New Formulas and Predictions for Running Fermion Masses at Higher Scales in SM, 2HDM, and MSSM

Current experimental data indicate that the Koide relation for the pole masses of charged leptons, which can be parametrized as $Q^{pole}_l = 2/3$, is valid up to the accuracy of $O(10^{-5})$. We show that the running masses of charged leptons fail in satisfying the Koide relation (i.e., $Q_l(\mu) \neq 2/3$), but the discrepancy between $Q_l (\mu)$ and $Q^{pole}_l$ is only about 0.2% at $\mu=M_Z$. The Koide-like relations for the running masses of neutrinos ($1/3 < Q_\nu(M_Z)...

In this paper the formulae are collected which are needed for the computation of the strong coupling constant and quark masses at different energy scales and for different number of active flavours. All equations contain the state-of-the-art QCD corrections up to three- and sometimes even four-loop order. For the practical implementation {\tt Mathematica} is used and a package containing useful procedures is provided.

In these proceedings we review two aspects of 2HDMs with generic Yukawa structures. The first part considers how recent deviations from the SM expectations in tauonic B decays (observed by BABAR) can be explained in a 2HDM of type III with sizable flavour violation in the up-sector. The second part discusses the matching of the MSSM on the 2HDM of type III. Here we focus on the recently calculated two-loop SQCD corrections to the Higgs-quark-quark couplings.

We derive one-loop renormalization group equations (RGE's) for Yukawa coupling parameters of quarks and for the vacuum expectation values of the Higgs doublets in a general framework of the Standard Model with two Higgs doublets (2HDM ``type III''). In the model, the neutral-Higgs-mediated flavor-changing neutral currents are allowed but are assumed to be reasonably suppressed at low energies. The popular ``type II'' and ``type I'' models are just special cases of this framew...

We report first results of an ongoing project devoted to the analytical calculation of the QCD $\beta$-function and the quark mass anomalous dimension at the five loop level.

Integrated forms of the one-loop evolution equations are given for the Yukawa couplings in the MSSM, valid for any value of $\tan \beta$, generalizable to virtually any number of Yukawa fermions, and including all gauge couplings. These forms turn out to have nice mathematical convergence properties which we prove, and we determine the ensuing convergence criteria. Furthermore, they allow to write down general sufficient and necessary conditions to avoid singularities in the ...

Running quark mass values $m_q(\mu)$ at some typical energy scales ($\mu=1$ GeV, $\mu=m_W$, and so on) are reviewed. The values depend considerably on the value of $\Lambda_{\overline{MS}}$, especially, the value of top quark mass at $\mu=1$ GeV does so. The relative ratios of light quark masses ($m_u$, $m_d$ and $m_s$) to heavy quark masses ($m_c$, $m_b$ and $m_t$) are still controversial.

We discuss Pad\'e-improvement of known four-loop order results based upon an asymptotic three-parameter error formula for Pad\'e-approximants. We derive an explicit formula estimating the next-order coefficient $R_4$ from the previous coefficients in a series $1+R_1 x + R_2x^2 + R_3x^3$. We show that such an estimate is within 0.18% of the known five-loop order term in the O(1) $\beta$-function, and within 10% of the known five-loop term in the O(1) anomalous mass-dimension f...

In the context of the Grand Unified MSSM, we investigate the fermion mass matrices at GUT scale. We note that from the experimental mass pattern the determinants of the Yukawa matrices at this scale can be unified with good precision. Taking the unification o determinants as an hypothesis, it gives two model independent predictions that in the MSSM turns out to determine an appropriate value for the product m_d m_s and tan(beta)~7-10 in the favored range. We then review a pre...

We revisit the renormalisation group equations (RGE) for general renormalisable gauge theories at one- and two-loop accuracy. We identify and correct various mistakes in the literature for the $\beta$-functions of the dimensionful Lagrangian parameters (the fermion mass, the bilinear and trilinear scalar couplings) as well as the dimensionless quartic scalar couplings. There are two sources for these discrepancies. Firstly, the known expressions for the scalar couplings assum...