % are also 2x2 matrices. These expectations are real-valued, and the nonzero contributions of the Higgs field on the physical vacuum are given by the diagonal matrix entries [95] ... 

If the coupling constant Y is comparable to the coupling constant g, then the Fermi expectation energies of the Fermions occur at the mean value for the Higgs field (4>0)- In this case the vacuum expectation of the vacuum is proportional to the identity matrix. This means that the masses acquired by the right chiral plus left chiral gauge bosons A + /iM are zero, while the left chiral minus right chiral... 

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