arXiv subjects

Markus Q. Huber

Publications and source records attributed to Markus Q. Huber.

At least 55 records · Page 3Linked to original sources

arXiv2014

Gluonic three-point correlations in pure Landau gauge QCD

We report on the first self-consistent solution of the Dyson-Schwinger equation (DSE) for the three-gluon vertex. Based on earlier results for the propagators which match data from lattice Monte-Carlo simulations, we obtain results for the three-gluon vertex that are in very good agreement with available lattice data likewise. Feeding these results back into the propagator DSEs leads to some changes especially in the gluon propagator. These changes allow us to assess previously used models for the three-gluon vertex and to systematically estimate the influence of neglected two-loop diagrams with four-gluon interactions. In the final step, a full iterative solution to the coupled DSEs of pure Landau gauge QCD without quarks is then obtained for the first time in an extended truncation which now dynamically includes the complete set of three-point vertex functions.

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arXiv2014

On propagators and vertices of Landau gauge Yang-Mills theory

We calculate the three-point functions of pure Landau gauge QCD and investigate their influence on the propagators. As expected, the ghost-gluon vertex leads only to minor modifications, while the three-gluon vertex has a sizeable impact on the mid-momentum regime of the gluon propagator. We describe an effective model of the three-gluon vertex that includes contributions from the neglected two-loop diagrams and thus allows to obtain propagators in good agreement with lattice results. We also determine the three-gluon vertex from these propagators and find good agreement with lattice results as well. In turn, these results allow us to assess the effect of the missing two-loop diagrams in the gluon propagator equation. Finally, we present the first self-consistent calculation that includes all two-and three-point functions.

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arXiv2013

On two- and three-point functions of Landau gauge Yang-Mills theory

We present results for the gluon and ghost propagators and the ghost-gluon vertex obtained from Dyson-Schwinger equations. In the zero temperature case we elaborate on the role of the three-gluon vertex and discuss a model that can capture its qualitative features like its anomalous dimensions and a zero crossing of the dressing function. Our results compare well with lattice data. At non-zero temperature we calculated the ghost propagator which agrees rather well with lattice results already within our simple truncation. These results are used to obtain the temperature dependence of the ghost-gluon vertex. We also explain why the ghost propagator does not react to the phase transition despite its direct coupling to the chromoelectric gluon.

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arXiv2013

On the influence of three-point functions on the propagators of Landau gauge Yang-Mills theory

We solve the Dyson-Schwinger equations of the ghost and gluon propagators of Landau gauge Yang-Mills theory together with that of the ghost-gluon vertex. The latter plays a central role in many truncation schemes for functional equations. By including it dynamically we can determine its influence on the propagators. We also suggest a new model for the three-gluon vertex motivated by lattice data which plays a crucial role to obtain stable solutions when the ghost-gluon vertex is included. We find that both vertices have a sizable quantitative impact on the mid-momentum regime and contribute to the reduction of the gap between lattice and Dyson-Schwinger equation results. Furthermore, we establish that the three-gluon vertex dressing turns negative at low momenta as suggested by lattice results in three dimensions.

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arXiv2013

How to determine the branch points of correlation functions in Euclidean space

Two-point correlators represented by either perturbative or non-perturbative integral equations in Euclidean space are considered. In general, it is difficult to determine the analytic structure of arbitrary correlators analytically. When relying on numerical methods to evaluate the analytic structure, exact predictions of, e.g., branch point locations (i.e., the multi-particle threshold) provide a useful check. These branch point locations can be derived by Cutkosky's cut rules. However, originally they were derived in Minkowski space for propagators with real masses and are thus not directly applicable in Euclidean space and for propagators of a more general form. Following similar considerations that led Karplus et al., Landau and Cutkosky more than 50 years ago to the mass summation formula that became known as Cutkosky's cut rules, we show how the position of branch points can be derived analytically in Euclidean space from propagators of very general form.

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arXiv2013

On the analytic structure of scalar glueball operators at Born level

We study the analytic structure of the two-point function of the operator F2 which is expected to describe a scalar glueball. The calculation of the involved integrals is complicated by nonanalytic structures in the integrands, which we take into account properly by identifying cuts generated by angular integrals and deforming the contours for the radial integration accordingly. The obtained locations of the branch points agree with Cutkosky's cut rules. As input we use different nonperturbative Landau gauge gluon propagators with different analytic properties as obtained from lattice and functional calculations. All of them violate positivity and describe thus gluons absent from the asymptotic physical space. The resulting spectral densities for the glueball candidate show a cut but no poles for lightlike momenta, which can be attributed to the employed Born approximation.

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arXiv2013

On the Analytic Structure of Scalar Glueball Operators

The correlator of the square of the Yang-Mills field-strength tensor corresponds to a scalar glueball, i.e., to a bound-state formed by gluonic ingredients only. It has quantum numbers 0++ and its mass, as predicted by different theoretical approaches, is expected to lie between 1 and 2 GeV. Here we restrict our considerations to the Born level, that is, we consider the correlator to zeroth order in the coupling. Gluonic self-interaction is taken into account indirectly by using non-perturbative gluon propagators. The employed closed expressions are motivated by lattice and Dyson-Schwinger studies. The analytic continuation of the integrals themselves is complicated by additional obstructive structures like branch cuts and poles that are induced by the inner integral in the complex plane of the outer integration variable. We deal with this problem by deforming the outer integration contour accordingly. For different input gluon propagators we find a positive glueball spectral density which is required for physical states. Poles are, however, absent which is most likely an artifact of working at Born level.

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arXiv2013

Going beyond the propagators of Landau gauge Yang-Mills theory

We present results for the propagators and the ghost-gluon vertex of Landau gauge Yang-Mills theory obtained from Dyson-Schwinger equations. Solving these three quantities simultaneously constitutes a new step in truncating these equations. We also introduce a new model for the three-gluon vertex that is motivated by lattice results. It features a zero crossing which is confirmed a posteriori by a Dyson-Schwinger calculation. Within our setup we can reproduce lattice data very well. We establish that also for the ghost-gluon vertex a difference between decoupling and scaling solutions is present. For the scaling solution we discuss the possibility of modifying the infrared exponents via an angle dependence of the ghost-gluon vertex. However, no such dependence is found in our calculations. Finally, we calculate the Schwinger function for the gluon propagator.

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arXiv2012

Two- and three-point functions in two-dimensional Landau-gauge Yang-Mills theory: Continuum results

We investigate the Dyson-Schwinger equations for the gluon and ghost propagators and the ghost-gluon vertex of Landau-gauge gluodynamics in two dimensions. While this simplifies some aspects of the calculations as compared to three and four dimensions, new complications arise due to a mixing of different momentum regimes. As a result, the solutions for the propagators are more sensitive to changes in the three-point functions and the ansaetze used for them at the leading order in a vertex a expansion. Here, we therefore go beyond this common truncation by including the ghost-gluon vertex self-consistently for the first time, while using a model for the three-gluon vertex which reproduces the known infrared asymptotics and the zeros at intermediate momenta as observed on the lattice. A separate computation of the three-gluon vertex from the results is used to confirm the stability of this behavior a posteriori. We also present further arguments for the absence of the decoupling solution in two dimensions. Finally, we show how in general the infrared exponent kappa of the scaling solutions in two, three and four dimensions can be changed by allowing an angle dependence and thus an essential singularity of the ghost-gluon vertex in the infrared.

hep-th↗

arXiv2012

CrasyDSE: A framework for solving Dyson-Schwinger equations

Dyson-Schwinger equations are important tools for non-perturbative analyses of quantum field theories. For example, they are very useful for investigations in quantum chromodynamics and related theories. However, sometimes progress is impeded by the complexity of the equations. Thus automatizing parts of the calculations will certainly be helpful in future investigations. In this article we present a framework for such an automatization based on a C++ code that can deal with a large number of Green functions. Since also the creation of the expressions for the integrals of the Dyson-Schwinger equations needs to be automatized, we defer this task to a Mathematica notebook. We illustrate the complete workflow with an example from Yang-Mills theory coupled to a fundamental scalar field that has been investigated recently. As a second example we calculate the propagators of pure Yang-Mills theory. Our code can serve as a basis for many further investigations where the equations are too complicated to tackle by hand. It also can easily be combined with DoFun, a program for the derivation of Dyson-Schwinger equations.

hep-th↗

arXiv2012

Algorithmic derivation of functional renormalization group equations and Dyson-Schwinger equations

We present the Mathematica application DoFun which allows to derive Dyson-Schwinger equations and renormalization group flow equations for n-point functions in a simple manner. DoFun offers several tools which considerably simplify the derivation of these equations from a given physical action. We discuss the application of DoFun by means of two different types of quantum field theories, namely a bosonic O(N) theory and the Gross-Neveu model.

hep-th↗

arXiv2011

On the infrared behaviour of QCD Green functions in the Maximally Abelian gauge

Functional equations like exact renormalisation group and Dyson-Schwinger equations have contributed to a better understanding of non-perturbative phenomena in quantum field theories in terms of the underlying Green functions. In Yang-Mills theory especially the Landau gauge has been used, as it is the most accessible gauge for these methods. In the maximally Abelian gauge first results have been obtained which are very encouraging because Abelian infrared dominance has been found: The Abelian part of the gauge field propagator is enhanced at low momenta and thereby dominates the dynamics in the infrared. Also the ambiguity of two different types of solutions (decoupling and scaling) exists in both gauges. It is demonstrated how the two solutions are related in the maximally Abelian gauge. As in all two-point Dyson-Schwinger equations of the MAG the infrared dominant diagrams are sunset diagrams, in addition, a BPHZ regularisation and renormalisation of a test system with a sunset-like diagram is presented.

hep-th↗

arXiv2011

Infrared scaling solutions beyond the Landau gauge: The maximally Abelian gauge and Abelian infrared dominance

Functional equations like exact renormalization group and Dyson-Schwinger equations have contributed to a better understanding of non-perturbative phenomena in quantum field theories in terms of the underlying Green functions. In Yang-Mills theory especially the Landau gauge has been used, as it is the most accessible gauge for these methods. The growing understanding obtained in this gauge allows to proceed to other gauges in order to obtain more information about the relation of different realizations of the confinement mechanism. In the maximally Abelian gauge first results are very encouraging as a variant of Abelian infrared dominance is found: The Abelian part of the gauge field propagator is enhanced at low momenta and thereby dominates the dynamics in the infrared. Its role is therefore similar to that of the ghost propagator in the Landau gauge, where one denotes the corresponding phenomenon as ghost dominance. Also the ambiguity of two different types of solutions (decoupling and scaling) exists in both gauges. Here we present how the two solutions are related in the maximally Abelian gauge. The intricacy of the system of functional equations in this gauge required the development of some new tools and methods as, for example, the automated derivation of the equations by the program DoFun. We also present results for linear covariant and ghost anti-ghost symmetric gauges.

hep-th↗

arXiv2010

Non-perturbative analysis of the Gribov-Zwanziger action

In the non-perturbative regime the usual gauge fixing is not sufficient due to the Gribov problem. To deal with it one can restrict the integration in the path integral to the first Gribov region by using the Gribov-Zwanziger action. In its local form it features additional auxiliary fields which mix with the gluon at the two-point level. We present an explicit infrared analysis of this action. We show that from the two possible scaling solutions obtained previously only one remains: It coincides exactly with the results from the Faddeev-Popov action, i.e., the ghost propagator is infrared enhanced and the gluon propagator infrared suppressed and the corresponding power law behavior is described by only one parameter kappa=0.5953. This corroborates the argument by Zwanziger that for functional equations it suffices to take into account the appropriate boundary conditions and no explicit restriction in the path integral measure is required.

hep-th↗

arXiv2010

On the infrared scaling solution of SU(N) Yang-Mills theories in the maximally Abelian gauge

An improved method for extracting infrared exponents from functional equations is presented. The generalizations introduced allow for an analysis of quite complicated systems such as Yang-Mills theory in the maximally Abelian gauge. Assuming the absence of cancellations in the appropriately renormalized integrals the only consistent scaling solution yields an infrared enhanced diagonal gluon propagator in support of the Abelian dominance hypothesis. This is explicitly shown for SU(2) and subsequently verified for SU(N), where additional interactions exist. We also derive the most infrared divergent scaling solution possible for vertex functions in terms of the propagators' infrared exponents. We provide general conditions for the existence of a scaling solution for a given system and comment on the cases of linear covariant gauges and ghost anti-ghost symmetric gauges.

hep-th↗

arXiv2010

On gauge fixing aspects of the infrared behavior of Yang-Mills Green functions

The infrared behavior of propagators and vertices is derived for the maximally Abelian gauge and the Gribov-Zwanziger action relying on functional equations. The derivation and analysis of Dyson-Schwinger equations increase considerably in complexity when going beyond the standard Landau gauge fixing and the available tools have to be improved. For the derivation of the equations a computer program (DoDSE) was developed in order to handle the plethora of terms. The process of determining possible infrared solutions is abstracted to obtain further insight into the structure of the so-called infrared scaling solutions. It is found that a few simple steps suffice to determine possible infrared scaling relations directly from the action. For the maximally Abelian gauge an infrared enhanced diagonal gluon propagator is found, while the off-diagonal degrees of freedom are infrared suppressed. This is in agreement with the idea of Abelian infrared dominance. Furthermore, it is proven that SU(2) and higher SU(N) have the same infrared behavior, although the corresponding actions differ. Under a suitable truncation the Dyson-Schwinger equations are solved in the deep infrared to obtain values for the exponents of the power laws. Restricting the integration in field configuration space to the Gribov region of the Landau gauge with the Gribov-Zwanziger action leads to two qualitatively equivalent infrared solutions. In both cases the gluon propagator is infrared suppressed and the infrared enhanced ghost propagator dominates the Dyson-Schwinger equations. This result corroborates the conjecture by Zwanziger that the functional integration can be cut at the first Gribov horizon and only the applied boundary conditions are important. For one solution the Dyson-Schwinger equations reduce in the deep infrared exactly to those obtained with the usual Faddeev-Popov gauge fixing.

hep-th↗

arXiv2010

Infrared singularities in Landau gauge Yang-Mills theory

We present a more detailed picture of the infrared regime of Landau gauge Yang-Mills theory. This is done within a novel framework that allows one to take into account the influence of finite scales within an infrared power counting analysis. We find that there are two qualitatively different infrared fixed points of the full system of Dyson-Schwinger equations. The first extends the known scaling solution, where the ghost dynamics is dominant and gluon propagation is strongly suppressed. It features in addition to the strong divergences of gluonic vertex functions in the previously considered uniform scaling limit, when all external momenta tend to zero, also weaker kinematic divergences, when only some of the external momenta vanish. The second solution represents the recently proposed decoupling scenario where the gluons become massive and the ghosts remain bare. In this case we find that none of the vertex functions is enhanced, so that the infrared dynamics is entirely suppressed. Our analysis also provides a strict argument why the Landau gauge gluon dressing function cannot be infrared divergent.

hep-th↗

arXiv2010

Infrared analysis of Dyson-Schwinger equations taking into account the Gribov horizon in Landau gauge

The low momentum behavior of the Landau gauge Gribov-Zwanziger action is investigated using the respective Dyson-Schwinger equations. Because of the mixing of the gluon and the auxiliary fields four scenarios can be distinguished for the infrared behavior. Two of them lead to inconsistencies and can be discarded. Another one corresponds to the case where the auxiliary fields behave exactly like the Faddeev-Popov ghosts and the same scaling relation as in standard Landau gauge, $\ka_A+2\ka_c=0$, is valid. Even the parameter $\ka$ is found to be the same, 0.595. The mixed propagators, which appear, are suppressed in all loops, and their anomalous infrared exponent can also be determined. A fourth case provides an even stricter scaling relation that includes also the mixed propagators, but possesses the same qualitative feature, i.e. the propagators of the Faddeev-Popov ghost and the auxiliary fields are infrared enhanced and the mixed and the gluon propagators are infrared suppressed. In this case the system of equations to obtain the parameter $\ka$ is non-linear in all variables.

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