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Gauge symmetry and cancellations

Cancellation of diagram contributions is an essential point both for symbolic and numerical processing, because a relatively small variation of one diagram contribution may lead to a significant error. Such variation can be caused either by finite precision of floating operations or by correction of Feynman rules, for instance, by including particle widths into consideration, or by removal of some diagram subset. We would like to stress again these obstacles to warn the user.

There are two well known examples of gauge cancellations. The first one is the ultraviolet cancellation of terms originating from the propagators of massive vector particles. This problem could be resolved by the calculation of squared matrix element in the t'Hooft - Feynman gauge.

The second example is the cancelation of double pole $(t^{-2})$ terms of t-channel photon propagator. There is a wide class of processes where the incoming electron goes out in the forward direction emitting a virtual photon like in Fig.. The corresponding diagrams have got the $1/t$ pole, where $t$ is the squared momentum of the virtual photon. For the above kinematics the photon appears very close to its mass shell ($t \approx 0$), hence this configuration gives a large contribution to the cross section.

For the squared matrix element we expect the $1/t^2$ pole, but it appears to be reduced up to $1/t$ pole [Budnev-1975] in the zero-electron-mass limit. This fact is caused by electro-magnetic U(1) gauge invariance. If diagrams of Fig. type contribute to your process, we strongly recommend to to set the 'Gauge invariance' switch ON (see Section ) to prevent the gauge symmetry breaking by width terms. Another way to solve this problem is the usage of the Weizsaecker-Williams approximation (see Section ).