huge cross section for mu+mu- > v v~ a

Asked by Gordan Krnjaic on 2020-06-19

We are trying to simulate the process: [mu+ mu- > v v~ a] which serves as  a background to monophoton dark matter searches at future muon colliders. When we run this ising mg5_aMC_v2_6_7 we find a 3 pb cross section almost independently of the beam energy (same result for 40 and 60 TeV) or the photon PT cuts we impose (20 GeV or 1 TeV), which naively seems very strange given that other electroweak processes have much smaller cross sections under the same operating conditions.

There are three possible reasons why this could be happening: 1) we're stupid and this is totally normal even though we're confused 2) we are not running MG correctly or 3) maybe there's a bug here. Do you have any insight into this issue?

Question information

Language:
English Edit question
Status:
Answered
For:
MadGraph5_aMC@NLO Edit question
Assignee:
Antonio Costantini Edit question
Last query:
2020-06-19
Last reply:
2020-06-21

Hi,

I have run such process with various debugging flag and everything seems ok for the phase-space integration.
For the physics this seems that you are dominated by the T-channel diagram (which is expected) and therefore everything seems consistant with this paper: 2005.10289.

I will assign one of our muon collider expert on this thread but I do not think that they are any bug/wierd results here.

Cheers,

Olivier

Hi Gordon,

I concur with what Olivier said.
What you are basically seeing here is the Coulomb singularity screened by the W-mass.

A much easier setup in which the above is made crystal clear is the following:

generate e+ mu+ > e+ mu+ / z

which features only one diagram being a photon t-channel.
If you disable all lepton cuts MadGraph will tell you this cross-section diverges, in agreement with the fact that this cross-section exhibit a Colomb singularity (see Eq. (5.65) and )5.66) of Peskin and Schroeder.

Now if instead you do:

generate e+ mu+ > e+ mu+ / a

which has the same t-channel but this time with a massive Z-boson instead of the photon, you will see that when disabling all cuts your cross-section is now finite but independent of the scattering energy.

This is because the Coulomb singularity has now been replaced by an enhancement of the form (s / M_Z^2) which compensates the (1/s) from the flux factor, thus leaving you with a finite and constant high-energy limit.

Cheers,

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