Description of the ancillary files of the article 
"Charged Current Drell-Yan production at N3LO"
By Claude Duhr, Falko Dulat and Bernhard Mistlberger

Files:
XS_zb.txt
XS_z.txt
XS_w.txt
XSReg.m
Distributions.m


Definitions:
nc= number of colours = 3
nf= number of light quark flavours = 5
zb=1-z=1-Q2/s
Q2= invariant mass squared
muf2= perturbative scale squared mu^2.
V2[1,2]= CKM matrix element squared:|V_{u d}|^2
V2[1,s]= sum of CKM matrix elements |V_{u d}|^2+|V_{u s}|^2+|V_{u b}|^2
V2[2,s]= sum of CKM matrix elements |V_{u d}|^2+|V_{c d}|^2
V2[3,s]= sum of CKM matrix elements |V_{c d}|^2+|V_{c s}|^2+|V_{c b}|^2
V2[s,s]= sum of CKM matrix elements |V_{u d}|^2+|V_{u s}|^2+|V_{u b}|^2+|V_{c d}|^2+|V_{c s}|^2+|V_{c b}|^2
All CKM matrix elements involving the top quark were set to zero.

The functions G[a1,a2,…,zb] are GPLs
The functions J[a1,a2,…,zb] are iterated integrals as defined in eq. 3.28 of arXiv:1802.00833.
The function t[i,j] are the elliptic integrals defined via eq. 3.14 of arXiv:1802.00833.




File content:
The files contain partonic coefficient functions for the production of W^- boson. 
Equivalent results for a W^+ boson can be obtained simply by charge conjugation.

The files contain a list of lists. 
For example load into Mathematica via:
lst=Get[“XSReg.m”];

The entry 
lst[[a,b]]
corresponds to the order (a-1) of the regular coefficient function of the initial state b:
b=1: d ubar
b=2: g ubar
b=3: g u
b=4: g g
b=5: u d
b=6: d d
b=7: d dbar
b=8: ubar c
b=9: ubar cbar  

Here, u, d, ubar, dbar, c, cbar and g refer to an up-quark, down quark, anti-up quark, anti-down quark, charm quark, anti-charm quark and gluon respectively.  

For example:
a=4, b=1
lst[[4,1]] corresponds to the regular N^3LO coefficient function for the d ubar initial state.

All other non-vanishing initial state combinations can be obtained from the above list.



The file XSReg.m contains the analytic results.
The file XS_zb.txt contains an expansion of the regular coefficient functions around the point zb=0=1-z.
The file XS_z.txt contains an expansion of the regular coefficient functions around the point z=0.
The file XS_w.txt contains an expansion of the regular coefficient functions around the point w=0=1/2-z.



The file Distributions.m contains a list with the distribution valued terms of the d ubar partonic coefficient function.
In this file 
delta[zb] corresponds to a Dirac delta function with argument zb.
PlusD[zb,a] corresponds to Plus distributions [Log(zb)^a/zb]_+.






