Inclusion of all fermions

What remains is the inclusions of hadrons in the model. In analogy to the leptons, left-handed SU 2) doublets and right-handed SU 2) singlets are build from the quarks of each family, which are initially assumed to be massless. For the first family with the up quark u and the down quark d we have for instance  

The meaning of the prime for the down quark will be discussed shortly. Analogously to the leptons, the following Lagrange density Cg for the quarks is added to the full model Lagrange density  

Y is again the weak hypercharge Y = 2 q — tz), which is 1/3 for u and d, 4/3 for Uij and —2/3 for dij. This ensures that the correct electric charges for the coupling of the up quark (+(2/3)e) and the down quark (—(l/3)e) to the field is obtained. The Yukawa term CYuk.,g( ), which assigns masses to the quarks upon symmetry breaking, differs from that for the leptons, since both the up and the down quark carry masses  

that in the Yukawa term only the unprimed down quarks appear. Here (a ) is the charge conjugate of the Higgs field (x)  

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