4 QCD: The Theory of Strong Interactions
129
of the minimal impact of the choice of input parton densities. We can write the
non-singlet evolution equations in the form:
d
dt
logF (x, t) =
α s (t)
2π
1
x
dy
y
F (y, t)
F (x, t)
P qq (
x
y
, α s (t))
(4.113)
where P qq is the splitting function. At present NLO and NNLO corrections are
known. It is clear from this form that, for example, the normalisation error on the
input density drops away, and the dependence on the input is reduced to a minimum
(indeed, only a single density appears here, while in general there are quark and
gluon densities). Unfortunately the data on non-singlet structure functions are not
very accurate. If we take the difference of data on protons and neutrons, F p − F n ,
experimental errors add up in the difference and finally are large. The F 3νN data are
directly non-singlet but are not very precise. A determination of α s from the CCFR
data on F 3νN has led to [86]:
α s (m Z ) = 0.119 ± 0.006
(4.114)
A recent analysis of the same data leads to α s (m Z ) = 0.119 ± 0.002 [87], but
the theoretical error associated with the method and with the choice adopted for the
scale ambiguities is not considered. A fit to non singlet structure functions in electroor muon-production extracted from proton and deuterium data at the NNLO level
was performed in Ref. [88] with the result:
α s (m Z ) = 0.114 ± 0.002
(4.115)
When one measures α s from scaling violations on F 2 from e or μ beams, the data
are abundant, the errors small but there is an increased dependence on input parton
densities and especially a strong correlation between the result on α s and the input
on the gluon density. There are complete and accurate derivations of α s from scaling
violations in F 2 . In a well known analysis by Santiago and Yndurain [89], the data
on protons from SLAC, BCDMS, E665 and HERA are used with NLO kernels plus
the NNLO first few moments. The analysis is based on an original method that uses
projections on a specially selected orthogonal basis, the Bernstein polynomials. The
quoted result is given by:
α s (m Z ) = 0.1163 ± 0.0014
(4.116)
(these authors also quote α s (m Z ) = 0.115 ± 0.006 for F 3 data in νN scattering). A
different analysis by Alekhin [90] of existing data off proton and deuterium targets
with NNLO kernels and a more conventional method leads to
α s (m Z ) = 0.114 ± 0.002
(4.117)
129
of the minimal impact of the choice of input parton densities. We can write the
non-singlet evolution equations in the form:
d
dt
logF (x, t) =
α s (t)
2π
1
x
dy
y
F (y, t)
F (x, t)
P qq (
x
y
, α s (t))
(4.113)
where P qq is the splitting function. At present NLO and NNLO corrections are
known. It is clear from this form that, for example, the normalisation error on the
input density drops away, and the dependence on the input is reduced to a minimum
(indeed, only a single density appears here, while in general there are quark and
gluon densities). Unfortunately the data on non-singlet structure functions are not
very accurate. If we take the difference of data on protons and neutrons, F p − F n ,
experimental errors add up in the difference and finally are large. The F 3νN data are
directly non-singlet but are not very precise. A determination of α s from the CCFR
data on F 3νN has led to [86]:
α s (m Z ) = 0.119 ± 0.006
(4.114)
A recent analysis of the same data leads to α s (m Z ) = 0.119 ± 0.002 [87], but
the theoretical error associated with the method and with the choice adopted for the
scale ambiguities is not considered. A fit to non singlet structure functions in electroor muon-production extracted from proton and deuterium data at the NNLO level
was performed in Ref. [88] with the result:
α s (m Z ) = 0.114 ± 0.002
(4.115)
When one measures α s from scaling violations on F 2 from e or μ beams, the data
are abundant, the errors small but there is an increased dependence on input parton
densities and especially a strong correlation between the result on α s and the input
on the gluon density. There are complete and accurate derivations of α s from scaling
violations in F 2 . In a well known analysis by Santiago and Yndurain [89], the data
on protons from SLAC, BCDMS, E665 and HERA are used with NLO kernels plus
the NNLO first few moments. The analysis is based on an original method that uses
projections on a specially selected orthogonal basis, the Bernstein polynomials. The
quoted result is given by:
α s (m Z ) = 0.1163 ± 0.0014
(4.116)
(these authors also quote α s (m Z ) = 0.115 ± 0.006 for F 3 data in νN scattering). A
different analysis by Alekhin [90] of existing data off proton and deuterium targets
with NNLO kernels and a more conventional method leads to
α s (m Z ) = 0.114 ± 0.002
(4.117)