Implement N3LO OME from 2512.13508

[felixhekhorn]

Double check if Eq. 17 + Eq. 38 of https://arxiv.org/pdf/2512.13508 present new results.

@giacomomagni could you maybe have a look? First, only if they are actually new stuff and only in case you have spare time some help on implementation would be appreciated 😇

[giacomomagni]

Hi @felixhekhorn,
I think this paper indeed contains a new piece of information (: , a new element A_{Qq,PS,s},
where the last s stands for "sea" (ie. valence - minus).
So I think this element should be added (with a minus sign in front ?) to the non singlet matching matrix in position (2,1),
connecting valence light quarks to h^- .

This line would be modified:

eko/src/ekore/operator_matrix_elements/unpolarized/space_like/as3/__init__.py

Line 161 in 2e3a834

[[A_qqNS(n, cache, nf, L, -1), 0.0], [0 + 0j, 0 + 0j]], np.complex128

to:

[[A_qqNS(n, cache, nf, L, -1), 0.0], [-A_Hq_sea(n, cache, nf, L), 0]], np.complex128

what do you think ?