822 research outputs found
Leading QCD-induced four-loop contributions to the -function of the Higgs self-coupling in the SM and vacuum stability
We present analytical results for the leading top-Yukawa and QCD contribution
to the -function for the Higgs self-coupling of the Standard
Model at four-loop level, namely the part independently
confirming a result given in [1]. We also give the contribution of the anomalous dimension of the Higgs field as well as the terms
to the top-Yukawa -function which can also be
derived from the anomalous dimension of the top quark mass. We compare the
results with the RG functions of the correlators of two and four scalar
currents in pure QCD and find a new relation between the anomalous dimension
of the QCD vacuum energy and the anomalous dimension
appearing in the RG equation of the correlator of two scalar currents. Together
with the recently computed top-Yukawa and QCD contributions to
[2,3] the -functions presented here constitute the leading four-loop
contributions to the evolution of the Higgs self-coupling. A numerical estimate
of these terms at the scale of the top-quark mass is presented as well as an
analysis of the impact on the evolution of up to the Planck scale and
the vacuum stability problem.Comment: v2: This is the version accepted by JHEP; extended discussion of the
numerics and vacuum stability analysis; references added; plot adde
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
Four-loop renormalization of QCD with a reducible fermion representation of the gauge group: anomalous dimensions and renormalization constants
We present analytical results at four-loop level for the renormalization
constants and anomalous dimensions of an extended QCD model with one coupling
constant and an arbitrary number of fermion representations. One example of
such a model is the QCD plus gluinos sector of a supersymmetric theory where
the gluinos are Majorana fermions in the adjoint representation of the gauge
group.
The renormalization constants of the gauge boson, ghost and fermion fields
are analytically computed as well as those for the ghost-gluon vertex, the
fermion-gluon vertex and the fermion mass. All other renormalization constants
can be derived from these. Some of these results were already produced in
Feynman gauge for the computation of the beta-function of this model, which was
recently published. Here we present results for an arbitrary gauge parameter.Comment: v2: version accepted by JHEP, extended discussion of the treatment of
Majorana spinor
Singlet Polarization Functions at O(\alpha_s^2)
We consider the three-loop singlet diagrams induced by axial-vector, scalar
and pseudo-scalar currents. Expansions for small and large external momentum
are presented. They are used in combination with conformal mapping and
Pad\'e approximations in order to arrive at results for the polarization
functions valid for all . Results are presented for the imaginary parts
which are directly related to physical quantities like the production of top
quarks or the decay of scalar or pseudo-scalar Higgs bosons.Comment: LaTeX, 15 pages, 10 figures included as ps-files. The complete paper
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
Five-Loop Vacuum Energy Beta Function in phi^4 Theory with O(N)-Symmetric and Cubic Interactions
The beta function of the vacuum energy density is analytically computed at
the five-loop level in O(N)-symmetric phi^4 theory, using dimensional
regularization in conjunction with the MSbar scheme. The result for the case of
a cubic anisotropy is also given. It is pointed out how to also obtain the beta
function of the coupling and the gamma function of the mass from vacuum graphs.
This method may be easier than traditional approaches.Comment: 16 pages, LaTeX; "note added" fixe
Precise Charm- and Bottom-Quark Masses: Theoretical and Experimental Uncertainties
Recent theoretical and experimental improvements in the determination of
charm and bottom quark masses are discussed. A new and improved evaluation of
the contribution from the gluon condensate to the
charm mass determination and a detailed study of potential uncertainties in the
continuum cross section for production is presented, together with a
study of the parametric uncertainty from the -dependence of our
results. The final results, MeV and
MeV, represent, together with a closely related lattice
determination MeV, the presently most precise
determinations of these two fundamental Standard Model parameters. A critical
analysis of the theoretical and experimental uncertainties is presented.Comment: 12 pages, presented at Quarks~2010, 16th International Seminar of
High Energy Physics, Kolomna, Russia, June 6-12, 2010; v2: references adde
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