Editing Standard Model (section)

==== Yukawa sector ====
The [[Yukawa interaction]] terms are:
<math display="block">\mathcal{L}_\text{Yukawa} = (Y_\text{u})_{mn}(\bar{Q}_\text{L})_m \tilde{\varphi}(u_\text{R})_n + (Y_\text{d})_{mn}(\bar{Q}_\text{L})_m \varphi(d_\text{R})_n + (Y_\text{e})_{mn}(\bar{\ell}_\text{L})_m {\varphi}(e_\text{R})_n + \mathrm{h.c.} </math>
where <math>Y_\text{u}</math>, <math>Y_\text{d}</math>, and <math>Y_\text{e}</math> are {{math|3 × 3}} matrices of Yukawa couplings, with the {{mvar|mn}} term giving the coupling of the generations {{mvar|m}} and {{mvar|n}}, and h.c. means Hermitian conjugate of preceding terms. The fields <math>Q_\text{L}</math> and <math>\ell_\text{L}</math> are left-handed quark and lepton doublets. Likewise, <math>u_\text{R}, d_\text{R}</math> and <math>e_\text{R}</math> are right-handed up-type quark, down-type quark, and lepton singlets. Finally <math>\varphi</math> is the Higgs doublet and <math>\tilde{\varphi} = i\tau_2\varphi^{*}</math> is its charge conjugate state.

The Yukawa terms are invariant under the SU(2){{sub|L}} × U(1){{sub|Y}} gauge symmetry of the Standard Model and generate masses for all fermions after spontaneous symmetry breaking.