arXiv subjects

Axel Maas

Publications and source records attributed to Axel Maas.

At least 73 records · Page 4Linked to original sources

arXiv2017

Pair production processes and flavor in gauge-invariant perturbation theory

Gauge-invariant perturbation theory is an extension of ordinary perturbation theory which describes strictly gauge-invariant states in theories with a Brout-Englert-Higgs effect. Such gauge-invariant states are composite operators which have necessarily only global quantum numbers. As a consequence, flavor is exchanged for custodial quantum numbers in the standard model, recreating the fermion spectrum in the process. Here, we study the implications of such a description, possibly also for the generation structure of the standard model. In particular, this implies that scattering processes are essentially bound-state-bound-state interactions, and require a suitable description. We analyze the implications for the pair-production process $e^+e^-\to{\bar f}f$ at a linear collider to leading order. We show how ordinary perturbation theory is recovered as the leading contribution. Developing a suitable PDF-type language, we also assess the impact of sub-leading contributions. We find that only for very heavy fermions in the final state, especially top quarks, sizable corrections could emerge. This gives an interesting, possibly experimentally testable, scenario for the formal field theory underlying the electroweak sector of the standard model.

hep-ph↗

arXiv2016

Influence of broken flavor and C and P symmetry on the quark propagator

Embedding QCD into the standard model breaks various symmetries of QCD explicitly, especially C and P. While these effects are usually perturbatively small, they can be amplified in extreme environments like merging neutron stars or by the interplay with new physics. To correctly treat these cases requires fully backcoupled calculations. To pave the way for later investigations of hadronic physics, we study the QCD quark propagator coupled to an explicit breaking. This substantially increases the tensor structure even for this simplest correlation function. To cope with the symmetry structure, and covering all possible quark masses, from the top quark mass to the chiral limit, we employ Dyson-Schwinger equations. While at weak breaking the qualitative effects have similar trends as in perturbation theory, even moderately strong breakings lead to qualitatively different effects, non-linearly amplified by the strong interactions.

hep-ph↗

arXiv2016

Gauge engineering and propagators

Beyond perturbation theory gauge-fixing becomes more involved due to the Gribov-Singer ambiguity: The appearance of additional gauge copies requires to define a procedure how to handle them. For the case of Landau gauge the structure and properties of these additional gauge copies will be investigated. Based on these properties gauge conditions are constructed to account for these gauge copies. The dependence of the propagators on the choice of these complete gauge-fixings will then be investigated using lattice gauge theory for Yang-Mills theory. It is found that the implications for the infrared, and to some extent mid-momentum behavior, can be substantial. In going beyond the Yang-Mills case it turns out that the influence of matter can generally not be neglected. This will be briefly discussed for various types of matter.

hep-lat↗

arXiv2016

Testing gauge-invariant perturbation theory

Gauge-invariant perturbation theory for theories with a Brout-Englert-Higgs effect, as developed by Fröhlich, Morchio and Strocchi, starts out from physical, exactly gauge-invariant quantities as initial and final states. These are composite operators, and can thus be considered as bound states. In case of the standard model, this reduces almost entirely to conventional perturbation theory. This explains the success of conventional perturbation theory for the standard model. However, this is due to the special structure of the standard model, and it is not guaranteed to be the case for other theories. Here, we review gauge-invariant perturbation theory. Especially, we show how it can be applied and that it is little more complicated than conventional perturbation theory, and that it is often possible to utilize existing results of conventional perturbation theory. Finally, we present tests of the predictions of gauge-invariant perturbation theory, using lattice gauge theory, in three different settings. In one case, the results coincide with conventional perturbation theory and with the lattice results. In a second case, it appears that the results of gauge-invariant perturbation theory agree with the lattice, but differ from conventional perturbation theory. In the third case both approaches fail due to quantum fluctuations.

hep-lat↗

arXiv2016

Quark Propagator with electroweak interactions in the Dyson-Schwinger approach

Motivated by the non-negligible dynamical backcoupling of the electroweak interactions with the strong interaction during neutron star mergers, we study the effects of the explicit breaking of C, P and flavor symmetry on the strong sector. The quark propagator is the simplest object which encodes the consequences of these breakings. To asses the impact, we study the influence of especially parity violation on the propagator for various masses. For this purpose the functional methods in form of Dyson-Schwinger-Equations are employed. We find that explicit isospin breaking leads to a qualitative change of behavior even for a slight explicit breaking, which is in contrast to the expectations from perturbation theory. Our results thus suggest that non-perturbative backcoupling effects could be larger than expected.

hep-ph↗

arXiv2016

A G2-QCD neutron star

The determination of the properties of neutron stars from the underlying theory, QCD, is still an unsolved problem. This is mainly due to the difficulty to obtain reliable results for the equation of state for cold, dense QCD. As an alternative route to obtain qualitative insights, we determine the structure of a neutron star for a modified version of QCD: By replacing the gauge group SU(3) with the exceptional Lie group G2, it is possible to perform lattice simulations at finite density, while still retaining neutrons. Here, results of these lattice simulations are used to determine the mass-radius relation of a neutron star for this theory. The results show that phase changes express themselves in this relation. Also, the radius of the most massive neutron stars is found to vary very little, which would make radius determinations much simpler if this would also be true in QCD.

astro-ph.HE↗

arXiv2016

The quenched SU(2) fundamental 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. As the analytic structure plays an important role in this question, high-precision data is necessary for lattice investigations. Also, it is interesting how this depends on the dimensionality of the theory. To make a study over a wide range of parameters possible this suggests to use scalar particles. This is done here: The propagator of a fundamental scalar is studied in two, three, and four dimensions in quenched SU(2) Yang-Mills theory in minimal Landau gauge, both in momentum space and position space. Particular emphasis is put on the effects of renormalization. The results suggest a quite intricate volume dependence and the presence of an intrinsic mass scale, but no obvious connection to confinement.

hep-lat↗

arXiv2016

Gauge invariance and the physical spectrum in the two-Higgs-doublet model

Observable states are gauge-invariant. In a non-Abelian gauge theory, these are necessarily composite operators. We investigate the spectrum of these operators in the two-Higgs-doublet model. For this purpose, we are working along the lines of the Fröhlich-Morchio-Strocchi mechanism to relate the physical spectrum to the spectrum of the elementary particles. We also investigate the consequences of spontaneous breaking of the global (custodial) symmetry group. Finally, we briefly comment on how to test the results using lattice methods.

hep-ph↗

arXiv2016

Towards the spectrum of a GUT from gauge invariance

The description of electroweak physics using perturbation theory is highly successful. Though not obvious, this is due to a subtle field-theoretical effect, the Fröhlich-Morchio-Strocchi mechanism, which links the physical spectrum to that of the elementary particles. This works because of the special structure of the standard model, and it is not a priori clear whether it works for structurally different theories. Candidates for conflicts are, e.g., grand unified theories. We study this situation in a toy model, a $SU(3)$ gauge theory with two Higgs fields and a breaking pattern $SU(3) \rightarrow SU(2) \rightarrow 1$. This mimics the weak-Higgs sector of the standard model. We determine the leading order predictions for the gauge invariant spectrum in this theory, and discuss a setup to test them using lattice gauge theory.

hep-ph↗

arXiv2015

Dyson-Schwinger equations and ${\cal N}=4$ SYM in Landau gauge

${\cal N}=4$ Super Yang-Mills theory is a highly constrained theory, and therefore a valuable tool to test the understanding of less constrained Yang-Mills theories. Our aim is to use it to test our understanding of both the Landau gauge beyond perturbation theory as well as truncations of Dyson-Schwinger equations in ordinary Yang-Mills theories. We derive the corresponding equations within the usual one-loop truncation for the propagators after imposing the Landau gauge. We find a conformal solution in this approximation, which surprisingly resembles many aspects of ordinary Yang-Mills theories. We furthermore identify which role the Gribov-Singer ambiguity in this context could play, should it exist in this theory.

hep-ph↗

arXiv2015

More on the properties of the first Gribov region in Landau gauge

Complete gauge-fixing beyond perturbation theory in non-Abelian gauge theories is a non-trivial problem. This is particularly evident in covariant gauges, where the Gribov-Singer ambiguity gives an explicit formulation of the problem. In practice, this is a problem if gauge-dependent quantities between different methods, especially lattice and continuum methods, should be compared: Only when treating the Gribov-Singer ambiguity in the same way is the comparison meaningful. To provide a better basis for such a comparison the structure of the first Gribov region in Landau gauge, a subset of all possible gauge copies satisfying the perturbative Landau gauge condition, will be investigated. To this end, lattice gauge theory will be used to investigate a two-dimensional projection of the region for SU(2) Yang-Mills theory in two, three, and four dimensions for a wide range of volumes and discretizations.

hep-lat↗

arXiv2015

A spectroscopical analysis of the phase diagram of Yang-Mills-Higgs theory

Yang-Mills-Higgs theory, being the standard-model Higgs sector for a suitable choice of gauge and custodial group, offers a rich set of physics. In particular, in some region of its parameter space it has QCD-like behavior, while in some other region it is Higgs-like. Therefore, it is possible to study a plethora of phenomena within a single theory. Here, the physics of the standard-model version is studied using lattice gauge theory. To this end, the low-lying spectrum in several different channels is obtained for more than 140 different sets of bare parameters throughout the phase diagram. The theory shows quite different behaviors in the different regions, from almost Yang-Mills-like to the one of an essentially free gas of massive photons. Especially, not always is the behavior as naively expected.

hep-lat↗

arXiv2015

Propagators and topology

Two popular perspectives on the non-perturbative domain of Yang-Mills theories are either in terms of the gluons themselves or in terms of collective gluonic excitations, i.e. topological excitations. If both views are correct, then they are only two different representations of the same underlying physics. One possibility to investigate this connection is by the determination of gluon correlation functions in topological background fields, as created by the smearing of lattice configurations. This is performed here for the minimal Landau gauge gluon propagator, ghost propagator, and running coupling, both in momentum and position space for SU(2) Yang-Mills theory. The results show that the salient low-momentum features of the propagators are qualitatively retained under smearing at sufficiently small momenta, in agreement with an equivalence of both perspectives. However, the mid-momentum behavior is significantly affected. These results are also relevant for the construction of truncations in functional methods, as they provide hints on necessary properties to be retained in truncations.

hep-lat↗

arXiv2015

Field theory as a tool to constrain new physics models

One of the major problems in developing new physics scenarios is that very often the parameters can be adjusted such that in perturbation theory almost all experimental low-energy results can be accommodated. It is therefore desirable to have additional constraints. Field-theoretical considerations can provide such additional constraints on the low-lying spectrum and multiplicities of models. Especially for theories with elementary or composite Higgs particle the Fröhlich-Morchio-Strocchi mechanism provides a route to create additional conditions, though showing it to be at work requires genuine non-perturbative calculations. The qualitative features of this procedure are discussed for generic 2-Higgs-doublet models, grand-unified theories, and technicolor-type theories.

hep-ph↗

arXiv2015

Some more details of minimal-Landau-gauge Yang-Mills propagators

The propagators of the elementary degrees of freedom of (minimal-)Landau-gauge Yang-Mills theory have been a useful tool in various investigations. However, in lattice calculations they show severe dependencies on lattice artifacts. This problem has been addressed for various subsets of lattice artifacts and various subsets of propagators over the time. Here, an extended study of all propagators in momentum space, and for the gluon also in position space, as well as derived quantities like the running coupling, is provided simultaneously for two, three, and four dimensions over one or more orders of magnitude in both physical volume and lattice spacing, in lower dimensions also over more than two orders of magnitude for the gauge group SU(2). Most of the known qualitative results are confirmed, but two quantities also indicate a slight, but possibly interesting deviation.

hep-lat↗

arXiv2014

On the phase diagram and the singlet scalar channel in Yang-Mills-Higgs theory

Yang-Mills-Higgs theory is quite a remarkable theory in that it shows very different behaviors without phase transitions. It is dominated by the Brout-Englert-Higgs mechanism in some domain of the phase diagram, while it is essentially QCD-like in another. It is expected that albeit there is no qualitative difference, there are substantially quantitative differences throughout the spectrum. This is investigated using lattice theory for the case of the scalar singlet channel for more than a hundred different points in the phase diagram. It is found that the results deviate partly substantially from the expectations in some cases, but in others justify the picture of a weakly interacting theory - even in cases of rather strong interactions at the ultraviolet cutoff.

hep-lat↗

arXiv2014

Observables in Higgsed Theories

In gauge theories, observable quantities have to be gauge-invariant. In general, this requires composite operators, which usually have substantially different properties, e.g. masses, than the elementary particles. Theories with a Higgs field, in which the Brout-Englert-Higgs effect is active, provide an interesting exception to this rule. Due to an intricate mechanism, the Fröhlich-Morchio-Strocchi mechanism, the masses of the composite operators with the same $J^P$ quantum numbers, but modified internal quantum numbers, have the same masses. This mechanism is supported using lattice gauge theory for the standard-model Higgs sector, i.e. Yang-Mills-Higgs theory with gauge group SU(2) and custodial symmetry group SU(2). Furthermore, the extension to the 2-Higgs-doublet-model is briefly discussed, and some preliminary results are presented.

hep-lat↗

arXiv2014

Exploratory study of the temperature dependence of magnetic vertices in SU(2) Landau gauge Yang--Mills theory

Vertices describe the interactions between the fundamental degrees of freedom, and are therefore of vital importance in many ab-initio descriptions of field theory, especially using functional methods. To this end, we present the first lattice study of the thermal behavior of (minimal) Landau-gauge SU(2) Yang--Mills three-point functions, i.e. three-gluon and ghost-gluon vertices. Focusing on the chromomagnetic sector, we find that the phase transition mainly affects the three-gluon vertex, while the ghost-gluon vertex is relatively inert.

hep-lat↗