Clarifications

[vbertone]

Hello,

first of all thanks for making this very useful code public.
I'm trying to use it to implement the approximated N3LO corrections to the DGLAP evolution in my own code and I've got a couple of technical questions concerning these expressions. Here they come:

1. Since in many of the N3LO expressions in split.F I see a factor $(4\pi)^4$, I was wondering what is the expansion parameter to be used: is it $\alpha_s$ or $\alpha_s/4\pi$? Put it another way, do I need to multiply the N3LO expressions by $\alpha_s^4$ or by $(\alpha_s/4\pi)^4$?
2. At line 975 of split.F there is the line:

          C(i) = C(i) + inv_A(i, j) * N(j)

Considering that the Fortran function reshape fills the resulting array column by column (rather than row by row), was this syntax actually meant? As a matter of fact, if I look, for example, at line 1372 of the same file, I see:

          C(i) = C(i) + inv_A(j, i) * N(j)

in which the indices i and j of the matrix inv_A are indeed exchanged, as I would have expected.
3) When including the $\delta$-term that derives from the +-priscripted singular term to the N3LO non-singlet splitting function at line 1310:

      if(ipm.eq.1) p3nsc = Pqqns3PexactC(y, FLAVOR) + p3nspba*(1.-y)*AL1

I noticed that the term p3nspba, on top of multiplying the expected $\ln(1-y)$, it also multiplies a factor $(1-y)$. What is the origin of this term?

Thank you in advance for you help.

Best regards,
Valerio