59 research outputs found
Higher Moments of Heavy Quark Vacuum Polarization
We present analytical calculation of the first seven moments of the heavy
quark vacuum polarization function in the three-loop order. The obtained
results are compared against the asymptotic formulas following from the
threshold singularities. We also discuss the dependence of the moments
within the BLM procedure.Comment: 9 pages, LaTeX, no figures, sprocl.sty provided (To appear in the
Proceedings of the Second Workshop on Continuous Advances in QCD,
Minneapolis, U.S.A., March 1996). Postscript also available at
ftp://www-ttp.physik.uni-karlsruhe.de/ttp96-22/ttp96-22.ps or at
http://www-ttp.physik.uni-karlsruhe.de/cgi-bin/preprints
Mass Corrections to the Vector Current Correlator
Three-loop QCD corrections to the vector current correlator are considered.
The large momentum procedure is applied in order to evaluate mass corrections
up to order . The inclusion of the first seven terms to the ratio
leads to reliable
predictions from the high energy region down to relatively close to threshold.Comment: 16 pages, LaTeX, 11 postscript figures. The complete paper, including
figures, is also available via anonymous ftp at
ftp://ttpux2.physik.uni-karlsruhe.de/ , or via www at
http://www-ttp.physik.uni-karlsruhe.de/cgi-bin/preprints
Double Bubble Corrections to Heavy Quark Production
Second order corrections to the heavy quark production
cross-section due to massless quarks and coloured scalars are calculated for
all energies above threshold. Based on the method introduced in this letter
also the gauge non-invariant second order corrections due to the pure gluonic
selfenergy insertion and a certain class of and
corrections are determined. For the special choice of
the gauge parameter, , the leading threshold and high energy behaviour
of the pure second order gluonic corrections to the cross-section are governed
by the gluonic self energy insertion.Comment: 9 pages, latex, 17 figures, the complete postscript file of this
preprint, including figures, is available via anonymous ftp at
ftp://www-ttp.physik.uni-karlsruhe.de/ttp96-04/ttp96-04.ps (129.13.102.139)
or via www at http://www-ttp.physik.uni-karlsruhe.de/cgi-bin/preprints
Recent progress in computing four-loop massive correlators
We report about recent progress in computing four-loop massive correlators.
The expansion of these correlators in the external momentum leads to vacuum
integrals. The calculation of these vacuum integrals can be used to determine
Taylor expansion coefficients of the vacuum polarization function and
decoupling functions in perturbative Quantum chromodynamics. New results at
four-loop order for the lowest Taylor expansion coefficient of the vacuum
polarization function and for the decoupling relation are presented.Comment: 4 pages, talk given at the 12th International Conference on Quantum
Chromodynamics, Montpellier, 4-8th July 200
Heavy Quark Vacuum Polarisation to Three Loops
The real and imaginary part of the vacuum polarisation function
induced by a massive quark is calculated in perturbative QCD up to order
. The method is described and the results are presented. This
extends the calculation by K\"all\'en and Sabry from two to three loops.Comment: 10 pages, Latex, figures in a separate file. The complete paper,
including figures, is also available via anonymous ftp at
ftp://www-ttp.physik.uni-karlsruhe.de/ , or via www at
http://www-ttp.physik.uni-karlsruhe.de/cgi-bin/preprints
Quartic Mass Corrections to
The influence of nonvanishing quark masses on the total cross section in
electron positron collisions and on the decay rate is calculated. The
corrections are expanded in and \as. Methods similar to those applied
for the quadratic mass terms allow to derive the corrections of order \as
m^4/s^2 and \as^2m^4/s^2. Coefficients which depend logarithmically on
and which cannot be absorbed in a running quark mass arise in order
\as^2. The implications of these results on electron positron annihilation
cross sections at LEP and at lower energies in particular between the charm and
the bottom threshold and for energies several GeV above the threshold
are discussed.Comment: 17 pages, LaTex (uses epsf.sty, figures appended as uuencoded ps- and
eps-files). A complete postscript file, including figures, is available via
anonymous ftp at ttpux2.physik.uni-karlsruhe.de (129.13.102.139) as
/pub/ttp94-08/ttp94-08.ps, Local preprint# TTP94-0
QCD Decoupling at Four Loops
We present the matching condition for the strong coupling contant alpha_s at
a heavy quark threshold to four loops in the modified minimal subtraction
scheme. Our results lead to further decrease of the theoretical uncertainty of
the evolution of the strong coupling constant through heavy quark thresholds.
Using a low energy theorem we furthermore derive the effective coupling of the
Higgs boson to gluons (induced by a virtual heavy quark) in four- and
(partially) through five-loop approximation.Comment: 21 pages, 2 figures, the complete paper is also available via the www
at http://www-ttp.physik.uni-karlsruhe.de/Preprints
Four-loop moments of the heavy quark vacuum polarization function in perturbative QCD
New results at four-loop order in perturbative QCD for the first two Taylor
coefficients of the heavy quark vacuum polarization function are presented.
They can be used to perform a precise determination of the charm- and
bottom-quark mass. Implications for the value of the quark masses are briefly
discussed.Comment: 8 pages, 13 figures; final version accepted for publication in the
journa
Adler Function, DIS sum rules and Crewther Relations
The current status of the Adler function and two closely related Deep
Inelastic Scattering (DIS) sum rules, namely, the Bjorken sum rule for
polarized DIS and the Gross-Llewellyn Smith sum rule are briefly reviewed. A
new result is presented: an analytical calculation of the coefficient function
of the latter sum rule in a generic gauge theory in order O(alpha_s^4). It is
demonstrated that the corresponding Crewther relation allows to fix two of
three colour structures in the O(alpha_s^4) contribution to the singlet part of
the Adler function.Comment: Talk presented at 10-th DESY Workshop on Elementary Particle Theory:
Loops and Legs in Quantum Field Theory, W\"orlitz, Germany, 25-30 April 201
Adler Function, Sum Rules and Crewther Relation of Order O(alpha_s^4): the Singlet Case
The analytic result for the singlet part of the Adler function of the vector
current in a general gauge theory is presented in five-loop approximation.
Comparing this result with the corresponding singlet part of the
Gross-Llewellyn Smith sum rule [1], we successfully demonstrate the validity of
the generalized Crewther relation for the singlet part. This provides a
non-trivial test of both our calculations and the generalized Crewther
relation. Combining the result with the already available non-singlet part of
the Adler function [2,3] we arrive at the complete
expression for the Adler function and, as a direct consequence, at the complete
correction to the annihilation into hadrons in
a general gauge theory.Comment: 4 pages, 1 figure. Final published versio
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