Editing Standard Model (section)

==== Quantum chromodynamics sector ====
{{Main|Quantum chromodynamics}}
The quantum chromodynamics (QCD) sector defines the interactions between quarks and gluons, which is a [[Yang–Mills theory|Yang–Mills gauge theory]] with SU(3) symmetry, generated by <math>T^a = \lambda^a/2</math>. Since leptons do not interact with gluons, they are not affected by this sector. The Dirac Lagrangian of the quarks coupled to the gluon fields is given by
<math display="block">\mathcal{L}_\text{QCD} = \overline{\psi} i\gamma^\mu D_{\mu} \psi - \frac{1}{4} G^a_{\mu\nu} G^{\mu\nu}_a,</math>
where <math>\psi</math> is a three component column vector of [[Dirac spinor]]s, each element of which refers to a quark field with a specific [[color charge]] (i.e. red, blue, and green) and summation over [[Flavour (particle physics)|flavor]] (i.e. up, down, strange, etc.) is implied. 

The gauge covariant derivative of QCD is defined by <math>D_{\mu} \equiv \partial_\mu - i g_\text{s}\frac{1}{2}\lambda^a G_\mu^a</math>, where
* {{math|''γ''{{isup|''μ''}}}} are the [[Dirac matrices]],
* {{math|''G''{{su|lh=0.9|b=''μ''|p=''a''}}}} is the 8-component (<math>a = 1, 2, \dots, 8</math>) SU(3) gauge field,
* {{math|''λ''{{su|lh=0.9|p=''a''}}}} are the 3 × 3 [[Gell-Mann matrices]], generators of the SU(3) color group,
* {{math|''G''{{su|lh=0.9|b=''μν''|p=''a''}}}} represents the [[gluon field strength tensor]], and
* {{math|''g''<sub>s</sub>}} is the strong coupling constant.

The QCD Lagrangian is invariant under local SU(3) gauge transformations; i.e., transformations of the form <math>\psi \rightarrow \psi' = U\psi</math>, where <math>U = e^{-i g_\text{s}\lambda^a \phi^{a}(x)}</math> is 3 × 3 unitary matrix with determinant 1, making it a member of the group SU(3), and <math>\phi^{a}(x)</math> is an arbitrary function of spacetime.