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RE: Towards a future 100-km-long particle collider at CERN
Let me try without showing any equation :)
We start with the Lagrangian describing the dynamics of the particle physics model. This Lagrangian is an equation containing everything (which particles we have, how they interact, what are their masses, etc.). The Lagrangian must include in particular a mass term for each of the massive particles. However, writing such a mass term would directly violate the symmetry principle you imposed to start with. So mass terms (and thus particle masses) are forbidden. I hope it helps (a little at least) :)
Okay, Lagrangian... I have to study some basics first )
Is it only interaction particles (bosons) which are predicted to be massless or matter particles (fermions) as well?
Both in this case. Only a specific class of fermions can be massive, called vector-like fermions (whose two chiralities behave the same), that can be massive. However, there is no such a vector-like fermion in the Standard Model.