Add new result for nf^2 N3LO P_gq and improve P_qqps

[giacomomagni]

This PR is to include results from https://arxiv.org/pdf/2310.01245.pdf

[giacomomagni]

I attach here the comparison with the analytic result in x-space:

Linear-x, relative difference:
pgq_rel_diff.pdf
pqq_ps_rel_diff.pdf

Log-x, absolute plot, in yellow the old approximation based on 5/10 moments.
For P_qq_ps the approximated result (in green) is not matching exactly with the analytic result
(as it happens for P_gq) because the small-x limit can't be imposed directly during the fit
as it will screw up the large-x suppression (1-x).
However the difference between green an blue is negligible to any practical purpose and
green mostly solves the discrepancy pointed out in https://arxiv.org/pdf/2308.07958.pdf

pgq_logx.pdf
pqq_ps_logx.pdf

[felixhekhorn]

I'm a bit confused ... can you please say again which color refers to what approximation? (in either case)

[giacomomagni]

I'm a bit confused ... can you please say again which color refers to what approximation? (in either case)

For the log plot:

green: new approximation based on the analytic result
blue: analytic result
yellow: approximation based on 5/10 moments

Note that for P_gq blue and green overlaps.

In the linear plot there is only the relative difference "green-blue/green"

[giacomomagni]

I realised there was an easy fix also for this last tiny detail of P_qqps at small-x: keeping the exact LL power and suppress the NLL only subtracting 1/n.
Now it matches spot on with the analytic.

pqq_ps_logx_new.pdf

I'm happy to merge.

[felixhekhorn]

good! do it! 🙃