A
bstract
We give a short account of recent advances in our understanding of the
π
- dependent terms in massless (Euclidean) 2-point functions as well as in generic anomalous dimensions (ADs) and
β
...-functions. We extend the considerations of
1
by two more loops, that is for the case of 6- and 7-loop correlators and 7- and 8-loop renormalization group (RG) functions. Our predictions for the (
π
-dependent terms) of the 7-loop RG functions for the case of the
O
(
n
) 𝜙
4
theory are in full agreement with the recent results from
2
. All available 7- and 8-loop results for QCD and the scalar
O
(
n
)
ϕ
4
theory obtained within the large
N
f
approach to the quantum field theory (see, e.g.
3
) are also in full agreement with our results.
A
bstract
We extend the
O
α
s
5
result of the analytic calculation of the quark mass anomalous dimension in pQCD 1 to the case of a generic gauge group. We present explicit formulas which express the ...relevant renormalization constants in terms of four-loop massless propagators. We also use our result to shed new light on the old puzzle of the absence of even zetas in results of perturbative calculations for a class of physical observables.
We analytically compute the five-loop term in the beta function which governs the running of α_{s}-the quark-gluon coupling constant in QCD. The new term leads to a reduction of the theory ...uncertainty in α_{s} taken at the Z-boson scale as extracted from the τ-lepton decays as well as to new, improved by one more order of perturbation theory, predictions for the effective coupling constants of the standard model Higgs boson to gluons and for its total decay rate to the quark-antiquark pairs.
A
bstract
Extending an argument of
1
for the case of 5-loop massless propagators we prove a host of new exact model-independent relations between contributions proportional to odd and even zetas in ...generic
M
S
¯
anomalous dimensions as well as in generic massless correlators. In particular, we find a new remarkable connection between coefficients in front of
ζ
3
and
ζ
4
in the 4-loop and 5-loop contributions to the QCD
β
-function respectively. It leads to a natural explanation of a simple mechanics behind mysterious cancellations of the
π
-dependent terms in one-scale Renormalization Group (RG) invariant Euclidean quantities recently discovered in
2
. We give a proof of this no-
π
theorem for a general case of (not necessarily scheme-independent) one-scale massless correlators. All
π
-dependent terms in the
six-loop
coefficient of an anomalous dimension (or a
β
-function) are shown to be explicitly expressible in terms of lower order coefficients for a general one-charge theory. For the case of a scalar
O
(
n
)
ϕ
4
theory all our predictions for
π
-dependent terms in 6-loop anomalous dimensions are in full agreement with recent results of
3
–
5
.
A
bstract
We derive explicit expressions for the elements of the {
β
}-expansion for the nonsinglet Adler
D
A
-function and Bjorken polarized sum rules
S
Bjp
in the N
4
LO using recent results by ...Chetyrkin for these quantities computed within extended QCD including any number of fermion representations. We discuss the properties of the {
β
}-expansion for
D
A
and
S
Bjp
at higher orders which follow from the Crewther
1
and the Broadhurst-Kataev
2
relation.
We compute the form factors of the photon-quark-anti-quark vertex and the effective vertex of a Higgs-boson and two gluons to three-loop order within massless perturbative quantum chromodynamics. ...These results provide building blocks for many third-order cross sections. Furthermore, this is the first calculation of complete three-loop vertex corrections.
We compute, for the first time, the order alpha(s)(4) contributions to the Bjorken sum rule for polarized electron-nucleon scattering and to the (nonsinglet) Adler function for the case of a generic ...color gauge group. We confirm at the same order a (generalized) Crewther relation which provides a strong test of the correctness of our previously obtained results: the QCD Adler function and the five-loop beta function in quenched QED. In particular, the appearance of an irrational contribution proportional to zeta(3) in the latter quantity is confirmed. We obtain the commensurate scale equation relating the effective strong coupling constants as inferred from the Bjorken sum rule and from the Adler function at order alpha(s)(4).
Corrections of order α(s)(4) for the axial singlet contributions for the decay rate of the Z boson into hadrons are evaluated in the limit of the heavy top quark mass. Combined with recently finished ...O(α(s)(4)) calculations of the nonsinglet corrections, the new results directly lead us to the first complete O(α(s)(4)) prediction for the total hadronic decay rate of the Z boson. The new O(α(s)(4)) term in Z-decay rate leads to a significant stabilization of the perturbative series, to a reduction of the theory uncertainty in the strong coupling constant α(s), as extracted from these measurements, and to a small shift of the central value.
The anomalous magnetic moment of the muon is one of the most fundamental observables. It has been measured experimentally with a very high precision and on theory side the contributions from ...perturbative QED have been calculated up to five-loop level by numerical methods. Contributions to the muon anomalous magnetic moment from certain diagram classes are also accessible by alternative methods. In this paper we present the evaluation of contributions to the QED corrections due to insertions of the vacuum polarization function at five-loop level.
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