D. Gutierrez-Reyes, I.Scimemi, A.Vladimirov
Matching coefficients for transversity TMD distributions at NNLO
based on arXiv:18??.????

Abstract:
This file contains the results of calculation of transversity and pretzelosity TMD PDF, and the small - b matching coefficients. The calculation for transversity TMD FF and the corresponding small - b matching coefficients are also included.
This is short version, that includes only final expressions.

VERSION:1.0

Table of content :
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))

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:
Through all the file the following convention for plus-distributions is used:
Only the singular at x->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]

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 FF 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 transversity TMD PDF

Q ← Q

Cpdf[q←q,1]=((4 CF Lμ x)/(-1+x))+CF (2 lζ Lμ-((Lμ)^2)-((π^2)/6)) DELTA[1-x];
Cpdf[q←q,2]=-((4 (CF^2) ((Lμ)^3) x)/(-1+x))+((2 CF (CA (-3+(3-2 (π^2)) x)+CF (3+x (-3+4 (π^2)+12 x))) Log[1-x])/(3 (-1+x)))+(-((4 CF x (-38 CA+10 TrNf+3 CF (12+(π^2)+6 x)))/(9 (-1+x)))+((4 (2 CA-3 CF) CF x ((Log[1-x])^2))/(-1+x))) Log[x]+(-((CF (-11 CA+9 CF+4 TrNf) x)/(3 (-1+x)))-((4 (CF^2) x Log[1-x])/(-1+x))) ((Log[x])^2)+((2 CA CF x ((Log[x])^3))/(3 (-1+x)))+((Lμ)^2) (((8 (CF^2) lζ x)/(-1+x))+((2 CF (11 CA-4 TrNf) x)/(3 (-1+x)))-((16 (CF^2) x Log[1-x])/(-1+x))+((8 (CF^2) x Log[x])/(-1+x)))+Lμ (-((2 CF (40 TrNf x+3 CF (-6+(12+(π^2)-6 x) x)+CA (9+x (-152+6 (π^2)+9 x))))/(9 (-1+x)))+(-((4 CF (-11 CA+9 CF+4 TrNf) x)/(3 (-1+x)))-((16 (CF^2) x Log[1-x])/(-1+x))) Log[x]+((4 CA CF x ((Log[x])^2))/(-1+x)))+(((8 (CA-CF) CF x Log[1-x])/(-1+x))+((8 (CA-3 CF) CF x Log[x])/(-1+x))) PolyLog[2,x]+((8 (CA-CF) CF x PolyLog[3,1-x])/(-1+x))+((8 CF (-2 CA+5 CF) x PolyLog[3,x])/(-1+x))-(1/(27 (-1+x)))2 CF (36 CF x ((π^2)+6 x) ArcTanh[1-2 x]+CA (63+x (-530+63 x+162 Zeta[3]))+2 (TrNf (-9+(74-9 x) x)+27 CF ((((-1+x))^2)+10 x Zeta[3])))+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)+8 TrNf (-328+45 (π^2)+252 Zeta[3])+CA (9712-1206 (π^2)+27 (π^4)-270 ((Log[2])^4)+6480 PolyLog[2,2,(1/2)]+18 (-308+45 Log[2]) Zeta[3])));

Q ← (OverBar[Q])

Cpdf[q←qbar,1]=0;
Cpdf[q←qbar,2]=-((2 (CA-2 CF) CF x ((Log[x])^3))/(3 (1+x)))+((Log[x])^2) (((8 (CA-2 CF) CF x Log[1-x])/(1+x))+((4 (CA-2 CF) CF x Log[1+x])/(1+x)))-((4 (CA-2 CF) CF x Log[x] ((π^2)+6 ((Log[1+x])^2)))/(3 (1+x)))+((8 (CA-2 CF) CF x Log[x] PolyLog[2,1-x])/(1+x))-((8 (CA-2 CF) CF x Log[x] PolyLog[2,-x])/(1+x))+Lμ (((2 (CA-2 CF) CF (-3+2 (π^2) x+3 (x^2)))/(3 (1+x)))-((4 (CA-2 CF) CF x ((Log[x])^2))/(1+x))+((16 (CA-2 CF) CF x Log[x] Log[1+x])/(1+x))+((16 (CA-2 CF) CF x PolyLog[2,-x])/(1+x)))+((8 (CA-2 CF) CF x PolyLog[3,-x])/(1+x))+((16 (CA-2 CF) CF x PolyLog[3,x])/(1+x))-((16 (CA-2 CF) CF x PolyLog[3,(x/(1+x))])/(1+x))+(((CA-2 CF) CF (-4 (π^2) x Log[1+x]+8 x ((Log[1+x])^3)+3 (-1+(x^2)+4 x Zeta[3])))/(3 (1+x)));

Matching coefficients for transversity 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 ← (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 transversity 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 ← (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 transversity TMD FF

Q -> Q

Cff[q->q,1]=CF (2 lζ Lμ-((Lμ)^2)-((π^2)/6)) DELTA[1-z]+((4 CF z (Lμ-2 Log[z]))/(-1+z));
Cff[q->q,2]=-((4 (CF^2) ((Lμ)^3) z)/(-1+z))+((2 (CA-CF) CF (3+2 (π^2)-3 z) z Log[1-z])/(3 (-1+z)))+(((2 CF (20 TrNf z+CF (-6+(39+4 (π^2)-9 z) z)+CA (3+z (-79+6 (π^2)+6 z))))/(3 (-1+z)))+((4 CF (-2 CA+3 CF) z ((Log[1-z])^2))/(-1+z))) Log[z]+(-((CF (-11 CA+45 CF+4 TrNf) z)/(3 (-1+z)))+((4 (2 CA-9 CF) CF z Log[1-z])/(-1+z))) ((Log[z])^2)+((2 CF (-9 CA+40 CF) z ((Log[z])^3))/(3 (-1+z)))+((Lμ)^2) (((8 (CF^2) lζ z)/(-1+z))+((2 CF (11 CA-4 TrNf) z)/(3 (-1+z)))-((16 (CF^2) z Log[1-z])/(-1+z))+((16 (CF^2) z Log[z])/(-1+z)))+Lμ (-((2 CF (40 TrNf z+3 CF (-6+(12+(π^2)-6 z) z)+CA (9+z (-152+6 (π^2)+9 z))))/(9 (-1+z)))-((16 (CF^2) lζ z Log[z])/(-1+z))+(((4 CF (-11 CA+9 CF+4 TrNf) z)/(3 (-1+z)))+((48 (CF^2) z Log[1-z])/(-1+z))) Log[z]+((4 (CA-8 CF) CF z ((Log[z])^2))/(-1+z)))+(((8 CF (-CA+CF) z Log[1-z])/(-1+z))+((16 CF (CA+2 CF) z Log[z])/(-1+z))) PolyLog[2,z]+((8 CF (-CA+CF) z PolyLog[3,1-z])/(-1+z))-((8 CF (3 CA+10 CF) z PolyLog[3,z])/(-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])))-(1/(27 (-1+z)))2 CF (CA (63+z (-530+63 z+54 Zeta[3]))+2 (TrNf (-9+(74-9 z) z)+27 CF ((((-1+z))^2)-20 z Zeta[3])));

Q -> (OverBar[Q])

Cff[q->qbar,1]=0;
Cff[q->qbar,2]=-2 (CA-2 CF) CF (-1+z) Log[z]+((6 (CA-2 CF) CF z ((Log[z])^3))/(1+z))+((12 CF (-CA+2 CF) z ((Log[z])^2) Log[1+z])/(1+z))+((8 CF (-CA+2 CF) z Log[z] PolyLog[2,-z])/(1+z))+Lμ (((2 (CA-2 CF) CF (-3+2 (π^2) z+3 (z^2)))/(3 (1+z)))+((4 CF (-CA+2 CF) z ((Log[z])^2))/(1+z))+((16 (CA-2 CF) CF z Log[z] Log[1+z])/(1+z))+((16 (CA-2 CF) CF z PolyLog[2,-z])/(1+z)))+((8 (CA-2 CF) CF z Log[z] PolyLog[2,z])/(1+z))+((8 CF (-CA+2 CF) z PolyLog[3,-z])/(1+z))+((16 CF (-CA+2 CF) z PolyLog[3,z])/(1+z))+((16 (CA-2 CF) CF z PolyLog[3,(1/(1+z))])/(1+z))+(((CA-2 CF) CF (4 (π^2) z Log[1+z]-8 z ((Log[1+z])^3)+3 (-1+(z^2)-4 z Zeta[3])))/(3 (1+z)));

Matching coefficients for transversity 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 -> (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 transversity 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 -> (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]