6 research outputs found
Three loop MSbar renormalization of QED in the 't~Hooft-Veltman gauge
Quantum electrodynamics (QED) fixed in the 't~Hooft-Veltman gauge is
renormalized to three loops in the MSbar scheme. The beta-functions and
anomalous dimensions are computed as functions of the usual QED coupling and
the additional coupling, xi, which is introduced as part of the nonlinear gauge
fixing condition. Similar to the maximal abelian gauge of quantum
chromodynamics, the renormalization of the gauge parameter is singular.Comment: 8 latex page
Two-loop three-gluon vertex in zero-momentum limit
The two-loop three-gluon vertex is calculated in an arbitrary covariant
gauge, in the limit when one of the external momenta vanishes. The differential
Ward-Slavnov-Taylor (WST) identity related to this limit is discussed, and the
relevant results for the ghost-gluon vertex and two-point functions are
obtained. Together with the differential WST identity, they provide another
independent way for calculating the three-gluon vertex. The renormalization of
the results obtained is also presented.Comment: 22 pages, LaTeX, including 4 figures, uses eps
Integrability and Transcendentality
We derive the two-loop Bethe ansatz for the sl(2) twist operator sector of
N=4 gauge theory directly from the field theory. We then analyze a recently
proposed perturbative asymptotic all-loop Bethe ansatz in the limit of large
spacetime spin at large but finite twist, and find a novel all-loop scaling
function. This function obeys the Kotikov-Lipatov transcendentality principle
and does not depend on the twist. Under the assumption that one may extrapolate
back to leading twist, our result yields an all-loop prediction for the
large-spin anomalous dimensions of twist-two operators. The latter also appears
as an undetermined function in a recent conjecture of Bern, Dixon and Smirnov
for the all-loop structure of the maximally helicity violating (MHV) n-point
gluon amplitudes of N=4 gauge theory. This potentially establishes a direct
link between the worldsheet and the spacetime S-matrix approach. A further
assumption for the validity of our prediction is that perturbative BMN
(Berenstein-Maldacena-Nastase) scaling does not break down at four loops, or
beyond. We also discuss how the result gets modified if BMN scaling does break
down. Finally, we show that our result qualitatively agrees at strong coupling
with a prediction of string theory.Comment: 45 pages LaTeX, 3 postscript figures. v2: Chapter on BMN scaling and
transcendentality added. v3: version accepted for publication in JSTA
Top Quark Contribution to Hadronic Decays of the Z-Boson at Alpha_s^2 in QCD
We evaluate the effect of a virtual top quark on the coefficient of
in the decay rates and
. We treat the dependence on the top
quark mass exactly instead of using a large mass expansion. The present work
completes the evaluation of the contributions to these
quantities. The calculation uses both the and
Collins-Wilczek-Zee renormalization prescriptions. The results can be applied
to the hadronic decays of the -lepton.Comment: 10 pages, REVTeX 3.0 with 4 postscript figures compressed with
uufiles, University of Oregon preprint OITS 54
Perturbative QCD Calculations of Total Cross Sections and Decay Widths in Hard Inclusive Processes
A summary of the current understanding of methods of analytical higher order
perturbative computations of total cross sections and decay widths in Quantum
Chromodynamics is presented. As examples, the total cross section in electron
positron annihilation, the hadronic decay rates of the tau lepton and Higgs
boson up to O(\alpha_s^2) and O(\alpha_s^3) are considered. The evaluation of
the four-loop QED \beta - function at an intermediate step of the calculation
is briefly described. The problem of renormalization group ambiguity of
perturbative results is considered and some of the existing prescriptions are
discussed. The problem of estimation of theoretical uncertainty in perturbative
calculations is briefly discussed.Comment: 83 pages, LaTeX, Reviews of Modern Physics style, 14 figures plus
figural equations (not included). Hard copy available upon request at
[email protected]. To be published in Reviews of Modern Physic