Gluonic NNLO polarized matching in `M scheme` about eko

[felixhekhorn]

• my current understanding is that the M scheme is defined by [1, Eq. (2.12)]
• whether that equation also hold for OME I don't know, but given that this relation is introduced at such a "high" level I expect it to be universal
• we know from [1, below Eq. (2.17)] $z_{gg} = z_{qg} = 0$ so I wonder if there is any additional transformation needed. To be specific: if OMEs follow a similar transformation as splitting functions (which might be reasonable) we can conclude from [1, Eq. (2.19)] that $A_{gg,M}^2= A_{gg,L}^2$

[1] https://arxiv.org/pdf/1409.5131.pdf

[giacomomagni]

• we know from [1, below Eq. (2.17)] zgg=zqg=0 so I wonder if there is any additional transformation needed. To be specific: if OMEs follow a similar transformation as splitting functions (which might be reasonable) we can conclude from [1, Eq. (2.19)] that Agg,M2=Agg,L2

Actually we might have some more hints. By looking at eq 85 and 86 of [1], you can see that they are as
eq 26 and 27 of [2], apart of a factor 4 \beta_0 ?!?
Unfortunately the transformation of A_qqNS is not written explicitly.

So there are good chances that A_gg transforms under an identity
but for according to Kay Schönwald A_{gq} is not correct.

[1] https://arxiv.org/pdf/2211.15337.pdf
[2] https://arxiv.org/pdf/2111.12401.pdf