Debugging sensitivity to etal variable

Asked by Peter Steinberg on 2017-06-16

I am trying to calculate gamma+gamma -> mu+ mu- gamma, without requiring observation of the final state gamma (e.g. through the deviations from pure back to back emission of the muons). I am using elastic photons (lpp=2 for both beams), and I require the muons have pT>4 GeV and |eta|<2.4 (ATLAS acceptance).

What I am trying to understand is how to get a reliable calculation despite not measuring the photons. To avoid singularities, I require
1) photon energy is at least 1 MeV (ea = 0.001)
2) the opening angle of the photon relative to a muon is 0.01 (dral = 0.01)
3) *no* requirement on the photon eta (etaa = -1.0)
4) For the record, i assume each proton beam has 2510 GeV

(the cards are embedded in the output file -

I found a few strange features, which I would like to understand better

1) when etal=2.5 or 2.6, the calculation runs successfully, however, when etal=2.7, the calculation takes much longer to run, generates a much larger cross section overall, and is unable to complete the requested number of events (a typical sign something is wrong). Presumably i'm running out of phase space, but i'm not sure how to test this (suggestions I received to set a minimum x for the elastic photon PDF can't be achieved since i don't see an option for this in MadGraph).

2) when I run the same script with 100k events, I get a much larger cross section than when i run 10k events, although the cross section for events with a large photon acoplanarity (== 1- delta-phi/pi) is the same. Thus it seems that small angle photon emission seems to change randomly despite having the same input cards file. For the record, both jobs finish with no obvious issues.

Thanks for any advice!

- Peter

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Dear Peter,

I confirmed the problem with your cuts.
I think we need a (tiny) pta or etaa to avoid collinear emissions along the beam lines.


Peter Steinberg (steinber) said : #2

Hi - I have been investigating your advice the last few weeks, and I find a very peculiar behavior in the generated cross sections calculated as a function of dimuon acoplanarity (Aco = 1 - |∆phi|/π)

If I stick to etal=2.5 (to avoid the issue I mentioned above), I find that requiring Aco>0.01 (the region I am mainly interested in) essentially cuts off the photon rapidity, pT and energy in reasonable ways (i.e. the rapidity cuts off around 4, the pT is >100 MeV and the energy > 150 MeV). Furthermore the ∆R between the photon and lepton is also cut off near 0.

See the plots here:

Thus, I thought it would be useful to run with a similar setup, but with pta>0.1 and ea>0.2. I thought this would reproduce the previous results at large acoplanairty. What I find instead is that while the shapes of all relevant distributions (dimuon and photon variables) are the same, given the same cuts, the cross sections in the second run are down by over a factor of 3. If I scale up by 3.34 (the ratio of the integral of the acoplanaity distributions in both cases) then the distributions are clearly identical.

Scaled-up plots are here:

Is there an obvious reason this should be happening? One conjecture I have is that somehow the radiation off of the internal muon line is somehow suppressed, since the cross sections I get out in the second case are very similar to what I get if I take gamma+gamma->mu+ mu- (without the additional final state photon) and I use Pythia8 to do a QED FSR shower. In principle, Pythia should be able to mock up the radiation off of the final state muons, but I presumed it could not model the radiation off of the internal line.

Is it possible to run the same process but disable certain diagrams, even if this breaks gauge invariance?

Thanks for any further advice (and please feel free to ask questions if something is not clear here).

- Peter