arXiv subjects

Axel Maas

Publications and source records attributed to Axel Maas.

At least 55 records · Page 3Linked to original sources

arXiv2020

Constraining the gauge-fixed Lagrangian in minimal Landau gauge

A continuum formulation of gauge-fixing resolving the Gribov-Singer ambiguity remains a challenge. Finding a Lagrangian formulation of operational resolutions in numerical lattice calculations, like minimal Landau gauge, would be one possibility. Such a formulation will here be constrained by reconstructing the Dyson-Schwinger equation for which the lattice minimal-Landau-gauge ghost propagator is a solution. It is found that this requires an additional term. As a by-product new, high precision lattice results for the ghost-gluon vertex in three and four dimensions are obtained.

hep-lat↗

arXiv2019

Probing standard-model Higgs substructures using tops and weak gauge bosons

Manifest gauge-invariance requires that observable states in the standard-model are described by composite operators, which involve additional Higgs contributions beyond perturbation theory. This field-theoretical effect has been confirmed in lattice simulations. It should also be experimentally accessible at high enough precision. Here a few estimates for such signatures at current and future collider experiments will be discussed.

hep-ph↗

arXiv2019

Exploring the Tan contact term in Yang-Mills theory

Reliably computing the free energy in a gauge theory like QCD is a challenging and resource-demanding endeavor. As an alternative, we explore here the possibility to obtain the associated thermodynamic anomaly by exploiting its relation to the Tan contact. Optimally, this would reduce the determination of the free energy to a high-precision calculation of two-point correlators. We study this possibility using the lattice and functional methods and compare them to the expected behavior for the SU(2) Yang-Mills case.

hep-ph↗

arXiv2019

Toward the spectrum of the SU(2) adjoint Higgs model

Scalar particles in the adjoint representation of a non-Abelian gauge theory play an important role in many scenarios beyond the standard model, especially of GUT type. For such theories manifestly gauge-invariant, massless, composite vector particles have been predicted, even at weak coupling, using the Fröhlich-Morchio-Strocchi mechanism. We use lattice gauge theory to investigate the simplest such theories, a single adjoint scalar coupled to an SU(2) Yang-Mills theory. The results support the existence of such a particle, in accordance with the prediction.

hep-lat↗

arXiv2019

The quenched SU(2) scalar-gluon vertex in minimal Landau gauge

The question of whether confining effects are visible in correlation functions is a long-standing one. Complementing investigations on the propagators of fundamental and adjoint scalar matter particles here the quenched scalar-gluon vertex is investigated. For this purpose a multitude of lattice setups in two, three, and four dimensions is analyzed in quenched SU(2) lattice gauge theory. Though both cases are quantitatively different, neither a qualitative difference nor any singularities are observed.

hep-lat↗

arXiv2019

Finite-density gauge correlation functions in QC2D

2-color QCD is the simplest QCD-like theory which is accessible to lattice simulations at finite density. It therefore plays an important role to test qualitative features and to provide benchmarks to other methods and models, which do not suffer from a sign problem. To this end, we determine the minimal-Landau-gauge propagators and 3-point vertices in this theory over a wide range of densities, the vacuum, and at both finite temperature and density. The results show that there is essentially no modification of the gauge sector in the low-temperature, low-density phase. Even outside this phase only mild modifications appear, mostly in the chromoelectric sector.

hep-lat↗

arXiv2019

The quenched SU(2) adjoint scalar propagator in minimal Landau gauge

It is a long-standing question whether the confinement of matter fields in QCD has an imprint in the (gauge-dependent) correlation functions, especially the propagators. In particular in the quenched case a fundamental difference could be expected between adjoint and fundamental matter. In a preceding investigation the propagator of a fundamental scalar has been studied, showing no obvious sign of confinement. Here, complementary, the adjoint scalar propagator is investigated over a wide range of parameters in the minimal Landau gauge using lattice gauge theory. This study is performed in two, three, and four dimensions in quenched SU(2) Yang-Mills theory, both in momentum space and position space. No conclusive difference between both cases is found.

hep-lat↗

arXiv2019

On the observable spectrum of theories with a Brout-Englert-Higgs effect

The physical, observable spectrum in gauge theories is made up from gauge-invariant states. The Fröhlich-Morchio-Strocchi mechanism allows in the standard model to map these states to the gauge-dependent elementary $W$, $Z$ and Higgs states. This is no longer necessarily the case in theories with a more general gauge group and Higgs sector. We classify and predict the physical spectrum for a wide range of such theories, with special emphasis on GUT-like cases, and show that discrepancies between the spectrum of elementary fields and physical particles frequently arise.

hep-ph↗

arXiv2019

Brout-Englert-Higgs physics: From foundations to phenomenology

The aim of this review is to describe the field-theoretical foundations of Brout-Englert-Higgs (BEH) physics, and to show how the usual phenomenology arises from it. This requires to give a precise and gauge-invariant meaning to the underlying physics. This is complicated by the fact that concepts like the Higgs vacuum expectation value or the separation between confinement and the BEH effect loose their meaning beyond perturbation theory. This is addressed by carefully constructing the corresponding theory space and the quantum phase diagram. The physical spectrum needs then to be also given in terms of gauge-invariant, i. e. composite, states. Using gauge-invariant perturbation theory, as developed by Froehlich, Morchio, and Strocchi, it is possible to rederive conventional perturbation theory. This derivation explicitly shows why the description of the standard model in terms of the unphysical, gauge-dependent, elementary states of the Higgs and W-bosons and Z-boson, but also of the elementary fermions, is adequate and successful. These are unavoidable consequences of the field theory underlying the standard model, from which the usual picture emerges. The validity of this emergence can only be tested non-perturbatively. Such tests, in particular using lattice gauge theory, will be reviewed as well. They fully confirm the underlying mechanisms. It will be seen that the structure of the standard model is very special, and qualitative changes occur beyond it. The extension beyond the standard model will therefore also be reviewed. Particular attention will be given to structural differences arising for phenomenology. Again, non-perturbative tests of these results will be reviewed. Finally, to make this review self-contained a brief discussion of issues like the triviality and hierarchy problem, and how they fit into a fundamental field-theoretical formulation, is included.

hep-ph↗

arXiv2019

Exploratory study of the off-shell properties of the weak vector bosons

Gauge invariance requires even in the weak interactions that physical, observable particles are described by gauge-invariant composite operators. Such operators have the same structure as those describing bound states, and consequently the physical versions of the $W^\pm$, the $Z$, and the Higgs should have some kind of substructure. To test this consequence, we use lattice gauge theory to study the physical weak vector bosons off-shell, especially their form-factor and weak radius, and compare the results to the ones for the elementary particles. We find that the physical particles show substantial deviations from the structure of a point-like particle. At the same time the gauge-dependent elementary particles exhibit unphysical behavior.

hep-lat↗

arXiv2018

Bound state properties from the Functional Renormalisation Group

We discuss an approach for accessing bound state properties, like mass and decay width, of a theory within the functional renormalisation group approach. An important cornerstone is the dynamical hadronization technique for resonant interaction channels. The general framework is exemplified and put to work within the two-flavour quark-meson model. This model provides a low-energy description of the dynamics of two-flavour QCD with quark and hadronic degrees of freedom. We compare explicitly the respective results for correlation functions and observables with first principle QCD results in a quantitative manner. This allows us to estimate the validity range of low energy effective models. We also present first results for pole masses and decay widths. Next steps involving real-time formulations of the functional renormalisation group are discussed.

hep-ph↗

arXiv2018

On observable particles in theories with a Brout-Englert-Higgs effect

Even at weak coupling the physical, observable spectrum of gauge theories with a Brout-Englert-Higgs effect can deviate from the elementary one of perturbation theory. This can be analytically described and treated using the Fröhlich-Morchio-Strocchi mechanism. We confirm this by lattice simulation for an SU(3) gauge theory with a fundamental scalar, a toy model for grand unification. We also show that this has experimentally observable consequence, e.g., in scattering cross-sections of lepton collisions in this toy model.

hep-lat↗

arXiv2018

The spectrum of an SU(3) gauge theory with a fundamental Higgs field

In gauge theories, the physical, experimentally observable spectrum consists only of gauge-invariant states. This spectrum can be different from the elementary spectrum even at weak coupling and in the presence of the Brout-Englert-Higgs effect. We demonstrate this for an SU(3) gauge theory with a single fundamental Higgs, a toy theory for grand-unified theories. The manifestly gauge-invariant approach of lattice gauge theory is used to determine the spectrum in four different channels. It is found to be qualitatively different from the elementary one, and especially from the one predicted by standard perturbation theory. The result can be understood in terms of the Froehlich-Morchio-Strocchi mechanism. In fact, we find that analytic methods based on this mechanism, a gauge-invariant extension of perturbation theory, correctly determines the spectrum, and gives already at leading order a reasonably good quantitative description. Together with previous results this supports that this approach is the analytic method of choice for theories with a Brout-Englert-Higgs effect.

hep-lat↗

arXiv2017

Dependence of the propagators on the sampling of Gribov copies inside the first Gribov region of Landau gauge

Beyond perturbation theory the number of gauge copies drastically increases due to the Gribov-Singer ambiguity. Any way of treating them defines, in principle, a new, non-perturbative gauge, and the gauge-dependent correlation functions can vary between them. Herein various such gauges will be constructed as completions of the Landau gauge inside the first Gribov region. The dependence of the propagators and the running coupling on these gauges will be studied for SU(2) Yang-Mills theory in two, three, and four dimensions using lattice gauge theory, and for a wide range of lattice parameters. While the gluon propagator is rather insensitive to the choice, the ghost propagator and the running coupling show a stronger dependence. It is also found that the influence of lattice artifacts is larger than in minimal Landau gauge.

hep-lat↗

arXiv2017

Constructing a neutron star in G2-QCD

The inner structure of neutron stars is still an open question. To make progress and understand the qualitative impact of gauge interactions on the neutron star structure we study neutron stars in a modified version of QCD. In this modification the gauge group of QCD is replaced by the exceptional Lie group G$_2$, which has neutrons and is accessible at finite density in lattice calculations. Using an equation of state constructed from lattice calculations we determine the mass-radius-relation for a neutron star in this theory using the Tolman-Oppenheimer-Volkoff equation. The results exhibit an influence of the non-trivial interactions on the mass-radius relation. However, the masses of the quarks are found to have little influence. We also give density profiles and the phase structure inside the neutron star. If the results carry over to full QCD, much of the internal structure of neutron stars could already be inferred from a precise measurement of the mass-radius relation.

astro-ph.HE↗

arXiv2017

Gluon and ghost correlation functions of 2-color QCD at finite density

2-color QCD, i. e. QCD with the gauge group SU(2), is the simplest non-Abelian gauge theory without sign problem at finite quark density. Therefore its study on the lattice is a benchmark for other non-perturbative approaches at finite density. To provide such benchmarks we determine the minimal-Landau-gauge 2-point and 3-gluon correlation functions of the gauge sector and the running gauge coupling at finite density. We observe no significant effects, except for some low-momentum screening of the gluons at and above the supposed high-density phase transition.

hep-lat↗

arXiv2017

A study of how the particle spectra of SU(N) gauge theories with a fundamental Higgs emerge

In gauge theories, the physical, experimentally observable spectrum consists only of gauge-invariant states. In the standard model the Fröhlich-Morchio-Strocchi mechanism shows that these states can be adequately mapped to the gauge-dependent elementary W, Z, Higgs, and fermions. In theories with a more general gauge group and Higgs sector, appearing in various extensions of the standard model, this has not to be the case. In this work we determine analytically the physical spectrum of $\mathrm{SU}(N>2)$ gauge theories with a Higgs field in the fundamental representation. We show that discrepancies between the spectrum predicted by perturbation theory and the observable physical spectrum arise. We confirm these analytic findings with lattice simulations for $N=3$.

hep-lat↗

arXiv2017

Implications of strict gauge invariance for particle spectra and precision observables

The discovery of the Higgs together with the excellent performance of the LHC allow to make precision tests of Brout-Englert-Higgs Physics, and especially its underlying field-theory. In this field theory strict gauge-invariance requires observable states to have a more involved structure than assumed in standard perturbation theory. This can lead to, likely rather very small, deviations in precision tests of the standard model. Here, the mechanism behind these deviations will be elucidated, and, as an example, its possible implications for the R ratio at future linear colliders will be estimated.

hep-ph↗