New results for two-loop off-shell three-point diagrams

A number of exact results for two-loop three-point diagrams with massless internal particles and arbitrary (off-shell) external momenta are presented. Divergent contributions are calculated in the framework of dimensional regularization.Comment: 10 pages, 3 figures, standard LaTEX (PS-file is also available by anonymous FTP at node VSFYS1.FI.UIB.NO in subdirectory DAVYDYCHEV, the file BERGEN94-03.PS), Bergen Scientific/Technical Report No.1994-0

Non-renormalization of the full <VVA> correlator at two-loop order

By explicit calculation of the two-loop QCD corrections we show that for singlet axial and vector currents the full off-shell correlation function in the limit of massless fermions is proportional to the one-loop result, when calculated in the MS-bar scheme. By the same finite renormalization which is needed to make the one-loop anomaly exact to all orders, we arrive at the conclusion that two-loop corrections are absent altogether, for the complete correlator not only its anomalous part. In accordance with the one-loop nature of the correlator, one possible amplitude, which seems to be missing by accident at the one-loop level, also does not show up at the two-loop level.Comment: 6 pages, 1 figur

Simplifications of four-point functions in N=4 supersymmetric Yang-Mills theory at two loops

The superconformal Ward identities combined with N=2 harmonic analyticity are used to evaluate two-loop four-point correlation functions of gauge-invariant operators in D=4, N=4 supersymmetric Yang-Mills theory in terms of the well-known one-loop box integral. The result is confirmed by a direct numerical computation

Explicit Results for the Anomalous Three Point Function and Non-Renormalization Theorems

Two-loop corrections for the correlator of the singlet axial and vector currents in QCD are calculated in the chiral limit for arbitrary momenta. Explicit calculations confirm the non-renormalization theorems derived recently by Vainshtein and Knecht et.al. We find that as in the one-loop case also at the two loops the correlator has only 3 independent form-factors instead of 4. From the explicit results we observe that the two-loop correction to the correlator is equal to the one-loop result times the constant factor C_2(R) alpha_s/pi in the MSbar scheme. This holds for the full correlator, for the anomalous longitudinal as well as for the non- anomalous thansversal amplitudes. The finite overall alpha_s dependent constant has to be normalized away by renormalizing the axial current according to Witten's algebraic/geometrical constraint on the anomalous Ward identity. Our observations, together with known facts, suggest that in perturbation theory the correlator is proportional to the one-loop term to all orders and that the non- renormalization theorem of the Adler-Bell-Jackiw anomaly carries over to the full correlator.Comment: 10 pages, 2 Postscript figures, uses axodraw.st

Threshold and pseudothreshold values of the sunset diagram

Analytic results for the threshold and pseudothreshold values of the sunset diagram with arbitrary masses are obtained in terms of dilogarithms of ratios of the masses.Comment: 11 pages, plain LaTe

A Short Note on Two-Loop Box Functions

It is shown that the two-loop four-point functions are similar in structure to the three-point two-loop functions for all mass cases and topologies. The result is derived by using a rotation to a (+,-,-,+) signature without spoiling analyticity properties.Comment: 7 pages, UTAS-PHYS-94-23, plain LATE

One-loop results for the quark-gluon vertex in arbitrary dimension

Results on the one-loop quark-gluon vertex with massive quarks are reviewed, in an arbitrary covariant gauge and in arbitrary space-time dimension. We show how it is possible to get on-shell results from the general off-shell expressions. The corresponding Ward-Slavnov-Taylor identity is discussed.Comment: 6 pages, LaTeX, including 1 figure, uses epsfig, requires espcrc2.sty, contribution to the Zeuthen Workshop "Loops and Legs in Gauge Theories" (Bastei, Germany, April 2000

Off-shell two loop QCD vertices

We calculate the triple gluon, ghost-gluon and quark-gluon vertex functions at two loops in the MSbar scheme in the chiral limit for an arbitrary linear covariant gauge when the external legs are all off-shell.Comment: 29 latex pages, 32 figures, anc directory contains txt file with electronic version of vertex functions for each of the three 3-point cases in the MSbar scheme and includes the projection matrice