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

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

Vacuum stability in the SM and the three-loop \beta-function for the Higgs self-interaction

In this article the stability of the Standard Model (SM) vacuum in the presence of radiative corrections and for a Higgs boson with a mass in the vicinity of 125 GeV is discussed. The central piece in this discussion will be the Higgs self-interaction $\lambda$ and its evolution with the energy scale of a given physical process. This is described by the $\beta$-function to which we recently computed analytically the dominant three-loop contributions. These are mainly the QCD and top-Yukawa corrections as well as the contributions from the Higgs self-interaction itself. We will see that for a Higgs boson with a mass of about 125 GeV the question whether the SM vacuum is stable and therefore whether the SM could be valid up to Planck scale cannot be answered with certainty due to large experimental uncertainties, mainly in the top quark mass.Comment: Extended version of a talk given at the ISSP 2012 in Erice, 23 June - 2 July 2012, part of the proceedings for this school; v2: references added; v3: references added; v4: references added, improved Fig. 1; v5: final version as submitted for publication, new Fig.

Quantum localization bounds Trotter errors in digital quantum simulation

A fundamental challenge in digital quantum simulation (DQS) is the control of an inherent error, which appears when discretizing the time evolution of a quantum many-body system as a sequence of quantum gates, called Trotterization. Here, we show that quantum localization-by constraining the time evolution through quantum interference-strongly bounds these errors for local observables, leading to an error independent of system size and simulation time. DQS is thus intrinsically much more robust than suggested by known error bounds on the global many-body wave function. This robustness is characterized by a sharp threshold as a function of the Trotter step size, which separates a localized region with controllable Trotter errors from a quantum chaotic regime. Our findings show that DQS with comparatively large Trotter steps can retain controlled errors for local observables. It is thus possible to reduce the number of gate operations required to represent the desired time evolution faithfully

Four-loop QCD β\beta-function with different fermion representations of the gauge group

We present analytical results at four-loop level for the $\beta$-function of the coupling of a generic gauge group and any number of different quark representations. From this we can directly derive the gluino contribution to the strong coupling $\beta$-function of supersymmetric extensions of the Standard Model.Comment: v2: reference added, version accepted by JHEP, v3: typo fixed in (3.4

Tensor networks for Lattice Gauge Theories and Atomic Quantum Simulation

We show that gauge invariant quantum link models, Abelian and non-Abelian, can be exactly described in terms of tensor networks states. Quantum link models represent an ideal bridge between high-energy to cold atom physics, as they can be used in cold-atoms in optical lattices to study lattice gauge theories. In this framework, we characterize the phase diagram of a (1+1)-d quantum link version of the Schwinger model in an external classical background electric field: the quantum phase transition from a charge and parity ordered phase with non-zero electric flux to a disordered one with a net zero electric flux configuration is described by the Ising universality class.Comment: 9 pages, 9 figures. Published versio

Optimal quantum control of Bose Einstein condensates in magnetic microtraps

Transport of Bose-Einstein condensates in magnetic microtraps, controllable by external parameters such as wire currents or radio-frequency fields, is studied within the framework of optimal control theory (OCT). We derive from the Gross-Pitaevskii equation the optimality system for the OCT fields that allow to efficiently channel the condensate between given initial and desired states. For a variety of magnetic confinement potentials we study transport and wavefunction splitting of the condensate, and demonstrate that OCT allows to drastically outperfrom more simple schemes for the time variation of the microtrap control parameters.Comment: 11 pages, 7 figure