2,910 research outputs found
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 and its evolution with the energy scale of
a given physical process. This is described by the -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.
Top-Yukawa effects on the -function of the strong coupling in the SM at four-loop level
We present analytical results for the QCD -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 contribution at
order , 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 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 -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
renormalization scheme.Comment: contribution to the proceedings of the European Physical Society
Conference on High Energy Physics, 201
Four-loop QCD -function with different fermion representations of the gauge group
We present analytical results at four-loop level for the -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 -function of supersymmetric extensions of the
Standard Model.Comment: v2: reference added, version accepted by JHEP, v3: typo fixed in
(3.4
Leading QCD-induced four-loop contributions to the -function of the Higgs self-coupling in the SM and vacuum stability
We present analytical results for the leading top-Yukawa and QCD contribution
to the -function for the Higgs self-coupling of the Standard
Model at four-loop level, namely the part independently
confirming a result given in [1]. We also give the contribution of the anomalous dimension of the Higgs field as well as the terms
to the top-Yukawa -function which can also be
derived from the anomalous dimension of the top quark mass. We compare the
results with the RG functions of the correlators of two and four scalar
currents in pure QCD and find a new relation between the anomalous dimension
of the QCD vacuum energy and the anomalous dimension
appearing in the RG equation of the correlator of two scalar currents. Together
with the recently computed top-Yukawa and QCD contributions to
[2,3] the -functions presented here constitute the leading four-loop
contributions to the evolution of the Higgs self-coupling. A numerical estimate
of these terms at the scale of the top-quark mass is presented as well as an
analysis of the impact on the evolution of up to the Planck scale and
the vacuum stability problem.Comment: v2: This is the version accepted by JHEP; extended discussion of the
numerics and vacuum stability analysis; references added; plot adde
Four-loop renormalization of QCD with a reducible fermion representation of the gauge group: anomalous dimensions and renormalization constants
We present analytical results at four-loop level for the renormalization
constants and anomalous dimensions of an extended QCD model with one coupling
constant and an arbitrary number of fermion representations. One example of
such a model is the QCD plus gluinos sector of a supersymmetric theory where
the gluinos are Majorana fermions in the adjoint representation of the gauge
group.
The renormalization constants of the gauge boson, ghost and fermion fields
are analytically computed as well as those for the ghost-gluon vertex, the
fermion-gluon vertex and the fermion mass. All other renormalization constants
can be derived from these. Some of these results were already produced in
Feynman gauge for the computation of the beta-function of this model, which was
recently published. Here we present results for an arbitrary gauge parameter.Comment: v2: version accepted by JHEP, extended discussion of the treatment of
Majorana spinor
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
- …