So let me elaborate, my problem is that I don't fully understand why the weak interaction is a chiral theory - I would like an answer with the Lagrange density and the Higgs field. I also want to know why symmetry is broken towards left-handed chirality and not right-handed (why left?).
I read that all theories are at their basic level chiral. But as I understand it, at low energies e.g for gluons, the Higgs field combines the two chiralities into a massive Dirac- particle which then does not break symmetry and turns QCD into a vector-theory. The weak interaction then breaks symmetry because its bosons have too high an energy for that and the mass term in the Lagrangian still breaks the symmetry?
I know this sounds very confusing or even wrong, but I did not really understand that and hope someone could elaborate. Why does the weak interaction break symmetry and how can you see that in its Lagrange-density compared to other interactions (e.g. the strong one)?