# Relation between gauge symmetry and mass difference

Usually (like in Georgi's Lie Algebra book) people argue the reason why Gellmann $SU(3)$ flavor symmetry (u,d,s) can't extend to $SU(4)$ (u,d,c,s) or higher flavour symmetry is the their mass difference is too large. But why we still have $SU(2)_L$ weak isospin symmetry even though the mass difference between up-type and down type can be very large (like charm,strange quark doublet; or neutrino electron doublet)?

• Su(2) is broken – JakobH Feb 3 '15 at 6:57

The electroweak gauge group $\mathrm{SU}(2)_L \times \mathrm{U}(1)_Y$ is broken into the electromagnetic $\mathrm{U}(1)_\text{em}$ by the Higgs field acquiring a non-zero vacuum expectation value, granting masses to the quark and $W^\pm,Z$ bosons. Thus, at the scale where up- and down-type quarks have very different masses, we do not have weak isospin symmetry.