where i = {r, g, b} represents color, are the Dirac matrices, is the 8-component () SU(3) gauge field, are the 3 × 3 Gell-Mann matrices, generators of the SU(3) color group, represents the gluon field strength tensor, is the strong coupling constant. Electroweak sector The electroweak sector is a Yang–Mills gauge theory with the symmetry group U(1) × SU(2)L, where is the U(1) gauge field, is the weak hypercharge – the generator of the U(1) group, is the 3-component SU(2) gauge field, are the Pauli matrices – infinitesimal generators of the SU(2) group – with subscript L to indicate that they only act on left-chiral fermions, and are the U(1) and SU(2) coupling constants respectively, () and are the field strength tensors for the weak isospin and weak hypercharge fields. Notice that the addition of fermion mass terms into the electroweak Lagrangian is forbidden, since terms of the form do not respect U(1) × SU(2)L gauge invariance. Neither is it possible to add explicit mass terms for the U(1) and SU(2) gauge fields. The Higgs mechanism is responsible for the generation of the gauge boson masses, and the fermion masses result from Yukawa-type interactions with the Higgs field. Higgs sector In the Standard Model, the Higgs field is a complex scalar of the group SU(2)L: where the superscripts + and 0 indicate the electric charge () of the components. The weak hypercharge () of both components is 1. Before symmetry breaking, the Higgs Lagrangian is which up to a divergence term, (i.e., after partial integration) can also be written as The Higgs self-coupling strength is approximately . This is not included in the table above because it can be derived from the mass (after symmetry breaking) and the vacuum expectation value. Yukawa sector The Yukawa interaction terms are where are matrices of Yukawa couplings, with the term giving the coupling of the generations and , and h.c. means Hermitian conjugate of preceding terms. Fundamental interactions The Standard Model describes three of the four fundamental interactions in nature; only gravity remains unexplained. In the Standard Model, such an interaction is described as an exchange of bosons between the objects affected, such as a photon for the electromagnetic force and a gluon for the strong interaction. Those particles are called force carriers or messenger particles. Gravity Despite being perhaps the most familiar fundamental interaction, gravity is not described by the Standard