|VOLUME 94 | ISSUE 11 |
|The analytical singlet αs4 QCD contributions into the e+e--annihilation Adler function and the generalized Crewther relations
A. L. Kataev
Institute for Nuclear Research RAS, 117312 Moscow, Russia
The generalized Crewther relations in the channels of the
non-singlet and vector quark currents are considered.
These relations follow from the double application of the operator product
expansion approach to the same
axial vector-vector-vector triangle amplitude in two regions,
adjoining to the angle sides
(x,y) (or p2,q2).
We assume that the generalized Crewther relations in
these two kinematic regimes result in the
existence of the same perturbation expression for two
products of the coefficient functions
of annihilation and deep-inelastic scattering
processes in the non-singlet and vector channels.
This feature explains
the conformal symmetry motivated cancellations
between the singlet αs3 corrections
to the Gross-Llewellyn Smith sum rule S GLS of ν N
deep inelastic scattering and the singlet αs3 correction
to the e+e--annihilation
Adler function DAV in the product
of the corresponding perturbative series. Taking into account
4-th order result for S GLS
and the perturbative effects of
the violation of the conformal symmetry in the generalized Crewther relation,
we obtain the analytical
contribution to the singlet αs4 correction to the
Its a-posteriori comparison with the recent result of
direct diagram-by-diagram evaluation of the singlet
4-th order corrections
to DAV- function demonstrates the coincidence of the predicted
and obtained ζ32-contributions to the singlet term. They
can be obtained
in the conformal invariant limit from the original Crewther relation.
Therefore, on the contrary to previous belief, the appearance
of ζ3-terms in the perturbative series in
quantum field theory gauge models
does not contradict to the property of the the conformal symmetry
and can be considered as regular feature.
The Banks-Zaks motivated
relation between our predicted and the obtained directly
corrections is mentioned. It
confirms the expectation, previously made by Baikov-Chetykin-Kuhn,
that at the 5-loop level the generalized Crewther relation in the channel
of vector currents may receive additional singlet contribution, which in
this order of perturbation theory is proportional
to the first coefficient of the QCD β-function.
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