Problem fitting NLO perturbative charm

[RoyStegeman]

There is a problem when trying to fit NLO perturbative charm. Namely positvity, integrability and the validation threhold all faill, and the arc-length is considerably higher than for the NNLO fitted charm fit. The chi2 per dataset is roughly:

Epoch: 16000
DEUTERON: 2.175608610661609 2.3023670685596955
NMC: 3.9632456661049837 3.615186803481158
NUCLEAR: 2.01407176617177 2.367892578125
HERACOMB: 3.3180955058396466 3.5468205448420074
DYE886: 4.116624774354877 2.5264210908309273
CDF: 3.2958807264055525 0.0
D0: 2.360400019465266 0.0
ATLAS: 10.5777060546875 14.483962038730054
CMS: 9.272918791728486 16.126761820778917
LHCb: 5.183324353448276 0.0
Total: training = 4.6053573349620995 validation = 5.3817704327135205

Below are tables containing experimental chi2s of NNPDF31 NLO fits:

1. fitted charm pdf: report (high chi2)
2. pert. charm pdf (still data cuts from the fitted charm pdf): report (good chi2)

I think report 2 suggests that the problem is not with the theory? I'm currently running a fit without generating a replica as @scarlehoff suggested.

[juanrojochacon]

Very nice! This is a reassuring check. So we can proceed with the fits as planned, no need to worry out F2c then.

And yes, the chi was never added to APFEL, it was only used in its predecessor FONLLdis which I wrote.

About why F2c is tiny but negative at large-x in the pert charm fit, this is a curious finding but completely irrelevant for the fits, so not sure it is worth the effort to spend time (right now) with it.

[juanrojochacon]

I guess this issue can be closed?

[RoyStegeman]

I guess this issue can be closed?

I would say so, if other people involved with this issue also agree with our conclusion.

[scarlehoff]

Thank you very much @RoyStegeman

Let's discuss it during the code meeting this afternoon so people can have a look.

The 10^-5 absolute difference (0.01 relative) in the x=10^-1 region seems consistent with what we see. I would like @felixhekhorn and @AleCandido input on whether this is the level of agreement one usually gets for the LH Benchmark.

In summary, the fact that the differences are, in absolute terms, of order 10^-5 makes me "numerically happy" so I agree with proceeding with the fits.

[juanrojochacon]

Well as someone who has run a lot of LH benchmarks in the past, I can confirm that this is a very decent accuracy (it could be further improved playing with numerics but I don't think it is needed here)

[Zaharid]

I am not sure I see the logic here: One of the possible explanations for the problem was the accuracy in the computation of the structure function. This appears to be shown to not be the explanation. But this was never the problem. Rather the problem is that we cannot seem to fit with this data postive, and there doesn't seem to be a compelling explanation as to why.

[juanrojochacon]

But this is completely irrelevant for the NNPDF4.0 fits. It is an interesting question but it can be studied later, once we have checked that F2c is computed correctly

[scarlehoff]

I am not sure I see the logic here: One of the possible explanations for the problem was the accuracy in the computation of the structure function. This appears to be shown to not be the explanation.

Instead, looking at the differences I can perfectly believe the problem is the accuracy.

[juanrojochacon]

there are other options, maybe the FONLL matching prescription is not ideal for large-x and low-scales (F2c is tiny there, so it was not optimised for this region). So the problem might be the accuracy (since F2c is very small there) but also a theoretical explanation is possible. In both cases, irrelevant for NNPDF4.0

[RoyStegeman]

Instead, looking at the differences I can perfectly believe the problem is the accuracy.

Well it could explain why an FK table generated using apfel returns an f2c of order -1e-5 for a strictly positive charm pdf. But this possible inaccuracy would be in the fk table during fitting as well. So if we fit with that FK table, then we should be able to force the f2c observables calculated using that fk table and input pdf to be positive.

So this check confirms that the F2c we are fitting to are good enough, but I don't think it can explain why we are not able to force f2c positive.

[scarlehoff]

Not necessarily. It's no the same a 1e-5 inaccuracy around 0 that somewhere where it is hidden by much larger numbers.

Of course, this is not a proof and if we had infinite time I would ask for perfect accuracy to see whether 1) that's the case 2) whether it changes anything for all other observables. But we don't have infinite time and I certainly wouldn't volunteer to fix a 1e-5 difference in apfel.