# Gauge invariance of the standard model

It is known that the standard model is $SU(3)_c \times SU(2)_L \times U(1)_Y$ gauge invariant. But, my question is: This is possible, when we write the Lagrangian in terms of weak eigenstates or in other words, our particles are all massless. The only way to give them mass is to have Higgs mechanism which breaks the symmetry and now the standard model is only $SU(3)_C \times U(1)_{EM}$ symmetric. Then why do we say that standard model is still $SU(3)_c \times SU(2)_L \times U(1)_Y$ gauge invariant as in nature we do have massive particles.

• Perhaps the related 190224 dismisses the question. The Higgs mechanism merely hides (realizes in the Nambu-Goldstone mode) the symmetry. – Cosmas Zachos Jul 5 '17 at 15:39