Unification scale vs. electroweak-triplet mass in the SU(5) + 24_F model at three loops

It was shown recently that the original SU(5) theory of Georgi and Glashow, augmented with an adjoint fermionic multiplet 24_F, can be made compatible both with neutrino masses and gauge coupling unification. In particular, the model predicts that either electroweak-triplet states are light, within the reach of the Large Hadron Collider (LHC), or proton decay will become accessible at the next generation of megaton-scale facilities. In this paper, we present the computation of the correlation function between the electroweak-triplet masses and the unification scale at the next-to-next-to-leading-order (NNLO). Such an accuracy on the theory side is necessary in order to settle the convergence of the perturbative expansion and to match the experimental precision on the determination of the electroweak gauge couplings at the Z-boson mass scale.Comment: 16 pages, 7 figures. One reference added. To appear in Phys. Rev.

Precision Calculations in Supersymmetric Theories

In this review article we report on the newest developments in precision calculations in supersymmetric theories. An important issue related to this topic is the construction of a regularization scheme preserving simultaneously gauge invariance and supersymmetry. In this context, we discuss in detail dimensional reduction in component field formalism as it is currently the preferred framework employed in the literature. Furthermore, we set special emphasis on the application of multi-loop calculations to the analysis of gauge coupling unification, the prediction of thelightest Higgs boson mass and the computation of the hadronic Higgs production and decay rates in supersymmetric models. Such precise theoretical calculations up to the fourth order in perturbation theory are required in order to cope with the expected experimental accuracy on the one hand, and to enable us to distinguish between the predictions of the Standard Model and those of supersymmetric theories on the other hand.Comment: 106 pages, 36 figure

On the gauge dependence of the Standard Model vacuum instability scale

After reviewing the calculation of the Standard Model one-loop effective potential in a class of linear gauges, we discuss the physical observables entering the vacuum stability analysis. While the electroweak-vacuum-stability bound on the Higgs boson mass can be formally proven to be gauge independent, the field value at which the effective potential turns negative (the so-called instability scale) is a gauge dependent quantity. By varying the gauge-fixing scheme and the gauge-fixing parameters in their perturbative domain, we find an irreducible theoretical uncertainty of at least two orders of magnitude on the scale at which the Standard Model vacuum becomes unstable.Comment: 24 pages, 4 figures. One reference added. To appear in JHE

Gamma(H→bbˉ)Gamma(H\to b\bar{b}) to order ααs\alpha\alpha_s

We compute the decay rate of the Standard Model Higgs boson to bottom quarks to order $\alpha\alpha_s$. We apply the optical theorem and calculate the imaginary part of three-loop corrections to the Higgs boson propagator using asymptotic expansions in appropriately chosen mass ratios. The corrections of order $\alpha\alpha_s$ are of the same order of magnitude as the ${\cal O}(\alpha_s^3)$ QCD corrections but have the opposite sign.Comment: 16 pages, 2 figures and 7 table

Critical behavior of Dirac fermions from perturbative renormalization

Gapless Dirac fermions appear as quasiparticle excitations in various condensed-matter systems. They feature quantum critical points with critical behavior in the 2+1 dimensional Gross-Neveu universality class. The precise determination of their critical exponents defines a prime benchmark for complementary theoretical approaches, such as lattice simulations, the renormalization group and the conformal bootstrap. Despite promising recent developments in each of these methods, however, no satisfactory consensus on the fermionic critical exponents has been achieved, so far. Here, we perform a comprehensive analysis of the Ising Gross-Neveu universality classes based on the recently achieved four-loop perturbative calculations. We combine the perturbative series in $4-\epsilon$ spacetime dimensions with the one for the purely fermionic Gross-Neveu model in $2+\epsilon$ dimensions by employing polynomial interpolation as well as two-sided Pad\'e approximants. Further, we provide predictions for the critical exponents exploring various resummation techniques following the strategies developed for the three-dimensional scalar $O(n)$ universality classes. We give an exhaustive appraisal of the current situation of Gross-Neveu universality by comparison to other methods. For large enough number of spinor components $N\geq 8$ as well as for the case of emergent supersymmetry $N=1$, we find our renormalization group estimates to be in excellent agreement with the conformal bootstrap, building a strong case for the validity of these values. For intermediate $N$ as well as in comparison with recent Monte Carlo results, deviations are found and critically discussed.Comment: 21 pages, 7 figures, 6 table