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)?

  • 1
    $\begingroup$ Su(2) is broken $\endgroup$ – jak Feb 3 '15 at 6:57

JakobH's comment as an answer:

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.

| cite | improve this answer | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.