SplittingFunction
SplittingFunction[pxy]
is a database of splitting functions in the MS scheme.
SplittingFunction["Pqq", x]
, SplittingFunction["Pqg", x]
, SplittingFunction["Pgq", x]
and SplittingFunction["Pgg", x]
yield the lowest order splitting functions.
SplittingFunction["PQQS",x]
, SplittingFunction["PQQNS",x]
and SplittingFunction["PQG",x]
are the next to leading order splitting functions.
SplittingFunction has an option Polarization.
SplittingFunction["Pqq", x, Polarization -> 0]
returns the unpolarized and SplittingFunction["Pqq", x, Polarization -> 1]
the polarized splitting functions.
See also
Overview, AnomalousDimension.
Examples
Unpolarized case:
In general the argument should be a string, but if the variables Pqq etc. have no value, you can omit the ““.
SplittingFunction[Pqq, Polarization -> 0] /. FCGV[z_] :> ToExpression[z]
CF(6δ(1−x)−4x+8(1−x1)+−4)
SplittingFunction[Pqg, Polarization -> 0] /. FCGV[z_] :> ToExpression[z]
(16x2−16x+8)Tf
SplittingFunction[Pgq, Polarization -> 0] /. FCGV[z_] :> ToExpression[z]
(4x+x8−8)CF
SplittingFunction[Pgg, Polarization -> 0] /. FCGV[z_] :> ToExpression[z]
8CA(−x2+1211δ(1−x)+x+(1−x1)++x1−2)−38NfTfδ(1−x)
SplittingFunction[aqq, Polarization -> 0] /. FCGV[z_] :> ToExpression[z]
CF((7−4ζ(2))δ(1−x)+2x+(2x+2)log((1−x)x)−4(1−xlog(x)+(1−xlog(1−x))+)−4)
SplittingFunction[agq, Polarization -> 0] /. FCGV[z_] :> ToExpression[z]
CF(−2x−x4+(−2x−x4+4)log((1−x)x)+2)
SplittingFunction[aqg, Polarization -> 0] /. FCGV[z_] :> ToExpression[z]
Tf((−8x2+8x−4)log((1−x)x)−4)
SplittingFunction[agg, Polarization -> 0] /. FCGV[z_] :> ToExpression[z]
Polarized case:
SplittingFunction[Pqq, Polarization -> 1] /. FCGV[z_] :> ToExpression[z]
CF(6δ(1−x)−4x+8(1−x1)+−4)
SplittingFunction[Pqg, Polarization -> 1] /. FCGV[z_] :> ToExpression[z]
(16x−8)Tf
SplittingFunction[Pgq, Polarization -> 1] /. FCGV[z_] :> ToExpression[z]
(8−4x)CF
SplittingFunction[Pgg, Polarization -> 1] /. FCGV[z_] :> ToExpression[z]
CA(322δ(1−x)−16x+8(1−x1)++8)−38NfTfδ(1−x)
SplittingFunction[aqq, Polarization -> 1] /. FCGV[z_] :> ToExpression[z]
CF((7−4ζ(2))δ(1−x)+8(1−x)+2x+(2x+2)log((1−x)x)−4(1−x1)+log(x)−4(1−xlog(1−x))+−4)
SplittingFunction[agq, Polarization -> 1] /. FCGV[z_] :> ToExpression[z]
CF(−4x+(2x−4)log((1−x)x)+2)
SplittingFunction[agqd, Polarization -> 1] /. FCGV[z_] :> ToExpression[z]
CF((2x−4)log((1−x)x)−2)
SplittingFunction[aqg, Polarization -> 1] /. FCGV[z_] :> ToExpression[z]
Tf((4−8x)log((1−x)x)−4)
SplittingFunction[aqgd, Polarization -> 1] /. FCGV[z_] :> ToExpression[z]
Tf((4−8x)log((1−x)x)−4)
SplittingFunction[agg, Polarization -> 1] /. FCGV[z_] :> ToExpression[z]
CA((967−4ζ(2))δ(1−x)+(8x−4)log((1−x)x)−4(1−xlog(x)+(1−xlog(1−x))+)+2)−920Tfδ(1−x)
SplittingFunction[aggd, Polarization -> 1] /. FCGV[z_] :> ToExpression[z]
CA((967−4ζ(2))δ(1−x)+(8x−4)log((1−x)x)−4(1−xlog(x)+(1−xlog(1−x))+)+2)−920Tfδ(1−x)
SplittingFunction[PQQS, Polarization -> 1] /. FCGV[z_] :> ToExpression[z]
CFTf(16(1−x)−16(x+1)log2(x)+(48x−16)log(x))
SplittingFunction[PQQNS, Polarization -> 1] /. FCGV[z_] :> ToExpression[z]
−8CF(CF−2CA)(x+1(x2+1)(−2ζ(2)−4Li2(−x)+log2(x)−4log(x+1)log(x))+4(1−x)+2(x+1)log(x))+CACF(1−x4(x2+1)log2(x)+8ζ(2)(x+1)+(9536−16ζ(2))(1−x1)++δ(1−x)(388ζ(2)−24ζ(3)+317)+94(53−187x)−34(5x−1−x22+5)log(x))+CFNf(−3(1−x)8(x2+1)log(x)+(−316ζ(2)−32)δ(1−x)+988x−980(1−x1)+−98)+CF2(−1−x16(x2+1)log(1−x)log(x)+δ(1−x)(−24ζ(2)+48ζ(3)+3)−40(1−x)−4(x+1)log2(x)−8(2x+1−x3)log(x))
SplittingFunction[PQG, Polarization -> 1] /. FCGV[z_] :> ToExpression[z]
4CATf(−8ζ(2)+(−16x−8)Li2(−x)−44x+(4−8x)log2(1−x)+(−8x−4)log2(x)+(16x−16)log(1−x)+(32x+4)log(x)+(−16x−8)log(x)log(x+1)+48)+4CFTf(8ζ(2)−16ζ(2)x+54x+(8x−4)log2(1−x)+(4x−2)log2(x)+(16−16x)log(1−x)+(8−16x)log(x)log(1−x)−18log(x)−44)
SplittingFunction[PGQ, Polarization -> 1] /. FCGV[z_] :> ToExpression[z]
(CACF).((16x+32)Li2(−x)+16ζ(2)x+9280x+(16−8x)log2(1−x)+(8x+16)log2(x)+(38x+380)log(1−x)+(16x−32)log(x)log(1−x)+(32−104x)log(x)+(16x+32)log(x)log(x+1)+9328)+(CFTf).(−932x+(332x−364)log(1−x)−9128)+CF2.(32x+(8x−16)log2(1−x)+(8−4x)log2(x)+(−8x−16)log(1−x)−(32x+64)log(x)+(36x+48)log(x)−68)
SplittingFunction[PGG, Polarization -> 1] /. FCGV[z_] :> ToExpression[z]
CATf(−332δ(1−x)+9608x−9160(1−x1)++(−332x−332)log(x)−9448)+CA2((64x+x+132+32)Li2(−x)+364δ(1−x)+ζ(2)(64x−16(1−x1)++x+116)+24ζ(3)δ(1−x)−9388x+9536(1−x1)++(−x+18+1−x8+32)log2(x)+(3232−3536x)log(x)+(64x−1−x32−32)log(1−x)log(x)+(64x+x+132+32)log(x+1)log(x)−9148)+CFTf(−8δ(1−x)+80x+(−16x−16)log2(x)+(16x−80)log(x)−80)