Two-loop renormalization of Wilson loop for Drell-Yan production

Abstract

We study the renormalization of the Wilson loop with a path corresponding to the Drell-Yan lepton pair production in two-loop approximation of perturbation theory. We establish the renormalization group equation in next-to-leading order and find a process specific anomalous dimension Gamma_DY in the corresponding approximation.

Figures (1)

• Figure 1: Integration path in the Wilson loop in Eq. (\ref{['WilsonLoop']}) is shown in $(a)$. Non-zero one-loop graph $(b)$. Different topologies of nonvanishing Feynman diagrams contributing to the Wilson loop $W_{\rm DY}$ at order ${\cal O} (\alpha_s^2)$ with maximal non-abelian factor in $(c)-(h)$. To complete the set one has to add mirror symmetrical graphs which can be taken into account by appropriate multiplicity factors, $m_\sigma$, for graphs displayed here: $m_b = m_c = m_d = m_f = 2$, $m_e = 1$, $m_g = m_h = 4$. Full blob stands for the sum of the vacuum polarization bubbles due to fermions, gluons and ghosts.