10 - H1 - Desy

8 Theoretical framework
α s
0.20
H1
Normalised Jet Cross Sections
Combined H1 data (incl., 2-, 3-jet)
α s
fit
Theory uncertainty
0.15
0.10
10
Q / GeV
10
2
Figure 1.5: The scale dependence of the strong coupling constant α s . Figure taken
from [13].
1.2.3 Factorisation theorem
The calculation of gluon radiations (q → qg, g → gg) and splittings (g → q¯q) in pQCD
gives rise to infrared divergencies. The introduction of a factorisation scale µ F cures
the problem in a similar way as the µ R does. Above the cut-off scale µ F collinear soft
radiations are absorbed into the parton density functions. Reliable pQCD calculations
are possible only for µ F ≫ Λ QCD .
Within the factorisation theorem, the proton structure function F 2 can be written as
a convolution of perturbatively calculable coefficient functions C i and parton density
functions f i/p (ξ), which could be interpreted as a probability of finding a parton of type
i carrying a fraction ξ of the protons longitudinal momentum:
F 2 (x, Q 2 ) = x ∑
i=q,¯q,g
∫ 1
x
( )
x
dξC i ξ , Q2
, µ2 F
, α
µ 2 R
µ 2 s (µ 2 R) f i/p (ξ, µ 2 F, µ 2 R). (1.12)
R
Based on the factorisation theorem, the ep cross section can be decomposed in the presence