Top-Yukawa effects on the β\beta-function of the strong coupling in the SM at four-loop level

We present analytical results for the QCD $\beta$-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 $\gamma_5$ contribution at order $y_t^4 g_s^4$, 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

Three-loop beta function for the Higgs self-coupling

In the last two years the renormalization group functions for the couplings and fields of the Standard Model have been computed at three-loop level. The evolution of the self-coupling $\lambda$ of the Standard Model Higgs boson is of particular importance due to its close connection with the stability of the Standard Model vacuum state. In this talk the three-loop corrections to the $\beta$-function for this crucial coupling are discussed. The calculation of three-loop $\beta$-functions and anomalous dimensions poses special technical challenges, such as the huge number of diagrams and the proper treatment of $\gamma_5$ in dimensional regularization. In order to avoid infrared divergences resulting from setting external momenta to zero in the case of the Higgs self-coupling an auxiliary mass is used to compute the ultraviolet divergences needed for the renormalization constants. This method is explained in some detail. Finally, an update for the status of the vacuum stability problem in the Standard Model up to the Planck scale is presented.Comment: Contribution to the proceedings of the Loops and Legs 2014 conferenc

Beta-function for the Higgs self-interaction in the Standard Model at three-loop level

The discovery of a Higgs particle has triggered numerous theoretical and experimental investigations concerning its production and decay rates and has led to interesting results concerning its interaction with fermions and gauge bosons. The self-interaction $\lambda$ of the Standard Model Higgs boson is particularly important due to its close connection with the stability of the SM vacuum. In this talk precision calculations for the evolution of this crucial coupling are presented and their impact on the question of vacuum stability is analysed. We also compare the theoretical precision resulting from the calculation of three-loop $\beta$-functions to the experimental uncertainties stemming from key parameters, such as the top mass, the Higgs mass and the strong coupling, and to the theoretical uncertainties introduced by the matching of experimental data to parameters in the theoretically favoured $\overline{\text{MS}}$ renormalization scheme.Comment: contribution to the proceedings of the European Physical Society Conference on High Energy Physics, 201

Volcanic impact on stratospheric aerosol chemistry

Samples collected by the National Center for Atmospheric Research (NCAR) using the multiple-filter sampler on the U-2 were analyzed. The sampler is capable of exposing a number of 110 mm filters in sequence to ram air flow. Two types of filters, IPC cellulose and polystrene, were used, both of which have high blank levels for the trace elements determined. The levels of most trace elements in the stratosphere are so low under normal circumstances that none can be seen. Results from the eruption of Mt. St. Helens, a mystery cloud (probably volcanic in origin) in 1982, and the El Chichonal eruption in 1983 are discussed. To improve the collection of particles for chemical analysis, a new sampling system was developed for use on the U-2. The sampler consisted of an electrostatic collection of particles between 1 and 0.001 micron diameter dierectly onto electron microscopic grids, followed by a thermal precipitation for the smaller particles. The system was built and tested in the laboratory, but never flown on the U-2