Singular Cross Sections in Muon Colliders

Abstract

We address the problem that the cross section for the collisions of unstable particles diverges, if calculated by standard methods. This problem is considered for beams much smaller than the decay length of the unstable particle, much larger than the decay length and finally also for pancake- shaped beams. We find that in all cases this problem can be solved by taking into account the production/propagation of the unstable particle and/or the width of the incoming wave packets in momentum space.Comment: 12 pages, 3 figures. References corrected. Removed one sentence about a fact that was known. Added explaination why one of our graphs is different as compared to one of the references. Clearified explaination in sec. 3.