D. Dudal

Ghent University, Gand, Flanders, Belgium

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Publications (92)165.98 Total impact

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    ABSTRACT: The Bose-ghost propagator has been proposed as a carrier of the confining force in Yang-Mills theories in minimal Landau gauge. We present the first numerical evaluation of this propagator, using lattice simulations for the SU(2) gauge group in the scaling region. Our data are well described by a simple fitting function, which is compatible with an infrared-enhanced Bose-ghost propagator. This function can also be related to a massive gluon propagator in combination with an infrared-free (Faddeev-Popov) ghost propagator. Since the Bose-ghost propagator can be written as the vacuum expectation value of a BRST-exact quantity and should therefore vanish in a BRST-invariant theory, our results provide the first numerical manifestation of BRST-symmetry breaking due to restriction of gauge-configuration space to the Gribov region.
    05/2014;
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    ABSTRACT: The Bose-ghost propagator has been proposed as a carrier of the confining force in Yang-Mills theories in minimal Landau gauge. We present the first numerical evaluation of this propagator, using lattice simulations for the SU(2) gauge group in the scaling region. Our data are well described by a simple fitting function, which is compatible with an infrared-enhanced Bose-ghost propagator. This function can also be related to a massive gluon propagator in combination with an infrared-free (Faddeev-Popov) ghost propagator. Since the Bose-ghost propagator can be written as the vacuum expectation value of a BRST-exact quantity and should therefore vanish in a BRST-invariant theory, our results provide the first numerical manifestation of BRST-symmetry breaking due to restriction of gauge-configuration space to the Gribov region.
    04/2014;
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    ABSTRACT: We address several aspects of gluon propagation at zero and finite temperature. In particular, we study the violation of spectral positivity, we discuss a method to extract the K\"all\'{e}n-Lehmann spectral density of a particle (be it elementary or bound state) propagator and apply it to compute gluon spectral densities from lattice data. Furthermore, we also consider the interpretation of the Landau gauge gluon propagator at finite temperature as a massive type bosonic propagator.
    01/2014;
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    ABSTRACT: A Padé approximation approach, rooted in an infrared moment technique, is employed to provide mass estimates for various glueball states in pure gauge theories. The main input in this analysis are theoretically well-motivated fits to lattice gluon propagator data, which are by now available for both SU(2)SU(2) and SU(3)SU(3) in 3 and 4 space–time dimensions. We construct appropriate gauge invariant and Lorentz covariant operators in the (pseudo)scalar and (pseudo)tensor sector. Our estimates compare reasonably well with a variety of lattice sources directly aimed at extracting glueball masses.
    Physics Letters B. 01/2014; 732:247–254.
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    ABSTRACT: We consider the problem of "measuring" the K\"all\'en-Lehmann spectral density of a particle (be it elementary or bound state) propagator by means of 4d lattice data. As the latter are obtained from operations at (Euclidean momentum squared) p^2>=0, we are facing the generically ill-posed problem of converting a limited data set over the positive real axis to an integral representation, extending over the whole complex p^2-plane. We employ a linear regularization strategy, commonly known as the Tikhonov method with Morozov discrepancy principle, with suitable adaptations to realistic data, e.g. with unknown threshold. An important virtue over the (standard) maximum entropy method is the possibility to also probe unphysical spectral densities, as, for example, of a confined gluon. We apply our proposal here to "physical" mock spectral data as a litmus test and then to the lattice SU(3) Landau gauge gluon at zero temperature.
    10/2013; 89(1).
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    ABSTRACT: An infrared moment technique, recently developed by some of us, is employed to provide mass estimates for various glueball states in pure gauge theories. The main input in this analysis are theoretically well-motivated fits to lattice gluon propagator data, which are by now available for both SU(2) and SU(3) in 3 and 4 space-time dimensions. We construct appropriate gauge invariant and Lorentz covariant operators in the (pseudo)scalar and (pseudo)tensor sector. Our final numbers compare reasonably well with a variety of lattice sources directly aimed at extracting glueball masses.
    10/2013;
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    Nele Callebaut, David Dudal
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    ABSTRACT: In this follow-up paper of 1105.2217 we further discuss the occurrence of a magnetically induced tachyonic instability of the rho meson in the two-flavour Sakai-Sugimoto model, uplifting two remaining approximations in the previous paper. That is, firstly, the magnetically induced splitting of the branes is now taken into account, evaluating without approximations the symmetrized trace which enters in the non-Abelian Dirac-Born-Infeld (DBI) action. This leads to an extra mass generating effect for the charged heavy-light rho meson through a holographic Higgs mechanism. Secondly, we compare the results in the approximation to second order in the field strength to the results using the full DBI-action. Both improvements cause an increase of the critical magnetic field for the onset of rho meson condensation. In addition, the stability in the scalar sector in the presence of the magnetic field is discussed.
    09/2013;
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    ABSTRACT: It is well accepted that dealing with the Gribov ambiguity has a major impact on correlation functions in gauge-fixed Yang-Mills theories, in particular in the low momentum regime where standard perturbation theory based on the Faddeev-Popov approach fails. Recent results, derived from functional tools (Dyson-Schwinger equations or exact RG) or the effective Gribov-Zwanziger action method, pointed towards e.g. gauge boson correlation functions that are not compatible with the properties of observable degrees of freedom. Although such an observation is a welcome feature for gauge theories exhibiting confinement, it would be a discomfort for gauge theories supplemented with Higgs fields, cfr. the experimental success of the electroweak model based on a SU(2) x U(1) gauge group. The purpose of this short note is to assure that the effective action resolution to the Gribov ambiguity reduces to the standard Faddeev-Popov method in the perturbative regime of sufficiently small coupling/large Higgs condensate, thereby not compromising the physical particle spectrum of massive gauge bosons and a massless photon for the SU(2) x U(1) gauge-Higgs model. The closer the theory gets to the limit of vanishing Higgs condensate, the more the Gribov problem resurfaces with all its consequences. We give some speculations w.r.t. the Fradkin-Shenker insights about the phase diagram.
    Annals of Physics. 09/2013;
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    ABSTRACT: An all orders algebraic proof of the multiplicative renormalizability of the novel formulation of the Gribov-Zwanziger action proposed in Phys. Rev. D 86, 045005 (2012) [arXiv:1205.3934], and allowing for an exact but spontaneously broken BRST symmetry, is provided.
    Annals of Physics 06/2013; · 3.32 Impact Factor
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    ABSTRACT: We study the structure of the gauge propagators of a 3d version of the electroweak interaction in terms of the Higgs vacuum expectation value nu, of the non-Abelian gauge coupling g, and of the Abelian gauge coupling g', when nonperturbative effects related to the non-Abelian gauge fixing are introduced by means of an adapted path integral measure. In the perturbative regime of small non-Abelian coupling g and sufficiently large nu, the well-known standard Z and W propagators are recovered, together with a massless photon. In general, depending on the relative magnitudes of g, g' and nu, we uncover a quite different propagator structure. In a later stage of research, the results here derived can be used to study the associated phase diagram in more depth.
    05/2013;
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    ABSTRACT: We introduce an effective quark model that is in principle dynamically derivable from the QCD action. An important feature is the incorporation of spontaneous chiral symmetry breaking in a renormalizable fashion. The quark propagator in the condensed vacuum exhibits complex conjugate poles, indicative of an unphysical spectral form, i.e. confined quarks. Moreover, the ensuing mass function can be fitted well to existing lattice data. To validate the physical nature of the new model, we identify not only a massless pseudoscalar (i.e. a pion) in the chiral limit, but we also present reasonable estimates for the rho meson mass and decay constant, employing a contact point interaction and a large N argument to simplify the diagrammatic spectral analysis. We stress that we do not use any experimental input to obtain our numbers, but only rely on our model and lattice quark data.
    03/2013;
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    N. Callebaut, D. Dudal
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    ABSTRACT: During heavy ion collisions, high temperatures and strong magnetic fields are generated. We employ the gauge-gravity duality to study the N_f=2 QCD phase diagram under these extreme conditions in the quenched approximation, in particular we use the non-antipodal Sakai-Sugimoto model (SSM). We take the different coupling of up and down flavours to the magnetic field into account geometrically, resulting in a split of the chiral phase transition according to flavour. We discuss the influence of the magnetic field on the chiral temperatures -in physical GeV units- in terms of the choice of the confinement scale in the model, extending hereby our elsewhere presented discussion of fixing the non-antipodal SSM parameters to the deconfinement phase. The flavour-dependent (T,L,eB) phase diagram, with variable asymptotic brane-antibrane separation L, is also presented, as a direct generalization of the known (T,L) phase diagram of the non-antipodal SSM at zero magnetic field. In particular, for sufficiently small L we are probing a NJL-like boundary field theory in which case we do find results very reminiscent of the predictions in NJL models.
    Physical review D: Particles and fields 03/2013; 87(10).
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    ABSTRACT: The quantization of non-Abelian gauge theories is known to be plagued by Gribov copies. Typical examples are the copies related to zero modes of the Faddeev–Popov operator, which give rise to singularities in the ghost propagator. In this work we present an exact and compact expression for the ghost propagator as a function of external gauge fields, in SU(N)SU(N) Yang–Mills theory in the Landau gauge. It is shown, to all orders, that the condition for the ghost propagator not to have a pole, the so-called Gribovʼs no-pole condition, can be implemented by demanding a non-vanishing expectation value for a functional of the gauge fields that turns out to be Zwanzigerʼs horizon function. The action allowing to implement this condition is the Gribov–Zwanziger action. This establishes in a precise way the equivalence between Gribovʼs no-pole condition and Zwanzigerʼs horizon condition.
    Physics Letters B 02/2013; 719(s 4–5):448–453. · 4.57 Impact Factor
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    ABSTRACT: In this proceeding, we explain a few steps for an alternative extraction of the spectral density of a two-point function (propagator) based on a discrete set of data points. We present a so-called Tikhonov regularization of this particular inverse problem. We test it on 2 cases: lattice 0++} glueball data and mock gluon data.
    01/2013;
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    ABSTRACT: We present an analytical study of continuum 4d SU(2) gauge Higgs models with a single Higgs field with fixed length in either the fundamental or adjoint representation. We aim at probing the renowned predictions of Fradkin & Shenker on the phase diagram in terms of confinement versus Higgs behaviour, obtained in lattice numerical simulations. We work in the Landau version of the 't Hooft R_\xi gauges in which case we can access potential nonperturbative physics related to the existence of the Gribov copies. In the fundamental case, we clearly show that in the perturbative regime of small gauge coupling constant g and large Higgs vacuum expectation value v, there is a Higgs phase with Yukawa gauge boson propagators without Gribov effects. For a small value of the Higgs vev v and/or large g, we enter a region with Gribov type propagators that have no physical particle interpretation: the gauge bosons are as such confined. The transition between both behaviours is found to be continuous. In the adjoint case, we find evidence of a more drastic transition between the different behaviours for the propagator of the off-diagonal gauge bosons, whereas the "photon", i.e. the diagonal component of the gauge field, is always confined, displaying a propagator of the Gribov type. These findings are in qualitative agreement with those of Fradkin & Shenker as well as with more recent numerical lattice simulations of the fundamental Higgs model. We also carefully discuss in which region of the parameter space (v,g) our approximations are trustworthy.
    Physical Review D 12/2012; · 4.69 Impact Factor
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    ABSTRACT: Either by solving the ghost propagator DSE or through a one-loop computation in the RGZ (Refined Gribov-Zwanziger) formalism, we show that a non-trivial ghost-gluon vertex is anyhow required to obtain a ghost propagator prediction compatible with the available corresponding lattice data in the SU(3) case. For the necessary gluon propagator input, we present RGZ tree level fits which account well for the gluon lattice data. Interestingly, this propagator can be rewritten in terms of a running gluon mass. A comparison of both DSE and RGZ results for the ghost propagator is furthermore provided. We also briefly discuss the connection between the RGZ and the OPE $d=2$ gluon condensate.
    Physical review D: Particles and fields 11/2012; 86(10).
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    ABSTRACT: The propagator of a physical degree of freedom ought to obey a K\"{a}ll\'{e}n-Lehmann spectral representation, with positive spectral density. The latter quantity is directly related to a cross section based on the optical theorem. The spectral density is a crucial ingredient of a quantum field theory with elementary and bound states, with a direct experimental connection as the masses of the excitations reflect themselves into (continuum) $\delta$-singularities. In usual lattice simulational approaches to the QCD spectrum the spectral density itself is not accessed. The (bound state) masses are extracted from the asymptotic exponential decay of the two-point function. Given the importance of the spectral density, each nonperturbative continuum approach to QCD should be able to adequately describe it or to take into proper account. In this work, we wish to present a first trial in extracting an estimate for the scalar glueball spectral density in SU(3) gluodynamics using lattice gauge theory.
    10/2012;
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    ABSTRACT: We study SU(2) three-dimensional Yang-Mills theories in presence of Higgs fields in the light of the Gribov phenomenon. By restricting the domain of integration in the functional integral to the first Gribov horizon, we are able to discuss a kind of transition between the Higgs and the confining phase in a semi-classical approximation. Both adjoint and fundamental representation for the Higgs field are considered, leading to a different phase structure.
    European Physical Journal C 10/2012; 73(3). · 5.25 Impact Factor
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    ABSTRACT: We study a toy model for an interacting scalar field theory in which the fundamental excitations are confined in the sense of having unphysical, positivity-violating propagators, a fact tracing back to a decomposition of these in propagators with complex conjugate mass poles (the so-called $i$-particles). Similar two-point functions show up in certain approaches to gluon or quark propagators in Yang-Mills gauge theories. We investigate the spectrum of our model and show that suitable composite operators may be constructed having a well-defined K\"all\'{e}n-Lehmann spectral representation, thus allowing for a particle interpretation. These physical excitations would correspond to the "mesons" of the model, the latter being bound states of two unphysical $i$-particles. The meson mass is explicitly estimated from the pole emerging in a resummed class of diagrams. The main purpose of this paper is thus to explicitly verify how a real mass pole can and does emerge out of constituent $i$-particles that have complex masses.
    International Journal of Modern Physics A 08/2012; 28(10). · 1.13 Impact Factor
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    ABSTRACT: We present an analytic description of numerical results for the Landau-gauge SU(2) gluon propagator D(p2), obtained from lattice simulations (in the scaling region) for the largest lattice sizes to date, in d=2, 3 and 4 space-time dimensions. Fits to the gluon data in 3d and in 4d show very good agreement with the tree-level prediction of the refined Gribov-Zwanziger (RGZ) framework, supporting a massive behavior for D(p2) in the infrared limit. In particular, we investigate the propagator’s pole structure and provide estimates of the dynamical mass scales that can be associated with dimension-two condensates in the theory. In the 2d case, fitting the data requires a noninteger power of the momentum p in the numerator of the expression for D(p2). In this case, an infinite-volume-limit extrapolation gives D(0)=0. Our analysis suggests that this result is related to a particular symmetry in the complex-pole structure of the propagator and not to purely imaginary poles, as would be expected in the original Gribov-Zwanziger scenario.
    Physical review D: Particles and fields 05/2012; 85(9).

Publication Stats

1k Citations
165.98 Total Impact Points

Institutions

  • 2002–2014
    • Ghent University
      • Department of Physics and Astronomy
      Gand, Flanders, Belgium
  • 2013
    • University of Coimbra
      • Center for Computational Physics
      Coímbra, Coimbra, Portugal
  • 2008–2009
    • Massachusetts Institute of Technology
      • Center for Theoretical Physics
      Cambridge, Massachusetts, United States
  • 2004
    • University of Liverpool
      • Department of Mathematical Sciences
      Liverpool, ENG, United Kingdom