301 research outputs found
The criterion of irreducibility of multi-loop Feynman integrals
The integration by parts recurrence relations allow to reduce some Feynman
integrals to more simple ones (with some lines missing). Nevertheless the
possibility of such reduction for the given particular integral was unclear.
The recently proposed technique for studying the recurrence relations as
by-product provides with simple criterion of the irreducibility.Comment: LaTeX, 6 pages, no figures, the complete paper, including figures, is
also available via anonymous ftp at
ftp://ttpux2.physik.uni-karlsruhe.de/ttp99/ttp99-52/ or via www at
http://www-ttp.physik.uni-karlsruhe.de/Preprints
The structure of generic anomalous dimensions and no- theorem for massless propagators
Extending an argument of [Baikov:2010hf] 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 \MSbar\ anomalous
dimensions as well as in generic massless correlators. In particular, we find a
new remarkable connection between coefficients in front of and
in the 4-loop and 5-loop contributions to the QCD -function
respectively. It leads to a natural explanation of a simple mechanics behind
mysterious cancellations of the -dependent terms in one-scale
Renormalization Group (RG) invariant Euclidian quantities recently discovered
in \cite{Jamin:2017mul}. We give a proof of this no- theorem for a general
case of (not necessarily scheme-independent) one-scale massless correlators.
All -dependent terms in the {\bf six-loop} coefficient of an anomalous
dimension (or a -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 theory all our predictions for -dependent
terms in 6-loop anomalous dimensions are in full agreement with recent results
of [Batkovich:2016jus],[Schnetz:2016fhy],[Kompaniets:2017yct].Comment: 25 page
Quark Mass and Field Anomalous Dimensions to
We present the results of the first complete analytic calculation of the
quark mass and field anomalous dimensions to in QCD
QCD Corrections to Hadronic Z and tau Decays
We present a brief (mainly bibliographical) report on recently performed
calculations of terms of order O(\alpha_s^4 n_f^2) and O(\alpha_s^4 n_f^2
m_q^2) for hadronic Z and \tau decay rates. A few details about the analytical
evaluation of the masters integrals appearing in the course of calculations are
presented.Comment: revised version (some references corrected); 3 pages, talk given at
International Europhysics Conference on High Energy Physics, Aachen, Germany,
17-23 July 200
Five-loop fermion anomalous dimension for a general gauge group from four-loop massless propagators
We extend the 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.Comment: An important reference [47] is correcte
Scalar Correlator at O(alpha_s^4), Higgs Decay into b-quarks and Bounds on the Light Quark Masses
We compute, for the first time, the absorptive part of the massless
correlator of two quark scalar currents in five loops. As physical applications
we consider the O(alpha_s^4) corrections to the decay rate of the Standard
Model Higgs boson into quarks, as well as the constraints on the strange quark
mass following from QCD sum rules.Comment: 5 pages, REVTeX4. Few references updated. The final version, accepted
for publication. The complete paper is also available via the www at
http://www-ttp.physik.uni-karlsruhe.de/Preprints
Hadronic Z- and tau-Decays in Order alpha_s^4
Using recently developed methods for the evaluation of five-loop amplitudes
in perturbative QCD, corrections of order alpha_s^4 for the cross section of
electron-positron annihilation into hadrons and for the decay rates of the
Z-boson and the tau-lepton into hadrons are evaluated. The new terms lead to a
significant stabilization of the perturbative series, to a reduction of the
theory uncertainly in the strong coupling constant alpha_s, as extracted from
these measurements, and to a small shift of the central value, moving two
central values closer together. The agreement between two values of alpha_s
measured at vastly different energies constitutes a striking test of asymptotic
freedom. Combining the results from Z and tau decays we find
alpha_s(M_Z)=0.1198 \pm 0.0015 as one of the most precise and presently only
result for the strong coupling constant in order alpha_s^4.Comment: few citations added, final published versio
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