gluon gluon fusion process can not agree with PDG result

Asked by panda on 2021-04-23

the corsssection of gluon gluon fusion process gg>h is about 15.71 pb calculated by madgraph.
the experiment result is around 48 pb , so why the madgraph result do not agree with the
experiment result.

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Olivier Mattelaer
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Hi,

First it is depending on how you generate the process. Did you use loop_sm and compute loop-induced processes or use the heft theory and compute a tree-level amplitude.
The heft theory does not include light quark in the loop and therefore over-estimate the result.

Second both those computation are performed at Leading Order and have large theoretical uncertainty associated to them.
As a matter of fact the typical method to estimate those theoretical error undershoot those effects and such cross-section increase above the theoretical error when going to NLO computation and NNLO computation is also barely compatible within that theoretical band (and increase again the cross-section). At N3LO, this seems to start to be under-control theoretically and compatible with experimental data.

So this is well know (and expected) that a LO prediction for such process is much below the experimental result.

panda (panda9536) said : #2

thanks and I use loop_sm to generate process. So you mean that if I want to get the right number NNLO and N3LO contribution need to be take into account , that's to say by only using loop_sm, the number will always be small.
So if I want to get a closer number to the experiment data, is heft theory a better choice ? since the loop_sm result is 3 times less than experiment data.

If you use heft, then you do not include the bottom loop which is actually a negative cross-section so the predicted cross-section will be higher

If you look at table 9 of https://arxiv.org/pdf/1507.00020.pdf.
You will see that loop-induced with m_b set to zero is at ~20 pb (agreeing with heft result)
while adding the bottom mass set the cross-section to ~ 18 GeV

> So if I want to get a closer number to the experiment data, is heft theory a better choice ?

The difference is 10% and you can see the impact on shape on Figure 2.
So as usual LO computation can not be trusted for the cross-section. You need to go to higher accuracy for that.
LO computation are typically used to predict the shape and re-scale (via K-factor) to more accurate cross-section.
So here you should just ignore the cross-section as a prediction and use the N3LO result for the cross-section.

Two loop computation is available for that process so you will likely found in POwHEG such process at NLO accuracy but still you will need to rescale the cross-section to the N3LO one since NLO still under-shoot the final result.

panda (panda9536) said : #4

Thanks Olivier Mattelaer, that solved my question.