7,535 research outputs found
On the renormalization of operator products: the scalar gluonic case
In this paper we study the renormalization of the product of two operators
in QCD. An insertion of two such
operators into a Greens function produces divergent contact
terms for .
In the course of the computation of the operator product expansion (OPE) of
the correlator of two such operators to three-loop order we discovered that divergent contact
terms remain not only in the leading Wilson coefficient , which is just
the VEV of the correlator, but also in the Wilson coefficient in front of
. As this correlator plays an important role for example in QCD sum rules
a full understanding of its renormalization is desireable.
This work explains how the divergences encountered in higher orders of an OPE
of this correlator should be absorbed in counterterms and derives an additive
renormalization constant for from first principles and to all orders in
perturnbation theory. The method to derive the renormalization of this operator
product is an extension of the ideas of a paper by Spiridonov and can be
generalized to other cases.Comment: v2: this is the version accepted by JHEP; more detailed discussion of
phenomenological application
Vacuum stability in the SM and the three-loop \beta-function for the Higgs self-interaction
In this article the stability of the Standard Model (SM) vacuum in the
presence of radiative corrections and for a Higgs boson with a mass in the
vicinity of 125 GeV is discussed. The central piece in this discussion will be
the Higgs self-interaction and its evolution with the energy scale of
a given physical process. This is described by the -function to which we
recently computed analytically the dominant three-loop contributions. These are
mainly the QCD and top-Yukawa corrections as well as the contributions from the
Higgs self-interaction itself. We will see that for a Higgs boson with a mass
of about 125 GeV the question whether the SM vacuum is stable and therefore
whether the SM could be valid up to Planck scale cannot be answered with
certainty due to large experimental uncertainties, mainly in the top quark
mass.Comment: Extended version of a talk given at the ISSP 2012 in Erice, 23 June -
2 July 2012, part of the proceedings for this school; v2: references added;
v3: references added; v4: references added, improved Fig. 1; v5: final
version as submitted for publication, new Fig.
Top-Yukawa effects on the -function of the strong coupling in the SM at four-loop level
We present analytical results for the QCD -function extended to the
gaugeless limit of the unbroken phase of the Standard Model at four-loop level.
Apart from the strong coupling itself we include the top-Yukawa contribution
and the Higgs self-coupling. We observe a non-naive contribution at
order , a feature not encountered in lower loop orders.Comment: v2: more sophisticated treatment and more detailed description of the
non-naive \gamma_5 contribution; Ref. added. v3: this the version published
in JHEP; references [49,50] fixed; v4: changed statement on p.8: a different
gamma_5 treatment only leads to a factor 3, not a factor 6 in the non-naive
part compared to the prescription used in this paper. Note added on recent
developments (p. 12
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