Yukowa potential and symmetry breaking

[sleventh]

Hello,

I am trying to shortly explain how the Yukowa potential breaks symmetry in weak interactions. I would like to use the mexican hat potential as a specific example. Unfortunately Wikipedia does not go very in depth or explain it very well. Link. Any help on understanding the collapse of states into one specific symmetry broken state happens would be much appreciated.

 

[bapowell]

The article explains that this particular potential has U(1) symmetry. This means that it is rotationally symmetric about an axis through the center of the hat.
When the Higgs field is at \phi=0 in the Mexican hat potential, this symmetry of the theory is manifest (all the matter and gauge fields and interactions exhibit the symmetry, as does the Higgs field.) However, once the field rolls off the top and reaches the true vacuum, it no longer possesses the symmetry and the symmetry is said to be broken (the Higgs field is no longer rotationally invariant -- it gets moved around the trough as you rotate). This movement along the trough corresponds to the Goldstone mode -- for each broken symmetry, you get a Goldstone mode. Movement in the radial direction, because the potential has nonzero 2nd derivatives there, results in massive excitations. This is the Higgs particle.

Also, your terminology is not correct -- the Higgs potential is not called the Yukawa potential.

 

[sleventh]

Thank you this helps and gives me material to work off of. Another question though: will the Yukawa potential exhibit a similar potential distribution as the higgs potential?

 

[bapowell]

The Yukawa potential does not have any fixed points under any symmetry that I know of. In particle physics, the Yukawa potential is not related to symmetry breaking: it describes certain types of interactions (like the Coulumb potential.)