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M. F. Zoller

Publications and source records attributed to M. F. Zoller.

11 recordsLinked to original sources
arXiv2017

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.

hep-ph↗
arXiv2016

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

We present analytical results for the QCD $β$-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 $γ_5$ contribution at order $y_t^4 g_s^4$, a feature not encountered in lower loop orders.

hep-ph↗
arXiv2016

Leading QCD-induced four-loop contributions to the $β$-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 $β$-function for the Higgs self-coupling $λ$ of the Standard Model at four-loop level, namely the part $\propto y_t^4 g_s^6$ independently confirming a result given in [1]. We also give the contribution $\propto y_t^2 g_s^6$ of the anomalous dimension of the Higgs field as well as the terms $\propto y_t g_s^8$ to the top-Yukawa $β$-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 $γ_0$ of the QCD vacuum energy and the anomalous dimension $γ_m^{SS}$ appearing in the RG equation of the correlator of two scalar currents. Together with the recently computed top-Yukawa and QCD contributions to $β_{g_s}$ [2,3] the $β$-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 $λ$ up to the Planck scale and the vacuum stability problem.

hep-ph↗
arXiv2016

OPE of the energy-momentum tensor correlator and the gluon condensate operator in massless QCD to three-loop order

The correlator of two gluonic operators plays an important role for example in transport properties of a Quark Gluon Plasma (QGP) or in sum rules for glueballs. In [1] an operator product expansion (OPE) at zero temperature was performed for the correlators of two scalar operators $O_1=-\frac{1}{4} G^{μν}G_{μν}$ and two QCD energy-momentum tensors $T^{μν}$. There we presented analytical two-loop results for the Wilson coefficient $C_1$ in front of the gluon condensate operator $O_1$. In this paper these results are extended to three-loop order. The three-loop Wilson coefficient $C_0$ in front of the unity operator $O_0=1$ was already presented in [1] for the $T^{μν}$-correlator. For the $O_1$-correlator the coefficient $C_0$ is known to four loop order from [2]. For the correlator of two pseudoscalar operators $\tilde{O}_1=\varepsilon_{μνρσ} G^{μν} G^{ρσ}$ both coefficients $C_0$ and $C_1$ were computed in [3] to three-loop order. At zero temperature $C_0$ and $C_1$ are the leading Wilson coefficients in massless QCD.

hep-ph↗
arXiv2014

OPE of the energy-momentum tensor correlator in massless QCD

We analytically calculate higher order corrections to coefficient functions of the operator product expansion (OPE) for the Euclidean correlator of two energy-momentum tensors in massless QCD. These are the three-loop contribution to the coefficient C_0 in front of the unity operator O_0=1 and the one and two-loop contributions to the coefficient C_1 in front of the gluon "condensate" operator O_1=-1/4 G^{μν} G_{μν}. For the correlator of two operators O_1 we present the coefficient C_1 at two-loop level.

hep-ph↗
arXiv2013

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 $λ$ 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 $β$-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.

hep-ph↗
arXiv2013

Vacuum stability in the SM and the three-loop β-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 $λ$ and its evolution with the energy scale of a given physical process. This is described by the $β$-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.

hep-ph↗
arXiv2013

OPE of the pseudoscalar gluonium correlator in massless QCD to three-loop order

In this paper analytical results are presented for higher order corrections to coefficient functions of the operator product expansion (OPE) for the correlator of two pseudoscalar gluonium operators \tilde{O}_1=G^{μν}\tilde{G}_{μν}. The Wilson coefficient in front of the scalar gluon condensate operator O_1=-1/4 G^{μν}G_{μν} is given at three-loop accuracy. The leading coefficient C_0 in front of the unity operator O_0=1 has been calculated up to three-loop order some time ago but has been checked independently in this work. It is interesting to see that the coefficient C_1 in the pseudoscalar case is finite, whereas contact terms appear in C_0 in this case and in both coefficients C_0 and C_1 in the cases of the scalar gluonium correlator and the energy momentum tensor correlator. For the corresponding Renormalization Group invariant Wilson coefficients which are also constructed the results are partially extended to four-loop accuracy. All results are given in the MSbar-scheme at zero temperature.

hep-ph↗
arXiv2012

Three-loop β-functions for top-Yukawa and the Higgs self-interaction in the Standard Model

We analytically compute the dominant contributions to the β-functions for the top-Yukawa coupling, the strong coupling and the Higgs self-coupling as well as the anomalous dimensions of the scalar, gluon and quark fields in the unbroken phase of the Standard Model at three-loop level. These are mainly the QCD and top-Yukawa corrections. The contributions from the Higgs self-interaction which are negligible for the running of the top-Yukawa and the strong coupling but important for the running of the Higgs self-coupling are also evaluated.

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