Two-Loop Sudakov Form Factor in a Theory with Mass Gap

TL;DR

The result is analyzed in the context of hard and infrared evolution equations and a matching procedure is established which relates the theories with and without mass gap, setting the stage for the complete calculation of the dominant two-loop corrections to electroweak processes at high energy.

Abstract

The two-loop Sudakov form factor is computed in a U(1) model with a massive gauge boson and a $U(1)\times U(1)$ model with mass gap. We analyze the result in the context of hard and infrared evolution equations and establish a matching procedure which relates the theories with and without mass gap setting the stage for the complete calculation of the dominant two-loop corrections to electroweak processes at high energy.

Figures (2)

• Figure 1: The two-loop correction to the form factor ${\cal F}_\alpha(M,Q)$ in LL (including $\alpha^2{\cal L}^4$), NLL (including $\alpha^2{\cal L}^3$), N$^2$LL (including $\alpha^2{\cal L}^2$), N$^3$LL (including $\alpha^2{\cal L}^1$) approximations and the complete two-loop correction as functions of the momentum transfer for $M=80$ GeV, $\alpha/(4\pi)=3\cdot 10^{-3}$.
• Figure 2: The same as Fig. \ref{['fig1']} after changing the argument of the logarithm.