M.Echevarria, I.Scimemi, A.Vladimirov
“Unpolarized Transverse Momentum Dependent Parton Distributions and Fragmentation Functions at next-to-next-to-leading order”
arXiv:16??.????

Abstract:
This file contains the results of calculation of unpolarized TMD PDF and TMD FF, and the small - bT matching coefficients.
This is shorten version, that includes only the final expression for coefficeint functions.

VERSION:1.0

Table of content :

(in the complete version of file)  Intermidiate results : (expressions for unsubtracted TMDs, soft factor, renormalization constants, as well as, their combination into TMD)
	1.Renormalization constants
	2.Soft factor
	3.unsubtracted TMD PDFs
	4.unsubtracted TMD FFs
	5.integrated PDFs
	6.integrated FFs
	5. TMD PDFs
	6. TMD FFs
	7. matching of TMD PDFs
	8. matching of TMD FFs
	
Final expressions : (expressions for matching coefficeints, including Logarithmical part)
	1.Matching coefficients for TMD PDF (complete expression)
	2.Matching coefficients for TMD PDF (logarithmical part)
	3.Matching coefficients for TMD PDF (finite part)
	4.Matching coefficients for TMD FF (complete expression)
	5.Matching coefficients for TMD FF (logarithmical part)
	6.Matching coefficients for TMD FF (finite part)

List of variables:

coupling constant:
as=((g^2)/(((4π))^2))

Dimension regularization:
ϵ=((4-d)/2),  d=4-2ϵ

color factors:
CF=(Subscript[C, F])=((((Subscript[N, c])^2)-1)/(2(Subscript[N, c])))
CA=(Subscript[C, A])=(Subscript[N, c])
TrNf=(Subscript[T, r])(Subscript[N, f])
TR=(Subscript[T, r])

Logarithms:
Lμ = ln(((((Subscript[b, T])^2)(μ^2))/(4 (e^(-2(Subscript[γ, E]))))))
lζ=ln(((μ^2)/ζ))

Special function:
DELTA[x] is Dirac delta-function

PLUS Distributions:
Though all the file the following convention for plus-distributions is used:
Only the singular at x,z->1 part of expression should be “plus”-regulated.
I.e.
f[x]=fr[x]+(SubPlus[(fs[x])]) 
where
fs[x]=Series[f[x],{x,1,-1}]
fr[x]=f[x]-fs[x]

Final expressions

The coefficient functions for TMD PDF given by variables Cpdf[f ← f, n]
Cpdf[f ← f, n]=(∑_(m,l)) Cpdf[f ← f, n,m,l] ((Subscript[L, μ])^(m-l))((Subscript[l, ζ])^l)
		= Exp[-D Lζ](∑_m)Cpdf[f ← f, n,m] ((Subscript[L, μ])^m)
		
The coefficient functions for TMD F given by variables Cff[f ← f, n]
Cff[f ← f, n]=(∑_(m,l)) Cff[f ← f, n,m,l] ((Subscript[L, μ])^(m-l))((Subscript[l, ζ])^l)
		= Exp[-D Lζ](∑_m)Cff[f ← f, n,m] ((Subscript[L, μ])^m)
Note: expression for finite part presented in the article are simplfied by means of various relations for (Subscript[Li, {2,3}])

Matching coefficients for TMD PDF

Q ← Q

Cpdf[q←q,1]=((2 CF (-(((-1+x))^2)+Lμ (1+(x^2))))/(-1+x))+CF (2 lζ Lμ-((Lμ)^2)-((π^2)/6)) DELTA[1-x];
Cpdf[q←q,2]=-((2 (CF^2) ((Lμ)^3) (1+(x^2)))/(-1+x))-((2 (CA-CF) CF ((π^2)+3 x+(-3+(π^2)) (x^2)) Log[1-x])/(3 (-1+x)))+(-((2 CF (CA (-29+(36-83 x) x)+10 TrNf (1+(x^2))+9 CF (5+x (-13+16 x))))/(9 (-1+x)))-4 (CA-3 CF) CF (-1+x) Log[1-x]+((2 (2 CA-3 CF) CF (1+(x^2)) ((Log[1-x])^2))/(-1+x))) Log[x]+(((CF (CA (11-(-12+x) x)+2 (CF (-9+6 (-1+x) x)-2 TrNf (1+(x^2)))))/(6 (-1+x)))-((2 (CF^2) (1+(x^2)) Log[1-x])/(-1+x))) ((Log[x])^2)+((CF (CA-CF+(CA+CF) (x^2)) ((Log[x])^3))/(3 (-1+x)))+((Lμ)^2) (((4 (CF^2) lζ (1+(x^2)))/(-1+x))+((CF (11 CA (1+(x^2))+2 (9 CF (((-1+x))^2)-2 TrNf (1+(x^2)))))/(3 (-1+x)))-((8 (CF^2) (1+(x^2)) Log[1-x])/(-1+x))+((2 (CF^2) (1+3 (x^2)) Log[x])/(-1+x)))+Lμ (-4 (CF^2) lζ (-1+x)+((CF (-16 TrNf (4+x (-3+4 x))-3 CF (84 (((-1+x))^2)+(π^2) (1+(x^2)))+CA (-6 (π^2) (1+(x^2))+4 (77+x (-87+77 x)))))/(9 (-1+x)))+8 (CF^2) (-1+x) Log[1-x]+(((2 CF (17 CA-4 (6 CF+TrNf)+(5 CA+6 CF-4 TrNf) (x^2)))/(3 (-1+x)))-((8 (CF^2) (1+(x^2)) Log[1-x])/(-1+x))) Log[x]+((2 CF (CA-CF+(CA+CF) (x^2)) ((Log[x])^2))/(-1+x)))+(-4 (CA-2 CF) CF (-1+x)+((4 (CA-CF) CF (1+(x^2)) Log[1-x])/(-1+x))+((4 (CA-3 CF) CF (1+(x^2)) Log[x])/(-1+x))) PolyLog[2,x]+((4 (CA-CF) CF (1+(x^2)) PolyLog[3,1-x])/(-1+x))-((4 (2 CA-5 CF) CF (1+(x^2)) PolyLog[3,x])/(-1+x))+((CF (27 CA (π^2) (((-1+x))^2)-27 CF (-22+(π^2)) (((-1+x))^2)+8 CA (1+x (99+x))-4 TrNf (19+x (18+19 x))-54 (3 CA+10 CF) (1+(x^2)) Zeta[3]))/(27 (-1+x)))+DELTA[1-x] ((((CF^2) ((Lμ)^4))/2)+((Lμ)^3) (-2 (CF^2) lζ+(2/9) CF (-11 CA+4 TrNf))+((Lμ)^2) (2 (CF^2) ((lζ)^2)+(1/3) CF lζ (11 CA-4 TrNf)+(1/18) CF (-134 CA+3 (2 CA-7 CF) (π^2)+40 TrNf))+Lμ ((1/9) CF (π^2) (-11 CA+4 TrNf)-(1/9) CF lζ (-134 CA+3 (2 CA+CF) (π^2)+40 TrNf))-(2/27) CF lζ (56 TrNf+CA (-202+189 Zeta[3]))+(1/648) CF (9 CF (π^4)+2 CA (4856-603 (π^2)+18 (π^4)-2772 Zeta[3])+8 TrNf (-328+45 (π^2)+252 Zeta[3])));

Q ← G

Cpdf[q←g,1]=-2 TR (2 (-1+x) x+Lμ (1-2 x+2 (x^2)));
Cpdf[q←g,2]=2 CF ((Lμ)^3) TR (1+2 (-1+x) x)-2 (CA-CF) TR x (-3+4 x) Log[1-x]+4 (CA-CF) TR (-1+x) x ((Log[1-x])^2)+(2/3) (CA-CF) TR (1+2 (-1+x) x) ((Log[1-x])^3)+(1/3) TR (CA (2+4 x)+CF (-1+2 x-4 (x^2))) ((Log[x])^3)+((Lμ)^2) (-4 CF lζ TR (1+2 (-1+x) x)+((TR (-3 CF x (7+4 x (-3+2 x))-2 CA (-1+x) (4+x (7+31 x))))/(3 x))+4 (CA+CF) TR (1+2 (-1+x) x) Log[1-x]+2 TR (CA (2+8 x)+CF (-1+2 x-4 (x^2))) Log[x])+((Log[x])^2) (-2 TR (-8 CA x+CF (1+2 (-1+x) x)) Log[1-x]+(1/6) TR (CA (-6+8 (3-11 x) x)+3 CF (1+4 (3-2 x) x)+12 CA (1+2 x (1+x)) Log[1+x]))+Log[x] (8 CF TR (-1+x) x Log[1-x]+2 CF TR (1+2 (-1+x) x) ((Log[1-x])^2)+(1/9) TR (4 CA (21-6 (5+(π^2)) x+68 (x^2))+3 CF (24+3 (15-8 x) x+(π^2) (2+4 (-1+x) x))+36 CA Log[1+x] (2 x (1+x)-(1+2 x (1+x)) Log[1+x])))+(((8 CA TR (-1+x) (2+x (-1+11 x)))/(3 x))+4 (-CA+CF) TR (1+2 (-1+x) x) Log[1-x]+4 TR (4 CA x+CF (-1-2 (-1+x) x)) Log[x]) PolyLog[2,1-x]+(8 CA TR x (1+x)-4 CA TR (1+2 x (1+x)) Log[x]) PolyLog[2,-x]+Lμ (-8 CF lζ TR (-1+x) x+((TR (3 CF x (5 (π^2) (1+2 (-1+x) x)-6 (10+x (-33+28 x)))+4 CA (-26+x (36+x (-135+6 (π^2)+116 x)))))/(9 x))+16 CF TR (-1+x) x Log[1-x]+4 (CA-CF) TR (1+2 (-1+x) x) ((Log[1-x])^2)+2 TR (CA (2+4 x)+CF (-1+2 x-4 (x^2))) ((Log[x])^2)+Log[x] (8 CF TR (1+2 (-1+x) x) Log[1-x]+(1/3) (-2 TR (3 CF (1+8 (-1+x) x)+CA (6+88 (x^2)))+24 CA TR (1+2 x (1+x)) Log[1+x]))+8 CA TR (1+2 x (1+x)) PolyLog[2,-x])+4 (CA-CF) TR (1+2 (-1+x) x) PolyLog[3,1-x]+4 CA TR (1+2 x (1+x)) PolyLog[3,-x]-4 TR (-8 CA x+CF (1+2 (-1+x) x)) PolyLog[3,x]-8 CA TR (1+2 x (1+x)) PolyLog[3,(x/(1+x))]+(1/(27 x))TR (27 CF x (-13+(75+2 (π^2) (-1+x)-72 x) x)+CA (344+2 x (-315+(387+18 (π^2)-298 x) x))+18 x (CA (1+2 x (1+x)) Log[1+x] (-(π^2)+2 ((Log[1+x])^2))-6 (CA (1+2 (-2+x) x)-8 CF (1+2 (-1+x) x)) Zeta[3]));

G ← Q

Cpdf[g←q,1]=2 CF (Lμ (2-(2/x)-x)+x);
Cpdf[g←q,2]=((2 CA CF ((Lμ)^3) (2+(-2+x) x))/x)+((2 CF (CA (-152+(152-43 x) x)+8 TrNf (5+(-5+x) x)+9 CF (16+x (-16+5 x))) Log[1-x])/(9 x))+((CF (CA (-22+(22-5 x) x)+3 CF (6+(-6+x) x)+4 TrNf (2+(-2+x) x)) ((Log[1-x])^2))/(3 x))-((2 (CA-CF) CF (2+(-2+x) x) ((Log[1-x])^3))/(3 x))-(1/3) CF (CF (-2+x)+2 CA (2+x)) ((Log[x])^3)+((Lμ)^2) (-((4 CA CF lζ (2+(-2+x) x))/x)+((CF (-3 CF (-4+x) x+8 TrNf (2+(-2+x) x)+2 CA (-53+x (46+x (-11+4 x)))))/(3 x))+((4 CF (CA+CF) (2+(-2+x) x) Log[1-x])/x)-((2 CF (CF (-2+x) x+4 CA (1+x+(x^2))) Log[x])/x))+((Log[x])^2) (((2 CA CF (2+(-2+x) x) Log[1-x])/x)+((CF x (-3 CF (4+3 x)+2 CA (36+x (9+8 x)))-12 CA CF (2+x (2+x)) Log[1+x])/(6 x)))+Log[x] (((4 CA CF (-22+x (24+x (-9+4 x))) Log[1-x])/(3 x))+((2 CA CF (2+(-2+x) x) ((Log[1-x])^2))/x)+((CF (x (45 CF (-3+x)-2 CA (249-6 x+88 (x^2)))+36 CA Log[1+x] ((x^2)+(2+x (2+x)) Log[1+x])))/(9 x)))+(4 CA CF x+((4 CA CF (2+x (2+x)) Log[x])/x)) PolyLog[2,-x]+Lμ (4 CA CF lζ x+((CF (2 (27 CF x (1+2 x)+40 TrNf (2+(-2+x) x))+CA (3 (π^2) (2+(-10+x) x)-4 (9+x (19+4 x+44 (x^2))))))/(9 x))+((4 CF (CA (-22+(22-17 x) x)+(9 CF+4 TrNf) (2+(-2+x) x)) Log[1-x])/(3 x))-((4 (CA-CF) CF (2+(-2+x) x) ((Log[1-x])^2))/x)-2 CF (CF (-2+x)+2 CA (2+x)) ((Log[x])^2)+Log[x] (((8 CA CF (2+(-2+x) x) Log[1-x])/x)-((2 CF (x (3 CF (4+5 x)-2 CA (36+x (15+8 x)))+12 CA (2+x (2+x)) Log[1+x]))/(3 x)))-((8 CA CF (2+x (2+x)) PolyLog[2,-x])/x))+(((8 CA CF (-1+x) (11+x (-1+2 x)))/(3 x))+((4 CA CF (6+x (-2+3 x)) Log[x])/x)) PolyLog[2,x]-((4 CA CF (2+x (2+x)) PolyLog[3,-x])/x)-((4 CA CF (10+x (-2+5 x)) PolyLog[3,x])/x)+((8 CA CF (2+x (2+x)) PolyLog[3,(x/(1+x))])/x)+(1/(27 x))CF (-27 CF (-10+x) x+8 TrNf (56+x (-56+13 x))+CA (-3 (π^2) (-44+x (48+x (-9+8 x)))+4 (-790+x (791+4 x (-67+38 x))))+18 CA (2+x (2+x)) Log[1+x] ((π^2)-2 ((Log[1+x])^2))+216 CA (6+x (-7+3 x)) Zeta[3]);

G ← G

Cpdf[g←g,1]=((4 CA Lμ (((1-x+(x^2)))^2))/((-1+x) x))+CA (2 lζ Lμ-((Lμ)^2)-((π^2)/6)) DELTA[1-x];
Cpdf[g←g,2]=-((4 (CA^2) ((Lμ)^3) (((1+(-1+x) x))^2))/((-1+x) x))+(2/3) CA (CA-2 TrNf) x Log[1-x]+(4/3) ((CA^2) (-2+x) x+CF TrNf (1+x)+((CA^2)/(-1+(x^2)))) ((Log[x])^3)+((Lμ)^2) (((8 (CA^2) lζ (((1+(-1+x) x))^2))/((-1+x) x))+((2 (-4 CA TrNf (((1+(-1+x) x))^2)+2 CF TrNf (-4+x+6 (x^2)+(x^3)-4 (x^4))+(CA^2) (55+x (-102+x (105+x (-102+55 x))))))/(3 (-1+x) x))-((16 (CA^2) (((1+(-1+x) x))^2) Log[1-x])/((-1+x) x))+((8 (CF TrNf x (-1+(x^2))+(CA^2) (1+(-3+x) (-1+x) (x^2))) Log[x])/((-1+x) x)))+((Log[x])^2) (-((4 (CA^2) (((1+(-1+x) x))^2) Log[1-x])/((-1+x) x))+((x (1+x) (4 CA TrNf (1+x)+6 CF TrNf (3+x)+(CA^2) (25+11 x (-1+4 x)))-12 (CA^2) (((1+x+(x^2)))^2) Log[1+x])/(3 x (1+x))))+Log[x] (((8 (CA^2) (-1+x) (11+x (-1+11 x)) Log[1-x])/(3 x))-((4 (CA^2) (((1+(-1+x) x))^2) ((Log[1-x])^2))/((-1+x) x))+((-x (1+x) (-216 CF TrNf (1+x)-4 CA TrNf (13+10 x)+(CA^2) (701+x (149+536 x)))+72 (CA^2) (((1+x+(x^2)))^2) ((Log[1+x])^2))/(9 x (1+x))))+((8 (CA^2) (((1+x+(x^2)))^2) Log[x] PolyLog[2,-x])/(x (1+x)))+Lμ ((1/(9 x (-1+(x^2))))2 (-12 CF TrNf (((-1+x))^2) (1+x) (-2+x (19+4 x))-4 CA TrNf (1+x) (23+x (-42+x (48+x (-42+23 x))))+(CA^2) (x (1+x) (109+x (-84+109 x))-3 (π^2) (1+x (-5+x (1+x (5+x (-1+5 x)))))))+(8 CF TrNf (1+x)+((8 (CA^2) (((1+x-(x^2)))^2))/(-1+(x^2)))) ((Log[x])^2)+Log[x] (-((16 (CA^2) (((1+(-1+x) x))^2) Log[1-x])/((-1+x) x))-((4 (-x (1+x) (4 CA TrNf (1+x)+18 CF TrNf (1+x)+(CA^2) (25+11 x (-1+4 x)))+12 (CA^2) (((1+x+(x^2)))^2) Log[1+x]))/(3 x (1+x))))-((16 (CA^2) (((1+x+(x^2)))^2) PolyLog[2,-x])/(x (1+x))))+(((8 (CA^2) (-1+x) (11+x (-1+11 x)))/(3 x))-((8 (CA^2) (3+x (-1+x (3+x-3 (x^2)+(x^3)))) Log[x])/(x (-1+(x^2))))) PolyLog[2,x]-((8 (CA^2) (((1+x+(x^2)))^2) PolyLog[3,-x])/(x (1+x)))+((8 (CA^2) (5+x (-1+x (5+x-5 (x^2)+(x^3)))) PolyLog[3,x])/(x (-1+(x^2))))+((16 (CA^2) (((1+x+(x^2)))^2) PolyLog[3,(x/(1+x))])/(x (1+x)))+(1/(27 x (-1+(x^2))))4 (-(1+x) (-18 CF TrNf (((-1+x))^2) (1+(-23+x) x)+(CA^2) (-790+3 (π^2) (((-1+x))^2) (11+x (-1+11 x))+x (1514+x (-1686+5 (319-167 x) x)))+CA TrNf (121+x (-231+x (276+x (-249+139 x)))))+9 (CA^2) ((-1+x) (((1+x+(x^2)))^2) Log[1+x] ((π^2)-2 ((Log[1+x])^2))-6 (6+x (-7+x (6+x (7+x (-6+7 x))))) Zeta[3]))+DELTA[1-x] ((((CA^2) ((Lμ)^4))/2)+((Lμ)^2) (2 (CA^2) ((lζ)^2)-(1/18) CA (CA (134+15 (π^2))-40 TrNf)+(1/3) CA lζ (11 CA-4 TrNf))+((Lμ)^3) (-2 (CA^2) lζ+(2/9) CA (-11 CA+4 TrNf))+Lμ ((1/9) CA (π^2) (-11 CA+4 TrNf)-(1/9) CA lζ (CA (-134+9 (π^2))+40 TrNf))-(2/27) CA lζ (56 TrNf+CA (-202+189 Zeta[3]))+(1/324) CA (4 TrNf (-328+45 (π^2)+252 Zeta[3])+CA (4856-603 (π^2)+18 (π^4)-135 ((Log[2])^4)+3240 PolyLog[2,2,(1/2)]+9 (-308+45 Log[2]) Zeta[3])));

Q ← Q’

Cpdf[q←qp,1]=0;
Cpdf[q←qp,2]=-((2 CF TR (-1+x) (172+x (-143+136 x)))/(27 x))+(4/9) CF TR (21-30 x+32 (x^2)) Log[x]-(1/3) CF TR (3+x (3+8 x)) ((Log[x])^2)+(2/3) CF TR (1+x) ((Log[x])^3)+((Lμ)^2) (-((2 CF TR (-1+x) (4+x (7+4 x)))/(3 x))+4 CF TR (1+x) Log[x])+Lμ (((8 CF TR (-1+x) (13+x (-5+22 x)))/(9 x))-(4/3) CF TR (3+x (9+8 x)) Log[x]+4 CF TR (1+x) ((Log[x])^2))+((8 CF TR (-1+x) (2+x (-1+2 x)) PolyLog[2,1-x])/(3 x));

Q ← (OverBar[Q])

Cpdf[q←qbar,1]=0;
Cpdf[q←qbar,2]=(((CA-2 CF) CF (1+(x^2)) ((Log[x])^3))/(3 (1+x)))+((Log[x])^2) (-((4 (CA-2 CF) CF (1+(x^2)) Log[1-x])/(1+x))-((2 (CA-2 CF) CF (1+(x^2)) Log[1+x])/(1+x)))+(((CA-2 CF) CF Log[x] (-3 (1+x) (3+11 x)+2 (π^2) (1+(x^2))+12 Log[1+x] ((((1+x))^2)+(1+(x^2)) Log[1+x])))/(3 (1+x)))+(-4 (CA-2 CF) CF (-1+x)-((4 (CA-2 CF) CF (1+(x^2)) Log[x])/(1+x))) PolyLog[2,1-x]+(4 (CA-2 CF) CF (1+x)+((4 (CA-2 CF) CF (1+(x^2)) Log[x])/(1+x))) PolyLog[2,-x]+Lμ (-((2 (CA-2 CF) CF (-12+(π^2)+(12+(π^2)) (x^2)))/(3 (1+x)))+((2 (CA-2 CF) CF (1+(x^2)) ((Log[x])^2))/(1+x))+((4 (CA-2 CF) CF Log[x] ((((1+x))^2)-2 (1+(x^2)) Log[1+x]))/(1+x))-((8 (CA-2 CF) CF (1+(x^2)) PolyLog[2,-x])/(1+x)))-((4 (CA-2 CF) CF (1+(x^2)) PolyLog[3,-x])/(1+x))-((8 (CA-2 CF) CF (1+(x^2)) PolyLog[3,x])/(1+x))+((8 (CA-2 CF) CF (1+(x^2)) PolyLog[3,(x/(1+x))])/(1+x))+(((CA-2 CF) CF (-45+45 (x^2)+(π^2) (((1+x))^2)+2 (1+(x^2)) Log[1+x] ((π^2)-2 ((Log[1+x])^2))-6 (1+(x^2)) Zeta[3]))/(3 (1+x)));

Matching coefficients for TMD PDF (logarithmical part)

Q ← Q

Cpdf[q←q,1,2,0]=Coefficient[Cpdf[q←q,1]/.lζ->0,((Lμ)^2)]
Cpdf[q←q,1,1,1]=Coefficient[Cpdf[q←q,1],Lμ lζ]
Cpdf[q←q,1,1,0]=Simplify@Coefficient[Cpdf[q←q,1]/.lζ->0,Lμ]

Cpdf[q←q,1,2]=Coefficient[Cpdf[q←q,1]/.lζ->Lμ,((Lμ)^2)]
Cpdf[q←q,1,1]=Simplify@Coefficient[Cpdf[q←q,1]/.lζ->Lμ,Lμ]

Cpdf[q←q,2,4,0]=Coefficient[Cpdf[q←q,2]/.lζ->0,((Lμ)^4)]
Cpdf[q←q,2,4,1]=Coefficient[Cpdf[q←q,2],((Lμ)^3)lζ]
Cpdf[q←q,2,4,2]=Coefficient[Cpdf[q←q,2],((Lμ)^2) ((lζ)^2)]
Cpdf[q←q,2,3,0]=Collect[Coefficient[Cpdf[q←q,2]/.lζ->0,((Lμ)^3) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←q,2,3,1]=Collect[Coefficient[Cpdf[q←q,2],((Lμ)^2)lζ ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←q,2,3,2]=Collect[Coefficient[Cpdf[q←q,2],Lμ ((lζ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←q,2,2,0]=Collect[Coefficient[Cpdf[q←q,2]/.lζ->0,((Lμ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←q,2,2,1]=Collect[Coefficient[Cpdf[q←q,2],Lμ lζ ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←q,2,2,2]=Collect[Coefficient[Cpdf[q←q,2]/.Lμ->0,((lζ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←q,2,1,0]=Collect[Coefficient[Cpdf[q←q,2]/.lζ->0,Lμ ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←q,2,1,1]=Collect[Coefficient[Cpdf[q←q,2]/.Lμ->0,lζ ],{DELTA[_],CF,CA,TrNf},Simplify]

Cpdf[q←q,2,4]=Collect[Coefficient[Cpdf[q←q,2]/.lζ->Lμ,((Lμ)^4) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←q,2,3]=Collect[Coefficient[Cpdf[q←q,2]/.lζ->Lμ,((Lμ)^3) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←q,2,2]=Collect[Coefficient[Cpdf[q←q,2]/.lζ->Lμ,((Lμ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←q,2,1]=Collect[Coefficient[Cpdf[q←q,2]/.lζ->Lμ,((Lμ)^1) ],{DELTA[_],CF,CA,TrNf},Simplify]

Q ← G

Cpdf[q←g,1,2,0]=Coefficient[Cpdf[q←g,1]/.lζ->0,((Lμ)^2)]
Cpdf[q←g,1,1,1]=Coefficient[Cpdf[q←g,1],Lμ lζ]
Cpdf[q←g,1,1,0]=Simplify@Coefficient[Cpdf[q←g,1]/.lζ->0,Lμ]

Cpdf[q←g,1,2]=Coefficient[Cpdf[q←g,1]/.lζ->Lμ,((Lμ)^2)]
Cpdf[q←g,1,1]=Simplify@Coefficient[Cpdf[q←g,1]/.lζ->Lμ,Lμ]

Cpdf[q←g,2,4,0]=Coefficient[Cpdf[q←g,2]/.lζ->0,((Lμ)^4)]
Cpdf[q←g,2,4,1]=Coefficient[Cpdf[q←g,2],((Lμ)^3)lζ]
Cpdf[q←g,2,4,2]=Coefficient[Cpdf[q←g,2],((Lμ)^2) ((lζ)^2)]
Cpdf[q←g,2,3,0]=Collect[Coefficient[Cpdf[q←g,2]/.lζ->0,((Lμ)^3) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←g,2,3,1]=Collect[Coefficient[Cpdf[q←g,2],((Lμ)^2)lζ ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←g,2,3,2]=Collect[Coefficient[Cpdf[q←g,2],Lμ ((lζ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←g,2,2,0]=Collect[Coefficient[Cpdf[q←g,2]/.lζ->0,((Lμ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←g,2,2,1]=Collect[Coefficient[Cpdf[q←g,2],Lμ lζ ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←g,2,2,2]=Collect[Coefficient[Cpdf[q←g,2]/.Lμ->0,((lζ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←g,2,1,0]=Collect[Coefficient[Cpdf[q←g,2]/.lζ->0,Lμ ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←g,2,1,1]=Collect[Coefficient[Cpdf[q←g,2]/.Lμ->0,lζ ],{DELTA[_],CF,CA,TrNf},Simplify]

Cpdf[q←g,2,4]=Collect[Coefficient[Cpdf[q←g,2]/.lζ->Lμ,((Lμ)^4) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←g,2,3]=Collect[Coefficient[Cpdf[q←g,2]/.lζ->Lμ,((Lμ)^3) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←g,2,2]=Collect[Coefficient[Cpdf[q←g,2]/.lζ->Lμ,((Lμ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←g,2,1]=Collect[Coefficient[Cpdf[q←g,2]/.lζ->Lμ,((Lμ)^1) ],{DELTA[_],CF,CA,TrNf},Simplify]

G ← Q

Cpdf[g←q,1,2,0]=Coefficient[Cpdf[g←q,1]/.lζ->0,((Lμ)^2)]
Cpdf[g←q,1,1,1]=Coefficient[Cpdf[g←q,1],Lμ lζ]
Cpdf[g←q,1,1,0]=Simplify@Coefficient[Cpdf[g←q,1]/.lζ->0,Lμ]

Cpdf[g←q,1,2]=Coefficient[Cpdf[g←q,1]/.lζ->Lμ,((Lμ)^2)]
Cpdf[g←q,1,1]=Simplify@Coefficient[Cpdf[g←q,1]/.lζ->Lμ,Lμ]

Cpdf[g←q,2,4,0]=Coefficient[Cpdf[g←q,2]/.lζ->0,((Lμ)^4)]
Cpdf[g←q,2,4,1]=Coefficient[Cpdf[g←q,2],((Lμ)^3)lζ]
Cpdf[g←q,2,4,2]=Coefficient[Cpdf[g←q,2],((Lμ)^2) ((lζ)^2)]
Cpdf[g←q,2,3,0]=Collect[Coefficient[Cpdf[g←q,2]/.lζ->0,((Lμ)^3) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[g←q,2,3,1]=Collect[Coefficient[Cpdf[g←q,2],((Lμ)^2)lζ ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[g←q,2,3,2]=Collect[Coefficient[Cpdf[g←q,2],Lμ ((lζ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[g←q,2,2,0]=Collect[Coefficient[Cpdf[g←q,2]/.lζ->0,((Lμ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[g←q,2,2,1]=Collect[Coefficient[Cpdf[g←q,2],Lμ lζ ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[g←q,2,2,2]=Collect[Coefficient[Cpdf[g←q,2]/.Lμ->0,((lζ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[g←q,2,1,0]=Collect[Coefficient[Cpdf[g←q,2]/.lζ->0,Lμ ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[g←q,2,1,1]=Collect[Coefficient[Cpdf[g←q,2]/.Lμ->0,lζ ],{DELTA[_],CF,CA,TrNf},Simplify]

Cpdf[g←q,2,4]=Collect[Coefficient[Cpdf[g←q,2]/.lζ->Lμ,((Lμ)^4) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[g←q,2,3]=Collect[Coefficient[Cpdf[g←q,2]/.lζ->Lμ,((Lμ)^3) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[g←q,2,2]=Collect[Coefficient[Cpdf[g←q,2]/.lζ->Lμ,((Lμ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[g←q,2,1]=Collect[Coefficient[Cpdf[g←q,2]/.lζ->Lμ,((Lμ)^1) ],{DELTA[_],CF,CA,TrNf},Simplify]

G ← G

Cpdf[g←g,1,2,0]=Coefficient[Cpdf[g←g,1]/.lζ->0,((Lμ)^2)]
Cpdf[g←g,1,1,1]=Coefficient[Cpdf[g←g,1],Lμ lζ]
Cpdf[g←g,1,1,0]=Simplify@Coefficient[Cpdf[g←g,1]/.lζ->0,Lμ]

Cpdf[g←g,1,2]=Coefficient[Cpdf[g←g,1]/.lζ->Lμ,((Lμ)^2)]
Cpdf[g←g,1,1]=Simplify@Coefficient[Cpdf[g←g,1]/.lζ->Lμ,Lμ]

Cpdf[g←g,2,4,0]=Coefficient[Cpdf[g←g,2]/.lζ->0,((Lμ)^4)]
Cpdf[g←g,2,4,1]=Coefficient[Cpdf[g←g,2],((Lμ)^3)lζ]
Cpdf[g←g,2,4,2]=Coefficient[Cpdf[g←g,2],((Lμ)^2) ((lζ)^2)]
Cpdf[g←g,2,3,0]=Collect[Coefficient[Cpdf[g←g,2]/.lζ->0,((Lμ)^3) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[g←g,2,3,1]=Collect[Coefficient[Cpdf[g←g,2],((Lμ)^2)lζ ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[g←g,2,3,2]=Collect[Coefficient[Cpdf[g←g,2],Lμ ((lζ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[g←g,2,2,0]=Collect[Coefficient[Cpdf[g←g,2]/.lζ->0,((Lμ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[g←g,2,2,1]=Collect[Coefficient[Cpdf[g←g,2],Lμ lζ ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[g←g,2,2,2]=Collect[Coefficient[Cpdf[g←g,2]/.Lμ->0,((lζ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[g←g,2,1,0]=Collect[Coefficient[Cpdf[g←g,2]/.lζ->0,Lμ ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[g←g,2,1,1]=Collect[Coefficient[Cpdf[g←g,2]/.Lμ->0,lζ ],{DELTA[_],CF,CA,TrNf},Simplify]

Cpdf[g←g,2,4]=Collect[Coefficient[Cpdf[g←g,2]/.lζ->Lμ,((Lμ)^4) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[g←g,2,3]=Collect[Coefficient[Cpdf[g←g,2]/.lζ->Lμ,((Lμ)^3) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[g←g,2,2]=Collect[Coefficient[Cpdf[g←g,2]/.lζ->Lμ,((Lμ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[g←g,2,1]=Collect[Coefficient[Cpdf[g←g,2]/.lζ->Lμ,((Lμ)^1) ],{DELTA[_],CF,CA,TrNf},Simplify]

Q ← Q’

Cpdf[q←qp,1,2,0]=Coefficient[Cpdf[q←qp,1]/.lζ->0,((Lμ)^2)]
Cpdf[q←qp,1,1,1]=Coefficient[Cpdf[q←qp,1],Lμ lζ]
Cpdf[q←qp,1,1,0]=Simplify@Coefficient[Cpdf[q←qp,1]/.lζ->0,Lμ]

Cpdf[q←qp,1,2]=Coefficient[Cpdf[q←qp,1]/.lζ->Lμ,((Lμ)^2)]
Cpdf[q←qp,1,1]=Simplify@Coefficient[Cpdf[q←qp,1]/.lζ->Lμ,Lμ]

Cpdf[q←qp,2,4,0]=Coefficient[Cpdf[q←qp,2]/.lζ->0,((Lμ)^4)]
Cpdf[q←qp,2,4,1]=Coefficient[Cpdf[q←qp,2],((Lμ)^3)lζ]
Cpdf[q←qp,2,4,2]=Coefficient[Cpdf[q←qp,2],((Lμ)^2) ((lζ)^2)]
Cpdf[q←qp,2,3,0]=Collect[Coefficient[Cpdf[q←qp,2]/.lζ->0,((Lμ)^3) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←qp,2,3,1]=Collect[Coefficient[Cpdf[q←qp,2],((Lμ)^2)lζ ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←qp,2,3,2]=Collect[Coefficient[Cpdf[q←qp,2],Lμ ((lζ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←qp,2,2,0]=Collect[Coefficient[Cpdf[q←qp,2]/.lζ->0,((Lμ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←qp,2,2,1]=Collect[Coefficient[Cpdf[q←qp,2],Lμ lζ ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←qp,2,2,2]=Collect[Coefficient[Cpdf[q←qp,2]/.Lμ->0,((lζ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←qp,2,1,0]=Collect[Coefficient[Cpdf[q←qp,2]/.lζ->0,Lμ ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←qp,2,1,1]=Collect[Coefficient[Cpdf[q←qp,2]/.Lμ->0,lζ ],{DELTA[_],CF,CA,TrNf},Simplify]

Cpdf[q←qp,2,4]=Collect[Coefficient[Cpdf[q←qp,2]/.lζ->Lμ,((Lμ)^4) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←qp,2,3]=Collect[Coefficient[Cpdf[q←qp,2]/.lζ->Lμ,((Lμ)^3) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←qp,2,2]=Collect[Coefficient[Cpdf[q←qp,2]/.lζ->Lμ,((Lμ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←qp,2,1]=Collect[Coefficient[Cpdf[q←qp,2]/.lζ->Lμ,((Lμ)^1) ],{DELTA[_],CF,CA,TrNf},Simplify]

Q ← (OverBar[Q])

Cpdf[q←qbar,1,2,0]=Coefficient[Cpdf[q←qbar,1]/.lζ->0,((Lμ)^2)]
Cpdf[q←qbar,1,1,1]=Coefficient[Cpdf[q←qbar,1],Lμ lζ]
Cpdf[q←qbar,1,1,0]=Simplify@Coefficient[Cpdf[q←qbar,1]/.lζ->0,Lμ]

Cpdf[q←qbar,1,2]=Coefficient[Cpdf[q←qbar,1]/.lζ->Lμ,((Lμ)^2)]
Cpdf[q←qbar,1,1]=Simplify@Coefficient[Cpdf[q←qbar,1]/.lζ->Lμ,Lμ]

Cpdf[q←qbar,2,4,0]=Coefficient[Cpdf[q←qbar,2]/.lζ->0,((Lμ)^4)]
Cpdf[q←qbar,2,4,1]=Coefficient[Cpdf[q←qbar,2],((Lμ)^3)lζ]
Cpdf[q←qbar,2,4,2]=Coefficient[Cpdf[q←qbar,2],((Lμ)^2) ((lζ)^2)]
Cpdf[q←qbar,2,3,0]=Collect[Coefficient[Cpdf[q←qbar,2]/.lζ->0,((Lμ)^3) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←qbar,2,3,1]=Collect[Coefficient[Cpdf[q←qbar,2],((Lμ)^2)lζ ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←qbar,2,3,2]=Collect[Coefficient[Cpdf[q←qbar,2],Lμ ((lζ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←qbar,2,2,0]=Collect[Coefficient[Cpdf[q←qbar,2]/.lζ->0,((Lμ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←qbar,2,2,1]=Collect[Coefficient[Cpdf[q←qbar,2],Lμ lζ ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←qbar,2,2,2]=Collect[Coefficient[Cpdf[q←qbar,2]/.Lμ->0,((lζ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←qbar,2,1,0]=Collect[Coefficient[Cpdf[q←qbar,2]/.lζ->0,Lμ ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←qbar,2,1,1]=Collect[Coefficient[Cpdf[q←qbar,2]/.Lμ->0,lζ ],{DELTA[_],CF,CA,TrNf},Simplify]

Cpdf[q←qbar,2,4]=Collect[Coefficient[Cpdf[q←qbar,2]/.lζ->Lμ,((Lμ)^4) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←qbar,2,3]=Collect[Coefficient[Cpdf[q←qbar,2]/.lζ->Lμ,((Lμ)^3) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←qbar,2,2]=Collect[Coefficient[Cpdf[q←qbar,2]/.lζ->Lμ,((Lμ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cpdf[q←qbar,2,1]=Collect[Coefficient[Cpdf[q←qbar,2]/.lζ->Lμ,((Lμ)^1) ],{DELTA[_],CF,CA,TrNf},Simplify]

Matching coefficients for TMD PDF (finite part)

Q ← Q

Cpdf[q←q,1,0]=Collect[Cpdf[q←q,1]/.{lζ->0,Lμ->0},DELTA[_],Simplify]

Cpdf[q←q,2,0]=Collect[Cpdf[q←q,2]/.{Lμ->0,lζ->0},{DELTA[_],CF,CA,TrNf},Simplify]

Q ← G

Cpdf[q←g,1,0]=Collect[Cpdf[q←g,1]/.{lζ->0,Lμ->0},DELTA[_],Simplify]

Cpdf[q←g,2,0]=Collect[Cpdf[q←g,2]/.{Lμ->0,lζ->0},{DELTA[_],CF,CA,TrNf},Simplify]

G ← Q

Cpdf[g←q,1,0]=Collect[Cpdf[g←q,1]/.{lζ->0,Lμ->0},DELTA[_],Simplify]

Cpdf[g←q,2,0]=Collect[Cpdf[g←q,2]/.{Lμ->0,lζ->0,PolyLog[2,2,1/2]->1/720 ((π^4)+30 ((Log[2])^4)-30 Log[8] Zeta[3])},{DELTA[_],CF,CA,TrNf},Simplify]

G ← G

Cpdf[g←g,1,0]=Collect[Cpdf[g←g,1]/.{lζ->0,Lμ->0},DELTA[_],Simplify]

Cpdf[g←g,2,0]=Collect[Cpdf[g←g,2]/.{Lμ->0,lζ->0,PolyLog[2,2,(1/2)]->(1/720) ((π^4)+30 ((Log[2])^4)-30 Log[8] Zeta[3])},{DELTA[_],CF,CA,TrNf},Simplify]

Q ← Q’

Cpdf[q←qp,1,0]=Collect[Cpdf[q←qp,1]/.{lζ->0,Lμ->0},DELTA[_],Simplify]

Cpdf[q←qp,2,0]=Collect[Cpdf[q←qp,2]/.{Lμ->0,lζ->0},{TR CF,PolyLog[2,1-x],Log[x]},Simplify]

Q ← (OverBar[Q])

Cpdf[q←qbar,1,0]=Collect[Cpdf[q←qbar,1]/.{lζ->0,Lμ->0},DELTA[_],Simplify]

Cpdf[q←qbar,2,0]=Collect[Cpdf[q←qbar,2]/.{Lμ->0,lζ->0},{PolyLog[_,_],Log[x]},Simplify]

Matching coefficients for TMD FF

Q -> Q

Cff[q->q,1]=CF (2 lζ Lμ-((Lμ)^2)-((π^2)/6)) DELTA[1-z]+((2 CF (-(((-1+z))^2)+Lμ (1+(z^2))-2 (1+(z^2)) Log[z]))/(-1+z));
Cff[q->q,2]=-((2 (CF^2) ((Lμ)^3) (1+(z^2)))/(-1+z))+((2 (CA-CF) CF (3-3 z+(π^2) (1+(z^2))) Log[1-z])/(3 (-1+z)))+(((2 CF (2 TrNf (9+z (-8+9 z))+CF (69+9 z (-14+9 z)+2 (π^2) (1+(z^2)))+CA (-93+(95-72 z) z+3 (π^2) (1+(z^2)))))/(3 (-1+z)))+4 (CA-7 CF) CF (-1+z) Log[1-z]-((2 (2 CA-3 CF) CF (1+(z^2)) ((Log[1-z])^2))/(-1+z))) Log[z]+(-((CF (CA (37-z (36+23 z))+2 (2 TrNf (1+(z^2))+3 CF (-22+z (34+3 z)))))/(6 (-1+z)))+((2 (2 CA-9 CF) CF (1+(z^2)) Log[1-z])/(-1+z))) ((Log[z])^2)+((CF (-9 CA (1+(z^2))+CF (29+51 (z^2))) ((Log[z])^3))/(3 (-1+z)))+((Lμ)^2) (((4 (CF^2) lζ (1+(z^2)))/(-1+z))+((CF (11 CA (1+(z^2))+2 (9 CF (((-1+z))^2)-2 TrNf (1+(z^2)))))/(3 (-1+z)))-((8 (CF^2) (1+(z^2)) Log[1-z])/(-1+z))+((2 (CF^2) (3+5 (z^2)) Log[z])/(-1+z)))+Lμ (((CF (-16 TrNf (4+z (-3+4 z))-3 CF (84 (((-1+z))^2)+(π^2) (1+(z^2)))+CA (-6 (π^2) (1+(z^2))+4 (77+z (-87+77 z)))))/(9 (-1+z)))+8 (CF^2) (-1+z) Log[1-z]+(((2 CF (6 CF (-5+8 z)+4 TrNf (1+(z^2))-CA (5+17 (z^2))))/(3 (-1+z)))+((24 (CF^2) (1+(z^2)) Log[1-z])/(-1+z))) Log[z]+((2 CF (CA-5 CF+(CA-11 CF) (z^2)) ((Log[z])^2))/(-1+z))+lζ (-4 (CF^2) (-1+z)-((8 (CF^2) (1+(z^2)) Log[z])/(-1+z))))+(4 (CA-6 CF) CF (-1+z)-((4 (CA-CF) CF (1+(z^2)) Log[1-z])/(-1+z))+((8 CF (CA+2 CF) (1+(z^2)) Log[z])/(-1+z))) PolyLog[2,z]-((4 (CA-CF) CF (1+(z^2)) PolyLog[3,1-z])/(-1+z))-((4 CF (3 CA+10 CF) (1+(z^2)) PolyLog[3,z])/(-1+z))+((CF (-9 CA (π^2) (((-1+z))^2)+9 CF (-30+13 (π^2)) (((-1+z))^2)+8 CA (1+z (99+z))-4 TrNf (19+z (18+19 z))-54 (CA-20 CF) (1+(z^2)) Zeta[3]))/(27 (-1+z)))+DELTA[1-z] ((((CF^2) ((Lμ)^4))/2)+((Lμ)^3) (-2 (CF^2) lζ+(2/9) CF (-11 CA+4 TrNf))+((Lμ)^2) (2 (CF^2) ((lζ)^2)+(1/3) CF lζ (11 CA-4 TrNf)+(1/18) CF (-134 CA+3 (2 CA-7 CF) (π^2)+40 TrNf))+Lμ ((1/9) CF (π^2) (-11 CA+4 TrNf)-(1/9) CF lζ (-134 CA+3 (2 CA+CF) (π^2)+40 TrNf))-(2/27) CF lζ (56 TrNf+CA (-202+189 Zeta[3]))+(1/648) CF (9 CF (π^4)+2 CA (4856-603 (π^2)+234 (π^4)-2772 Zeta[3])+8 TrNf (-328+45 (π^2)+252 Zeta[3])));

Q -> G

Cff[q->g,1]=((2 CF ((z^2)-Lμ (2-2 z+(z^2))+2 (2-2 z+(z^2)) Log[z]))/z);
Cff[q->g,2]=((2 (CF^2) ((Lμ)^3) (2+(-2+z) z))/z)+((2 (CA-CF) CF (2+(-2+z) z) ((Log[1-z])^3))/(3 z))-((CF (11 CF (-2+z) z+CA (80+44 z+62 (z^2))) ((Log[z])^3))/(3 z))+((Log[1-z])^2) (2 CF (-CA+CF) z-((2 (5 CA-4 CF) CF (2+(-2+z) z) Log[z])/z))+((Lμ)^2) (-((4 (CF^2) lζ (2+(-2+z) z))/z)+((CF (2 CA (-1+z) (31+z (7+4 z))-3 CF (12+z (-16+9 z))))/(3 z))+((4 CF (CA+CF) (2+(-2+z) z) Log[1-z])/z)-((2 CF (CF (4+3 (-2+z) z)+4 CA (1+z+(z^2))) Log[z])/z))+Log[1-z] (-((2 (CA-CF) CF (3 z+2 (π^2) (2+(-2+z) z)))/(3 z))+((4 CF (6 CF (z^2)+CA (22+z (-24+(15-4 z) z))) Log[z])/(3 z))+((2 (11 CA-4 CF) CF (2+(-2+z) z) ((Log[z])^2))/z))-((2 CA CF (π^2) (2+z (2+z)) Log[1+z])/(3 z))+((4 CA CF (2+z (2+z)) ((Log[1+z])^3))/(3 z))+Log[z] (((CF (-9 CF ((3+z) (-16+13 z)+6 (π^2) (2+(-2+z) z))+2 CA (54+12 (π^2) (2+(-2+z) z)+z (735+z (147+88 z)))))/(9 z))+4 CA CF z Log[1+z])+((Log[z])^2) (((CF (-3 CF z (8+z)+2 CA (-212+3 z (32+z (-3+8 z)))))/(6 z))+((6 CA CF (2+z (2+z)) Log[1+z])/z))+(4 CA CF z+((4 CA CF (2+z (2+z)) Log[z])/z)) PolyLog[2,-z]+(((8 CA CF (11+z (-12+(9-2 z) z)))/(3 z))-((4 (CA-CF) CF (2+(-2+z) z) Log[1-z])/z)+((4 CF (CA (2+(-6+z) z)-8 CF (2+(-2+z) z)) Log[z])/z)) PolyLog[2,z]+Lμ (((CF (3 CF (-24+22 z-8 (z^2)+3 (π^2) (2+(-2+z) z))+4 CA (3 (5+3 (-3+z) z)-2 (π^2) (2+(-1+z) z))))/(3 z))+((4 (CA-CF) CF (2+(-2+z) z) ((Log[1-z])^2))/z)+((2 CF (3 CF (-2+z) z+2 CA (8+z (6+7 z))) ((Log[z])^2))/z)+Log[1-z] (-8 (CF^2) z-((24 CA CF (2+(-2+z) z) Log[z])/z))+lζ (4 (CF^2) z+((8 (CF^2) (2+(-2+z) z) Log[z])/z))+Log[z] (((2 CF (3 CF (12+z (-12+7 z))-2 CA (-62+z (36+z (9+8 z)))))/(3 z))-((8 CA CF (2+z (2+z)) Log[1+z])/z))-((8 CA CF (2+z (2+z)) PolyLog[2,-z])/z)-((16 (CA-CF) CF (2+(-2+z) z) PolyLog[2,z])/z))-((4 (CA-CF) CF (2+(-2+z) z) PolyLog[3,1-z])/z)+((4 CA CF (2+z (2+z)) PolyLog[3,-z])/z)+((4 CF (8 CF (2+(-2+z) z)+CA (14+z (-6+7 z))) PolyLog[3,z])/z)-((8 CA CF (2+z (2+z)) PolyLog[3,(1/(1+z))])/z)+(1/(27 z))CF (27 CF (z (-38-3 (-11+(π^2)) z)-4 (2+(-2+z) z) Zeta[3])+2 CA (1564-558 z-693 (z^2)-340 (z^3)+6 (π^2) (-1+z) (11+z (-1+2 z))-108 (8+z (-9+4 z)) Zeta[3]));

G -> Q

Cff[g->q,1]=-2 TR (2 (-1+z) z+Lμ (1-2 z+2 (z^2))+(-2+4 z-4 (z^2)) Log[z]);
Cff[g->q,2]=2 CA ((Lμ)^3) TR (1+2 (-1+z) z)+(2/9) TR (4 TrNf (5+16 (-1+z) z)-9 CF ((π^2) (1+2 (-1+z) z)-2 (4+9 (-1+z) z))+CA (9 (π^2) (1+2 (-1+z) z)-2 (38+91 (-1+z) z))) Log[1-z]+(1/3) TR (9 CF+4 TrNf+2 (15 CF+4 TrNf) (-1+z) z+CA (-11-34 (-1+z) z)) ((Log[1-z])^2)-(2/3) (CA-CF) TR (1+2 (-1+z) z) ((Log[1-z])^3)+(1/3) TR (2 CA (11+62 z)-11 CF (1-2 z+4 (z^2))) ((Log[z])^3)+((Lμ)^2) (-4 CA lζ TR (1+2 (-1+z) z)+((TR (z (3 CF (-1+4 z)+8 TrNf (1+2 (-1+z) z))+CA (8-2 z (8+z (-40+47 z)))))/(3 z))+4 (CA+CF) TR (1+2 (-1+z) z) Log[1-z]+(-2 CF TR+4 (6 CA+CF) TR z-8 (CA+CF) TR (z^2)) Log[z])+Log[z] (((2 TR (-3 z (4 TrNf+8 TrNf (-1+z) z+CF (9+30 (-1+z) z))+CA (-8+z (45-90 z+86 (z^2)))) Log[1-z])/(3 z))+2 (2 CA-3 CF) TR (1+2 (-1+z) z) ((Log[1-z])^2)+(1/(9 z))TR (2 CA (24-z (165+(699-38 z) z+18 (π^2) (1+2 (-1+z) z)))+3 z (-8 TrNf (5+8 (-1+z) z)+CF ((π^2) (2+4 (-1+z) z)-3 (8+z (-73+76 z))))+72 CA (z^2) (1+z) Log[1+z]))+((Log[z])^2) (-2 (2 CA-9 CF) TR (1+2 (-1+z) z) Log[1-z]+((TR (4 CA (16+z (-22+(35-59 z) z))+z (8 TrNf (1+2 (-1+z) z)+3 CF (-7-52 z+68 (z^2)))-36 CA z (1+2 z (1+z)) Log[1+z]))/(6 z)))+(8 CA TR z (1+z)-4 CA TR (1+2 z (1+z)) Log[z]) PolyLog[2,-z]+(((8 TR (-1+z) (-12 CF (z^2)+CA (2+z (-1+11 z))))/(3 z))-4 CA TR (5+2 z (-7+5 z)) Log[z]) PolyLog[2,z]+Lμ ((1/(9 z))TR (CA (-24+z (-16+428 z-692 (z^2)+3 (π^2) (9+2 z (-5+9 z))))-2 z (-40 TrNf (1+2 (-1+z) z)+3 CF ((π^2) (2+4 (-1+z) z)-3 (8+z (-9+10 z)))))+(4/3) TR (CA (-11-10 (-1+z) z)+(9 CF+4 TrNf) (1+2 (-1+z) z)) Log[1-z]-4 (CA-CF) TR (1+2 (-1+z) z) ((Log[1-z])^2)-2 TR (-3 CF+6 CF (1-2 z) z+CA (6+28 z)) ((Log[z])^2)+lζ (-8 CA TR (-1+z) z+8 CA TR (1+2 (-1+z) z) Log[z])+Log[z] (-24 CF TR (1+2 (-1+z) z) Log[1-z]+((2 TR (z (CF (9+12 (1-3 z) z)-8 TrNf (1+2 (-1+z) z))+4 CA (-4+z (7+z (-23+33 z)))+12 CA z (1+2 z (1+z)) Log[1+z]))/(3 z)))+8 CA TR (1+2 z (1+z)) PolyLog[2,-z]+16 (CA-CF) TR (1+2 (-1+z) z) PolyLog[2,z])-4 CA TR (1+2 z (1+z)) PolyLog[3,-z]+4 TR (8 CF (1+2 (-1+z) z)+CA (3+2 z (-7+3 z))) PolyLog[3,z]+8 CA TR (1+2 z (1+z)) PolyLog[3,(1/(1+z))]+(1/(27 z))TR (CA (-296+2 z (-1223+z (139+774 z))+3 (π^2) (8+z (21-60 z+76 (z^2))))+z (4 TrNf (-9 (π^2) (1+2 (-1+z) z)+8 (7+17 (-1+z) z))-9 CF ((π^2) (9+14 (-1+z) z)-3 (63+z (-101+56 z))))+18 CA z (1+2 z (1+z)) Log[1+z] ((π^2)-2 ((Log[1+z])^2))-216 z (CA+4 CF-(CA+8 CF) z+2 (CA+4 CF) (z^2)) Zeta[3]);

G -> G

Cff[g->g,1]=CA (2 lζ Lμ-((Lμ)^2)-((π^2)/6)) DELTA[1-z]+((4 CA (((1-z+(z^2)))^2) (Lμ-2 Log[z]))/((-1+z) z));
Cff[g->g,2]=-((4 (CA^2) ((Lμ)^3) (((1+(-1+z) z))^2))/((-1+z) z))-(2/3) CA (CA-2 TrNf) Log[1-z]+((1/(9 (-1+z) z))(-8 CF TrNf (-1+z) (-6+z (135+z (81+82 z)))+4 CA TrNf (46+z (-91+z (90+z (-71+46 z))))+(CA^2) (-536+60 (π^2) (((1+(-1+z) z))^2)+z (-1123+z (726+z (-407+1072 z)))))-((8 (CA^2) (-1+z) (11+z (-1+11 z)) Log[1-z])/(3 z))+((4 (CA^2) (((1+(-1+z) z))^2) ((Log[1-z])^2))/((-1+z) z))) Log[z]+(((44 CF TrNf (-1+z) z (((1+z))^2)+4 (CA^2) (20+z (11+(-1+z) z (1+z) (-42+11 z)))) ((Log[z])^3))/(3 z (-1+(z^2))))+((Lμ)^2) (((8 (CA^2) lζ (((1+(-1+z) z))^2))/((-1+z) z))+((2 (-4 CA TrNf (((1+(-1+z) z))^2)+2 CF TrNf (-4+z+6 (z^2)+(z^3)-4 (z^4))+(CA^2) (55+z (-102+z (105+z (-102+55 z))))))/(3 (-1+z) z))-((16 (CA^2) (((1+(-1+z) z))^2) Log[1-z])/((-1+z) z))+((8 (2 (CA^2) (1+(((-1+z))^3) z)+CF TrNf z (-1+(z^2))) Log[z])/((-1+z) z)))+((Log[z])^2) (-((28 (CA^2) (((1+(-1+z) z))^2) Log[1-z])/((-1+z) z))+(1/(3 z (-1+(z^2))))((1+z) (4 CA TrNf (4+(-1+z) z (3+z (-9+4 z)))+2 CF TrNf (-1+z) (16+z (21+z (15+16 z)))+(CA^2) (220-3 z (93+z (-48+43 z))))+36 (CA^2) (-1+z) (((1+z+(z^2)))^2) Log[1+z]))+((8 (CA^2) (((1+z+(z^2)))^2) Log[z] PolyLog[2,-z])/(z (1+z)))+Lμ ((1/(9 z (-1+(z^2))))2 (8 CF TrNf (((-1+z))^2) (1+z) (13+z (-5+22 z))-4 CA TrNf (1+z) (23+z (-42+z (48+z (-42+23 z))))+(CA^2) (z (1+z) (109+z (-84+109 z))-3 (π^2) (1+z (-5+z (1+z (5+z (-1+5 z)))))))-((16 (CA^2) lζ (((1+(-1+z) z))^2) Log[z])/((-1+z) z))-((8 (3 CF TrNf (-1+z) z (((1+z))^2)+(CA^2) (4+z (-1+(-3+z) z) (-3+z (-1+3 z)))) ((Log[z])^2))/(z (-1+(z^2))))+Log[z] (((48 (CA^2) (((1+(-1+z) z))^2) Log[1-z])/((-1+z) z))-((4 (1+z) (-4 CA TrNf z (1+z)+2 CF TrNf (8+3 z (3+z))+(CA^2) (-88+z (47+z (-61+44 z))))+48 (CA^2) (((1+z+(z^2)))^2) Log[1+z])/(3 z (1+z))))-((16 (CA^2) (((1+z+(z^2)))^2) PolyLog[2,-z])/(z (1+z))))+(-((8 (CA^2) (-1+z) (11+z (-1+11 z)))/(3 z))+((8 (CA^2) (7+z (-5+z (7+z (5+z (-7+5 z))))) Log[z])/(z (-1+(z^2))))) PolyLog[2,z]+((8 (CA^2) (((1+z+(z^2)))^2) PolyLog[3,-z])/(z (1+z)))-((8 (CA^2) (15+z (-11+z (15+z (11+z (-15+11 z))))) PolyLog[3,z])/(z (-1+(z^2))))-((16 (CA^2) (((1+z+(z^2)))^2) PolyLog[3,(1/(1+z))])/(z (1+z)))+(1/(27 z (-1+(z^2))))4 ((1+z) (2 CF TrNf (((-1+z))^2) (139+z (409+301 z))+CA TrNf (-139+z (249+z (-276+11 (21-11 z) z)))+(CA^2) (-817+3 (π^2) (((-1+z))^2) (11+z (-1+11 z))+z (1029-2 z (129+z (-555+431 z)))))+9 (CA^2) ((-1+z) (((1+z+(z^2)))^2) Log[1+z] (-(π^2)+2 ((Log[1+z])^2))+6 (9+z (-10+z (9+z (10+z (-9+10 z))))) Zeta[3]))+DELTA[1-z] ((((CA^2) ((Lμ)^4))/2)+((Lμ)^2) (2 (CA^2) ((lζ)^2)-(1/18) CA (CA (134+15 (π^2))-40 TrNf)+(1/3) CA lζ (11 CA-4 TrNf))+((Lμ)^3) (-2 (CA^2) lζ+(2/9) CA (-11 CA+4 TrNf))+Lμ ((1/9) CA (π^2) (-11 CA+4 TrNf)-(1/9) CA lζ (CA (-134+9 (π^2))+40 TrNf))-(2/27) CA lζ (56 TrNf+CA (-202+189 Zeta[3]))+(1/648) CA (CA (9712-1206 (π^2)+477 (π^4)-5544 Zeta[3])+8 TrNf (-328+45 (π^2)+252 Zeta[3])));

Q -> Q’

Cff[q->qp,1]=0;
Cff[q->qp,2]=((2 CF TR (-1+z) (148+z (859+436 z)))/(27 z))-((4 CF TR (-12+z (174+z (51+32 z))) Log[z])/(9 z))-((CF TR (-32+3 z (11+z (11+8 z))) ((Log[z])^2))/(3 z))+(22/3) CF TR (1+z) ((Log[z])^3)+((Lμ)^2) (-((2 CF TR (-1+z) (4+z (7+4 z)))/(3 z))+4 CF TR (1+z) Log[z])+Lμ (-((4 CF TR (-1+z) (-2+z (19+4 z)))/(3 z))+((4 CF TR (-8+z (3+z (15+8 z))) Log[z])/(3 z))-12 CF TR (1+z) ((Log[z])^2))-((8 CF TR (-1+z) (2+z (-1+2 z)) PolyLog[2,1-z])/(3 z));

Q -> (OverBar[Q])

Cff[q->qbar,1]=0;
Cff[q->qbar,2]=-((3 (CA-2 CF) CF (1+(z^2)) ((Log[z])^3))/(1+z))+((2 (CA-2 CF) CF ((Log[z])^2) (-2 (1+z) (2+z)+3 (1+(z^2)) Log[1+z]))/(1+z))+Log[z] (-4 (CA-2 CF) CF (-1+z) Log[1-z]+(CA-2 CF) CF (-19+5 z+4 (1+z) Log[1+z]))+(4 (CA-2 CF) CF (1+z)+((4 (CA-2 CF) CF (1+(z^2)) Log[z])/(1+z))) PolyLog[2,-z]+Lμ (-((2 (CA-2 CF) CF (-12+(π^2)+(12+(π^2)) (z^2)))/(3 (1+z)))+((2 (CA-2 CF) CF (1+(z^2)) ((Log[z])^2))/(1+z))+((4 (CA-2 CF) CF Log[z] ((((1+z))^2)-2 (1+(z^2)) Log[1+z]))/(1+z))-((8 (CA-2 CF) CF (1+(z^2)) PolyLog[2,-z])/(1+z)))+(-4 (CA-2 CF) CF (-1+z)-((4 (CA-2 CF) CF (1+(z^2)) Log[z])/(1+z))) PolyLog[2,z]+((4 (CA-2 CF) CF (1+(z^2)) PolyLog[3,-z])/(1+z))+((8 (CA-2 CF) CF (1+(z^2)) PolyLog[3,z])/(1+z))-((8 (CA-2 CF) CF (1+(z^2)) PolyLog[3,(1/(1+z))])/(1+z))-(((CA-2 CF) CF (45-45 (z^2)-(π^2) (1+z) (-1+3 z)+2 (1+(z^2)) Log[1+z] ((π^2)-2 ((Log[1+z])^2))-6 (1+(z^2)) Zeta[3]))/(3 (1+z)));

Matching coefficients for TMD FF (logarithmical part)

Q -> Q

Cff[q->q,1,2,0]=Coefficient[Cff[q->q,1]/.lζ->0,((Lμ)^2)]
Cff[q->q,1,1,1]=Coefficient[Cff[q->q,1],Lμ lζ]
Cff[q->q,1,1,0]=Simplify@Coefficient[Cff[q->q,1]/.lζ->0,Lμ]

Cff[q->q,1,2]=Coefficient[Cff[q->q,1]/.lζ->Lμ,((Lμ)^2)]
Cff[q->q,1,1]=Simplify@Coefficient[Cff[q->q,1]/.lζ->Lμ,Lμ]

Cff[q->q,2,4,0]=Coefficient[Cff[q->q,2]/.lζ->0,((Lμ)^4)]
Cff[q->q,2,4,1]=Coefficient[Cff[q->q,2],((Lμ)^3)lζ]
Cff[q->q,2,4,2]=Coefficient[Cff[q->q,2],((Lμ)^2) ((lζ)^2)]
Cff[q->q,2,3,0]=Collect[Coefficient[Cff[q->q,2]/.lζ->0,((Lμ)^3) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->q,2,3,1]=Collect[Coefficient[Cff[q->q,2],((Lμ)^2)lζ ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->q,2,3,2]=Collect[Coefficient[Cff[q->q,2],Lμ ((lζ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->q,2,2,0]=Collect[Coefficient[Cff[q->q,2]/.lζ->0,((Lμ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->q,2,2,1]=Collect[Coefficient[Cff[q->q,2],Lμ lζ ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->q,2,2,2]=Collect[Coefficient[Cff[q->q,2]/.Lμ->0,((lζ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->q,2,1,0]=Collect[Coefficient[Cff[q->q,2]/.lζ->0,Lμ ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->q,2,1,1]=Collect[Coefficient[Cff[q->q,2]/.Lμ->0,lζ ],{DELTA[_],CF,CA,TrNf},Simplify]

Cff[q->q,2,4]=Collect[Coefficient[Cff[q->q,2]/.lζ->Lμ,((Lμ)^4) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->q,2,3]=Collect[Coefficient[Cff[q->q,2]/.lζ->Lμ,((Lμ)^3) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->q,2,2]=Collect[Coefficient[Cff[q->q,2]/.lζ->Lμ,((Lμ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->q,2,1]=Collect[Coefficient[Cff[q->q,2]/.lζ->Lμ,((Lμ)^1) ],{DELTA[_],CF,CA,TrNf},Simplify]

Q -> G

Cff[q->g,1,2,0]=Coefficient[Cff[q->g,1]/.lζ->0,((Lμ)^2)]
Cff[q->g,1,1,1]=Coefficient[Cff[q->g,1],Lμ lζ]
Cff[q->g,1,1,0]=Simplify@Coefficient[Cff[q->g,1]/.lζ->0,Lμ]

Cff[q->g,1,2]=Coefficient[Cff[q->g,1]/.lζ->Lμ,((Lμ)^2)]
Cff[q->g,1,1]=Simplify@Coefficient[Cff[q->g,1]/.lζ->Lμ,Lμ]

Cff[q->g,2,4,0]=Coefficient[Cff[q->g,2]/.lζ->0,((Lμ)^4)]
Cff[q->g,2,4,1]=Coefficient[Cff[q->g,2],((Lμ)^3)lζ]
Cff[q->g,2,4,2]=Coefficient[Cff[q->g,2],((Lμ)^2) ((lζ)^2)]
Cff[q->g,2,3,0]=Collect[Coefficient[Cff[q->g,2]/.lζ->0,((Lμ)^3) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->g,2,3,1]=Collect[Coefficient[Cff[q->g,2],((Lμ)^2)lζ ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->g,2,3,2]=Collect[Coefficient[Cff[q->g,2],Lμ ((lζ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->g,2,2,0]=Collect[Coefficient[Cff[q->g,2]/.lζ->0,((Lμ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->g,2,2,1]=Collect[Coefficient[Cff[q->g,2],Lμ lζ ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->g,2,2,2]=Collect[Coefficient[Cff[q->g,2]/.Lμ->0,((lζ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->g,2,1,0]=Collect[Coefficient[Cff[q->g,2]/.lζ->0,Lμ ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->g,2,1,1]=Collect[Coefficient[Cff[q->g,2]/.Lμ->0,lζ ],{DELTA[_],CF,CA,TrNf},Simplify]

Cff[q->g,2,4]=Collect[Coefficient[Cff[q->g,2]/.lζ->Lμ,((Lμ)^4) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->g,2,3]=Collect[Coefficient[Cff[q->g,2]/.lζ->Lμ,((Lμ)^3) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->g,2,2]=Collect[Coefficient[Cff[q->g,2]/.lζ->Lμ,((Lμ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->g,2,1]=Collect[Coefficient[Cff[q->g,2]/.lζ->Lμ,((Lμ)^1) ],{DELTA[_],CF,CA,TrNf},Simplify]

G -> Q

Cff[g->q,1,2,0]=Coefficient[Cff[g->q,1]/.lζ->0,((Lμ)^2)]
Cff[g->q,1,1,1]=Coefficient[Cff[g->q,1],Lμ lζ]
Cff[g->q,1,1,0]=Simplify@Coefficient[Cff[g->q,1]/.lζ->0,Lμ]

Cff[g->q,1,2]=Coefficient[Cff[g->q,1]/.lζ->Lμ,((Lμ)^2)]
Cff[g->q,1,1]=Simplify@Coefficient[Cff[g->q,1]/.lζ->Lμ,Lμ]

Cff[g->q,2,4,0]=Coefficient[Cff[g->q,2]/.lζ->0,((Lμ)^4)]
Cff[g->q,2,4,1]=Coefficient[Cff[g->q,2],((Lμ)^3)lζ]
Cff[g->q,2,4,2]=Coefficient[Cff[g->q,2],((Lμ)^2) ((lζ)^2)]
Cff[g->q,2,3,0]=Collect[Coefficient[Cff[g->q,2]/.lζ->0,((Lμ)^3) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[g->q,2,3,1]=Collect[Coefficient[Cff[g->q,2],((Lμ)^2)lζ ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[g->q,2,3,2]=Collect[Coefficient[Cff[g->q,2],Lμ ((lζ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[g->q,2,2,0]=Collect[Coefficient[Cff[g->q,2]/.lζ->0,((Lμ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[g->q,2,2,1]=Collect[Coefficient[Cff[g->q,2],Lμ lζ ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[g->q,2,2,2]=Collect[Coefficient[Cff[g->q,2]/.Lμ->0,((lζ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[g->q,2,1,0]=Collect[Coefficient[Cff[g->q,2]/.lζ->0,Lμ ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[g->q,2,1,1]=Collect[Coefficient[Cff[g->q,2]/.Lμ->0,lζ ],{DELTA[_],CF,CA,TrNf},Simplify]

Cff[g->q,2,4]=Collect[Coefficient[Cff[g->q,2]/.lζ->Lμ,((Lμ)^4) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[g->q,2,3]=Collect[Coefficient[Cff[g->q,2]/.lζ->Lμ,((Lμ)^3) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[g->q,2,2]=Collect[Coefficient[Cff[g->q,2]/.lζ->Lμ,((Lμ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[g->q,2,1]=Collect[Coefficient[Cff[g->q,2]/.lζ->Lμ,((Lμ)^1) ],{DELTA[_],CF,CA,TrNf},Simplify]

G -> G

Cff[g->g,1,2,0]=Coefficient[Cff[g->g,1]/.lζ->0,((Lμ)^2)]
Cff[g->g,1,1,1]=Coefficient[Cff[g->g,1],Lμ lζ]
Cff[g->g,1,1,0]=Simplify@Coefficient[Cff[g->g,1]/.lζ->0,Lμ]

Cff[g->g,1,2]=Coefficient[Cff[g->g,1]/.lζ->Lμ,((Lμ)^2)]
Cff[g->g,1,1]=Simplify@Coefficient[Cff[g->g,1]/.lζ->Lμ,Lμ]

Cff[g->g,2,4,0]=Coefficient[Cff[g->g,2]/.lζ->0,((Lμ)^4)]
Cff[g->g,2,4,1]=Coefficient[Cff[g->g,2],((Lμ)^3)lζ]
Cff[g->g,2,4,2]=Coefficient[Cff[g->g,2],((Lμ)^2) ((lζ)^2)]
Cff[g->g,2,3,0]=Collect[Coefficient[Cff[g->g,2]/.lζ->0,((Lμ)^3) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[g->g,2,3,1]=Collect[Coefficient[Cff[g->g,2],((Lμ)^2)lζ ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[g->g,2,3,2]=Collect[Coefficient[Cff[g->g,2],Lμ ((lζ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[g->g,2,2,0]=Collect[Coefficient[Cff[g->g,2]/.lζ->0,((Lμ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[g->g,2,2,1]=Collect[Coefficient[Cff[g->g,2],Lμ lζ ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[g->g,2,2,2]=Collect[Coefficient[Cff[g->g,2]/.Lμ->0,((lζ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[g->g,2,1,0]=Collect[Coefficient[Cff[g->g,2]/.lζ->0,Lμ ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[g->g,2,1,1]=Collect[Coefficient[Cff[g->g,2]/.Lμ->0,lζ ],{DELTA[_],CF,CA,TrNf},Simplify]

Cff[g->g,2,4]=Collect[Coefficient[Cff[g->g,2]/.lζ->Lμ,((Lμ)^4) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[g->g,2,3]=Collect[Coefficient[Cff[g->g,2]/.lζ->Lμ,((Lμ)^3) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[g->g,2,2]=Collect[Coefficient[Cff[g->g,2]/.lζ->Lμ,((Lμ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[g->g,2,1]=Collect[Coefficient[Cff[g->g,2]/.lζ->Lμ,((Lμ)^1) ],{DELTA[_],CF,CA,TrNf},Simplify]

Q -> Q’

Cff[q->qp,1,2,0]=Coefficient[Cff[q->qp,1]/.lζ->0,((Lμ)^2)]
Cff[q->qp,1,1,1]=Coefficient[Cff[q->qp,1],Lμ lζ]
Cff[q->qp,1,1,0]=Simplify@Coefficient[Cff[q->qp,1]/.lζ->0,Lμ]

Cff[q->qp,1,2]=Coefficient[Cff[q->qp,1]/.lζ->Lμ,((Lμ)^2)]
Cff[q->qp,1,1]=Simplify@Coefficient[Cff[q->qp,1]/.lζ->Lμ,Lμ]

Cff[q->qp,2,4,0]=Coefficient[Cff[q->qp,2]/.lζ->0,((Lμ)^4)]
Cff[q->qp,2,4,1]=Coefficient[Cff[q->qp,2],((Lμ)^3)lζ]
Cff[q->qp,2,4,2]=Coefficient[Cff[q->qp,2],((Lμ)^2) ((lζ)^2)]
Cff[q->qp,2,3,0]=Collect[Coefficient[Cff[q->qp,2]/.lζ->0,((Lμ)^3) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->qp,2,3,1]=Collect[Coefficient[Cff[q->qp,2],((Lμ)^2)lζ ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->qp,2,3,2]=Collect[Coefficient[Cff[q->qp,2],Lμ ((lζ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->qp,2,2,0]=Collect[Coefficient[Cff[q->qp,2]/.lζ->0,((Lμ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->qp,2,2,1]=Collect[Coefficient[Cff[q->qp,2],Lμ lζ ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->qp,2,2,2]=Collect[Coefficient[Cff[q->qp,2]/.Lμ->0,((lζ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->qp,2,1,0]=Collect[Coefficient[Cff[q->qp,2]/.lζ->0,Lμ ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->qp,2,1,1]=Collect[Coefficient[Cff[q->qp,2]/.Lμ->0,lζ ],{DELTA[_],CF,CA,TrNf},Simplify]

Cff[q->qp,2,4]=Collect[Coefficient[Cff[q->qp,2]/.lζ->Lμ,((Lμ)^4) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->qp,2,3]=Collect[Coefficient[Cff[q->qp,2]/.lζ->Lμ,((Lμ)^3) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->qp,2,2]=Collect[Coefficient[Cff[q->qp,2]/.lζ->Lμ,((Lμ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->qp,2,1]=Collect[Coefficient[Cff[q->qp,2]/.lζ->Lμ,((Lμ)^1) ],{DELTA[_],CF,CA,TrNf},Simplify]

Q -> (OverBar[Q])

Cff[q->qbar,1,2,0]=Coefficient[Cff[q->qbar,1]/.lζ->0,((Lμ)^2)]
Cff[q->qbar,1,1,1]=Coefficient[Cff[q->qbar,1],Lμ lζ]
Cff[q->qbar,1,1,0]=Simplify@Coefficient[Cff[q->qbar,1]/.lζ->0,Lμ]

Cff[q->qbar,1,2]=Coefficient[Cff[q->qbar,1]/.lζ->Lμ,((Lμ)^2)]
Cff[q->qbar,1,1]=Simplify@Coefficient[Cff[q->qbar,1]/.lζ->Lμ,Lμ]

Cff[q->qbar,2,4,0]=Coefficient[Cff[q->qbar,2]/.lζ->0,((Lμ)^4)]
Cff[q->qbar,2,4,1]=Coefficient[Cff[q->qbar,2],((Lμ)^3)lζ]
Cff[q->qbar,2,4,2]=Coefficient[Cff[q->qbar,2],((Lμ)^2) ((lζ)^2)]
Cff[q->qbar,2,3,0]=Collect[Coefficient[Cff[q->qbar,2]/.lζ->0,((Lμ)^3) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->qbar,2,3,1]=Collect[Coefficient[Cff[q->qbar,2],((Lμ)^2)lζ ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->qbar,2,3,2]=Collect[Coefficient[Cff[q->qbar,2],Lμ ((lζ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->qbar,2,2,0]=Collect[Coefficient[Cff[q->qbar,2]/.lζ->0,((Lμ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->qbar,2,2,1]=Collect[Coefficient[Cff[q->qbar,2],Lμ lζ ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->qbar,2,2,2]=Collect[Coefficient[Cff[q->qbar,2]/.Lμ->0,((lζ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->qbar,2,1,0]=Collect[Coefficient[Cff[q->qbar,2]/.lζ->0,Lμ ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->qbar,2,1,1]=Collect[Coefficient[Cff[q->qbar,2]/.Lμ->0,lζ ],{DELTA[_],CF,CA,TrNf},Simplify]

Cff[q->qbar,2,4]=Collect[Coefficient[Cff[q->qbar,2]/.lζ->Lμ,((Lμ)^4) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->qbar,2,3]=Collect[Coefficient[Cff[q->qbar,2]/.lζ->Lμ,((Lμ)^3) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->qbar,2,2]=Collect[Coefficient[Cff[q->qbar,2]/.lζ->Lμ,((Lμ)^2) ],{DELTA[_],CF,CA,TrNf},Simplify]
Cff[q->qbar,2,1]=Collect[Coefficient[Cff[q->qbar,2]/.lζ->Lμ,((Lμ)^1) ],{DELTA[_],CF,CA,TrNf},Simplify]

Matching coefficients for TMD FF (finite part)

Q -> Q

Cff[q->q,1,0]=Collect[Cff[q->q,1]/.{lζ->0,Lμ->0},DELTA[_],Simplify]

Cff[q->q,2,0]=Collect[Cff[q->q,2]/.{Lμ->0,lζ->0},{DELTA[_],CF,CA,TrNf},Simplify]

Q -> G

Cff[q->g,1,0]=Collect[Cff[q->g,1]/.{lζ->0,Lμ->0},DELTA[_],Simplify]

Cff[q->g,2,0]=Collect[Cff[q->g,2]/.{Lμ->0,lζ->0},{DELTA[_],CF,CA,TrNf},Simplify]

G -> Q

Cff[g->q,1,0]=Collect[Cff[g->q,1]/.{lζ->0,Lμ->0},DELTA[_],Simplify]

Cff[g->q,2,0]=Collect[Cff[g->q,2]/.{Lμ->0,lζ->0},{DELTA[_],CF,CA,TrNf},Simplify]

G -> G

Cff[g->g,1,0]=Collect[Cff[g->g,1]/.{lζ->0,Lμ->0},DELTA[_],Simplify]

Cff[g->g,2,0]=Collect[Cff[g->g,2]/.{Lμ->0,lζ->0},{DELTA[_],CF,CA,TrNf},Simplify]

Q -> Q’

Cff[q->qp,1,0]=Collect[Cff[q->qp,1]/.{lζ->0,Lμ->0},DELTA[_],Simplify]

Cff[q->qp,2,0]=Collect[Cff[q->qp,2]/.{Lμ->0,lζ->0},{DELTA[_],CF,CA,TrNf},Simplify]

Q -> (OverBar[Q])

Cff[q->qbar,1,0]=Collect[Cff[q->qbar,1]/.{lζ->0,Lμ->0},DELTA[_],Simplify]

Cff[q->qbar,2,0]=Collect[Cff[q->qbar,2]/.{Lμ->0,lζ->0},{DELTA[_],CF,CA,TrNf},Simplify]