36 research outputs found
Three-loop SM beta-functions for matrix Yukawa couplings
We present the extension of our previous results for three-loop Yukawa
coupling beta-functions to the case of complex Yukawa matrices describing the
flavour structure of the SM. The calculation is carried out in the context of
unbroken phase of the SM with the help of the MINCER program in a general
linear gauge and cross-checked by means of MATAD/BAMBA codes. In addition,
ambiguities in Yukawa matrix beta-functions are studied.Comment: 9 pages, references added, version accepted by PL
Three-loop Higgs self-coupling beta-function in the Standard Model with complex Yukawa matrices
Three-loop renormalization group equations for the Higgs self-coupling and
Higgs mass parameter are recalculated in the case of complex Yukawa matrices,
which encompass general flavour structure of the Standard Model. In addition,
the anomalous dimensions both for the quantum Higgs field and its vacuum
expectation value are presented in the -scheme. A numerical
study of the latter quantities is carried out for a certain set of initial
parameters.Comment: 14 pages, 2 figures, report numbers added, figures redraw
Three-loop massive tadpoles and polylogarithms through weight six
We evaluate the three-loop massive vacuum bubble diagrams in terms of
polylogarithms up to weight six. We also construct the basis of irrational
constants being harmonic polylgarithms of arguments .Comment: 26 pages, 4 ancillary files, v3: version published in JHEP: minor
additions, file with results for massive three-loop form-factor integrals
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On the -quark running mass in QCD and the SM
We consider electroweak corrections to the relation between the running
mass of the quark in the five-flavor
QCDQED effective theory and its counterpart in the Standard Model (SM).
As a bridge between the two parameters, we use the pole mass of the
quark, which can be calculated in both models. The running mass is not a
fundamental parameter of the SM Lagrangian, but the product of the running
Yukawa coupling and the Higgs vacuum expectation value. Since there exist
different prescriptions to define the latter, the relations considered in the
paper involve a certain amount of freedom. All the definitions can be related
to each other in perturbation theory. Nevertheless, we argue in favor of a
certain gauge-independent prescription and provide a relation which can be
directly used to deduce the value of the Yukawa coupling of the quark at
the electroweak scale from its effective QCD running mass. This approach allows
one to resum large logarithms systematically. Numerical analysis
shows that, indeed, the corrections to the proposed relation are much smaller
than those between and .Comment: 19 pages, 4 figures, misprints corrected (thanks to S. Martin),
results not affecte