AnomalousDimension
AnomalousDimension[name]
is a database of anomalous dimensions of twist 2 operators.
AnomalousDimension["gnsqg0"]
yields the non-singlet one-loop contribution to the anomalous dimension γS,qg(0),m in the MS-bar scheme etc.
See also
Overview, SplittingFunction, SumS, SumT.
Examples
Polarized case:
SetOptions[AnomalousDimension, Polarization -> 1]
{Polarization→1,Simplify→FullSimplify}
γNS,qq(0) polarized:
AnomalousDimension[gnsqq0]
CF(8S1(m−1)+m4+m+14−6)
γS,qg(0) polarized:
AnomalousDimension[gsqg0]
(m8−m+116)Tf
γS,gq(0)polarized:
AnomalousDimension[gsgq0]
(m+14−m8)CF
γS,gg(0) polarized:
AnomalousDimension[gsgg0]
CA(8S1(m−1)−m8+m+116−322)+38Tf
γPS,qq(0) polarized:
AnomalousDimension[gpsqq1]
16(m32−m21+m+11+(m+1)23+(m+1)32−m1)CFTf
γNS,qq(1) polarized:
AnomalousDimension[gnsqq1]
−CACF(−m16S~2(m−1)−m+116S~2(m−1)+16S~3(m−1)−32S~12(m−1)+3m244−9536S1(m−1)+388S2(m−1)−16S3(m−1)+9m212−9(m+1)748−3(m+1)24−(m+1)316+317)−(CF2(m32S~2(m−1)+m+132S~2(m−1)−32S~3(m−1)+64S~12(m−1)+m38+m216S1(m−1)+(m+1)216S1(m−1)+m16S2(m−1)+m+116S2(m−1)−24S2(m−1)+32S12(m−1)+32S21(m−1)−m40+m+140+(m+1)216+(m+1)340+3))−CFNf(−3m28+980S1(m−1)−316S2(m−1)−9m8+9(m+1)88−3(m+1)28−32)
γS,qg(1) polarized:
AnomalousDimension[gsqg1]
16CATf(−m2S~2(m−1)+m+14S~2(m−1)+m32−m22S1(m−1)−m23−mS12(m−1)+m+12S12(m−1)+(m+1)24S1(m−1)−mS2(m−1)+m+12S2(m−1)−m4+m+13+(m+1)28+(m+1)312)+8CFTf(−m32−m21+m2S12(m−1)−m+14S12(m−1)−m2S2(m−1)+m+14S2(m−1)+m14−m+119−(m+1)28+(m+1)34)
γS,gq(1) polarized:
AnomalousDimension[gsgq1]
8CACF(m4S~2(m−1)−m+12S~2(m−1)−m34+3m228−m2S12(m−1)+m+1S12(m−1)+3m16S1(m−1)−3(m+1)5S1(m−1)+m2S2(m−1)−m+1S2(m−1)−9m56−9(m+1)20−3(m+1)238−(m+1)36)+32CFTf(−3m22−3m2S1(m−1)+3(m+1)S1(m−1)+9m7−9(m+1)2+3(m+1)21)+4CF2(m34+m28S1(m−1)−m212+m4S12(m−1)−m+12S12(m−1)−m8S1(m−1)+m+12S1(m−1)−(m+1)24S1(m−1)+m4S2(m−1)−m+12S2(m−1)+m15−m+16+(m+1)23−(m+1)32)
γS,gg(1) polarized:
v1 = AnomalousDimension[gsgg1]
4CA2(m8S~2(m−1)−m+116S~2(m−1)+4S~3(m−1)−8S~12(m−1)−m38+m28S1(m−1)+3m258−(m+1)216S1(m−1)+9134S1(m−1)+m8S2(m−1)−m+116S2(m−1)+4S3(m−1)−8S12(m−1)−8S21(m−1)−9m107+9(m+1)241−3(m+1)286−(m+1)348−316)+32CATf(−3m21−95S1(m−1)+9m14−9(m+1)19−3(m+1)21+31)+8(m34−m210−m+110+(m+1)22+(m+1)34+m10+1)CFTf
γS,gg(1) polarized (different representation):
v2 = AnomalousDimension[GSGG1];
Check that all odd moments give the same for the two representations of γS,gg(1):
Table[v1 - v2 /. OPEm -> ij, {ij, 1, 17, 2}] // Simplify
{0,0,0,0,0,0,0,0,0}