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 $\overline{MS}$-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 $e^{k i \pi/3}$.Comment: 26 pages, 4 ancillary files, v3: version published in JHEP: minor additions, file with results for massive three-loop form-factor integrals adde

On the bb-quark running mass in QCD and the SM

We consider electroweak corrections to the relation between the running $\overline{\mathrm{MS}}$ mass $m_b$ of the $b$ quark in the five-flavor QCD$\times$QED effective theory and its counterpart in the Standard Model (SM). As a bridge between the two parameters, we use the pole mass $M_b$ of the $b$ 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 $y_b$ 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 $b$ quark at the electroweak scale from its effective QCD running mass. This approach allows one to resum large logarithms $\ln(m_b/M_t)$ systematically. Numerical analysis shows that, indeed, the corrections to the proposed relation are much smaller than those between $y_b$ and $M_b$.Comment: 19 pages, 4 figures, misprints corrected (thanks to S. Martin), results not affecte

Synchrotron aging and the radio spectrum of SN 1993J

We combine the GMRT low frequency radio observations of SN 1993J with the VLA high frequency radio data to get a near simultaneous spectrum around day 3200 since explosion. The low frequency measurements of the supernova determine the turnover frequency and flux scale of the composite spectrum and help reveal a steepening in the spectral index, $\Delta \alpha \sim 0.6$, in the optically thin part of the spectrum. This is the first observational evidence of a break in the radio spectrum of a young supernova. We associate this break with the phenomenon of synchrotron aging of radiating electrons. From the break in the spectrum we calculate the magnetic field in the shocked region independent of the equipartition assumption between energy density of relativistic particles and magnetic energy density. We determine the ratio of these two energy densities and find that this ratio is in the range: $8\times 10^{-6}-5\times 10^{-4}$. We also predict the nature of the evolution of the synchrotron break frequency with time, with competing effects due to diffusive Fermi acceleration and adiabatic expansion of the radiative electron plasma.Comment: 12 pages, 2 figures. Accepted for publication in ApJ