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

The two-loop Sudakov form factor is computed in a $\mathrm{U}(1)$ model with a massive gauge boson and a $\mathrm{U}(1)\times \mathrm{U}(1)$ 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.