Lately, I have some read some papers about the hidden sector of particle physics which combines with the Standard Model through the so-called Higgs portal. Let the Lagrangian for this be composed of two simple scalar fields like this:

$L=\partial_\mu \phi_{SM} \partial_\nu \phi_{SM} +\partial_\mu \phi_H \partial_\nu \phi_H -V(\phi_{SM},\phi_H)$

where $\phi_{SM}$ relates to the Standard Model and $\phi_H$ relates to the hidden sector.

Assuming that the potential is:

$V(\phi_{SM},\phi_H)=-1/2 \mu^2 {\phi_H} ^2 + 1/4 \lambda {\phi_H}^4 - 1/2 \mu^2 {\phi_{SM}} ^2 + 1/4 \lambda {\phi_{SM}}^4+ 1/4 \lambda_{mix} \phi_H^2 \phi_{SM}^2$

And since both of the fields gain a nonzero VEV like this:

$\phi_H$=$v_H+h(x)/2^{1/2}$

$\phi_{SM}$=$v_{SM}+h(x)/2^{1/2}$

How would the spontaneous symmetry breaking mechanism then work? I am interested in how exactly the Higgs mechanism would work mathematically when two different mimimas "v" are involved.

This post imported from StackExchange Physics at 2014-06-25 21:00 (UCT), posted by SE-user user33941