How would you modify your answer to Problem D.6 to take account of mixing between the quark doublets (u, d) and (c, s)? In particular, obtain the equations analogous to (D.71a) and (D.71b) for left handed d and s quarks, instead of electrons. Hence confirm that the charged current couplings are consistent with (8.17) and that there are no terms corresponding to strangeness-changing neutral currents, in agreement with the discussion of Section 10.1.1.

Data From Problem D.6

Our treatment of the electroweak interactions of massless leptons may be extended to massless quarks by invoking lepton€“quark symmetry between the doublets (ν_e, e^ˆ’) and (u, d) where we neglect quark mixing.

+ a V ) v(r, t)e = dt (D.71a) - 3 (g sin Ow + g' cos Ow) ( a A) (r, t)e - (g cosw -g' sin Ow) (6 a Z)(r,t)e. a Z)(r, t)e. + a . V ) (r, t)v = 2gw (0 a . w*) v(r,t)e t +5 (g sin Ow g'cos Ow) (o a A) (r, t)v (D.71b) +5 (g cosw +g' sin Ow) (6 a Z)(r,t)v.