High-energy hadron-hadron collisions are described using the Quantum Chromodynamics (QCD). The presence of a high energy scale and the property of asymptotic freedom of QCD allow the use perturbative methods in order to compute partonic cross sections. Since the partons are highly energetic, they have a high probability to radiate additional soft gluons. The study of the soft gluon radiation spectrum in QCD involves some non-trivial color algebra depending of the number of parents in the process. The soft anomalous dimension matrix is a matrix in color space encoding possible transitions between color states due to radiations.
For the gg -> gg processes, it has been remarked that some eigenvalues of this matrix have an unexpected symmetry relating external and internal degrees of freedom. In order to explore if this symmetry if fortuitous or not, effective methods to perform the color algebra are needed. The pictorial representation (i.e. birdtracks) of color algebra is such a tool. I will discuss how one can easily obtain the soft anomalous dimension matrix for 2 -> 2 processes involving QCD partons, and a generalization for a broader range of representations.
