ZHee vs. ZHvv: difference when computing on-shell cross sections?

Asked by Philipp Windischhofer on 2020-04-24

Dear experts,

I am trying to understand the results I am getting for the cross sections of the ZH(e+ e-) and ZH(ve ve~) processes, computed in different ways (see below). I am using a fresh installation of MG 2.6.7 out of the box as well as the default "sm" model.

Without further ado, here are the cross sections I obtain with this setup:


> generate p p > H e+ e-
0.0126 +- 4.945e-05 pb

> generate p p > Z H, Z > e+ e-
0.01906 +- 2.466e-05 pb


> generate p p > H ve ve~
0.03808 +- 6.823e-05 pb

> generate p p > Z H, Z > ve ve~
0.03767 +- 7.368e-05 pb


There are some features that confuse me, and I would like to understand if there is a problem in this way of using MG, or whether this is an actual physics effect.

* Restricting the Z to be onshell only has a small effect on the ZH(ve ve~) cross section, but modifies the ZH(e+ e-) cross section much more severely.

* In case the Z is forced to be onshell, the ratio ZH(ve ve~) / ZH(e+ e-) is about 2, which agrees well with the ratio of the branching fractions Br(Z -> ve ve~) / Br(Z -> e+ e-), as I would expect. In case there is no restriction on the Z, this ratio is about 3. The diagrams that MG prints for both cases are identical.

At this point, I would greatly appreciate any input as to where this might be coming from, or what the origin of the effect could be.

Many thanks for your help!


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Philipp Windischhofer
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Olivier Mattelaer suggests this article as an answer to your question:
FAQ #2442: “why production and decay cross-section didn't agree.”.

Ha! Thanks a lot for your answer. For posterity, the culprit was the "etal" cut that I had missed and that only applies to *charged* leptons. Disabling this cut leads to the expected outcome.