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Test scale variation schemes difference. #346

Merged
merged 11 commits into from
Feb 15, 2024
Merged

Test scale variation schemes difference. #346

merged 11 commits into from
Feb 15, 2024

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giacomomagni
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This PR aims to close issue #201 and provide a reasonable test for the difference between the
scale variations kernels, at least for FFNS.

A further test at PDF level would be possible, but even more complicated.

@giacomomagni giacomomagni linked an issue Feb 13, 2024 that may be closed by this pull request
@giacomomagni giacomomagni marked this pull request as draft February 13, 2024 12:37
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giacomomagni commented Feb 14, 2024

I believe to have solved the issue, however already at NLO the remaining O[as^2] has a quite lengthy expression...
Moreover at LO, if check the difference with the exact result everything is fine, but if we do an expansion in L or a0, to reach a good agreement I have to retain 3 orders.

@felixhekhorn felixhekhorn added the benchmarks Benchmark (or infrastructure) related label Feb 14, 2024
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felixhekhorn commented Feb 14, 2024

  • I reshuffled the test a bit: lowering L and dropping thus the 3. order
  • now this is a hard math statement: the difference is proportional $a_0 * L$, which we see is not well behaved
  • in fact, even for $Q_0^2=99^2$ (and xif2 = 0.9) I can not drop the second order

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  • I reshuffled the test a bit: lowering L and dropping thus the 3. order
  • now this is a hard math statement: the difference is proportional a0∗L, which we see is not well behaved
  • in fact, even for Q12=992 (and xif2 = 0.9) I can not drop the second order

Thanks, this is fine, in real life we are even using xif=0.5, so even worst!!
And if one choose a lower $Q^2$ even even a0, a1 can be larger! (from NLO the difference depends also on a1)

Not sure we can do much, apart coding the complete analytic expansion (as I did for LO in previous commits),
and verify it matches at NLO. Then if you take the series of that expression you can see it's $\mathcal{O}(as^2)$

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I added another stupid test, that checks expanded is linear in $L$

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I extended the test to NLO.
Given that numbers are so close to 1, not sure we are actually testing anything but still...
I think we can merge @felixhekhorn

@giacomomagni giacomomagni marked this pull request as ready for review February 14, 2024 17:16
@giacomomagni giacomomagni merged commit 6d93e13 into master Feb 15, 2024
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@giacomomagni giacomomagni deleted the issue_#201 branch February 15, 2024 10:15
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Test scale variations expanded against exponentiated
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