Calculations of the infrared behavior of quantum chromodynamics: The color-singlet quark form factor in the near-mass-shell regime

Abstract

We explicitly calculate at the two-loop approximation the near-mass-shell infrared behavior of the color-singlet quark form factor in quantum chromodynamics (QCD). The sum of all contributions can be reexpressed by the simple form $F_1^{\mathrm{}\left(0\right)\mathrm{}}=\exp \left[B_1\mathrm{}\right(g\left(k\right);G=-1\left)\right]$, where $B_1\mathrm{}\left(g\right(k);G = -1)$ is the one-loop contribution, in the Landau gauge, evaluated by substituting the expansion coupling $g_{\lambda }$ by the infrared invariant charge $k^2\left(\frac{\partial }{\partial k^2}\right)g\left(k^2\right)=\beta \left(g\right(k^2\left)\right)$;$g(k^2 = {\lambda }^2) = g_{\lambda }$. Various techniques to study the infrared structure of QCD diagrams are outlined.