I'm trying to understand the SSB and explicit symmetry breaking.
If we have a complex scalar field theory with Mexican hat potential,
$$\phi(x)=\frac{\sigma(x)}{\sqrt{2}}e^{i\Pi(x)/v}$$
choice of the vacuum will break the symmetry spontaneously (but our Lagrangian will still have a $U(1)$ symmetry) that's why we're gonna have massless Goldstone boson. However if the Lagrangian doesn't respect this symmetry (symmetry being explicitly broken) we're gonna have light mass bosons (pions etc.)
To sum it up;
For each generator of a global continuous symmetry that's broken spontaneously there exist a massless scalar field (Goldstone boson).
If the symmetry is broken spontaneously and explicitly, these bosons are massive (Pseudo-Goldstone boson).
Can someone give an example where the symmetry is broken spontaneously and explicitly?
