Analytic structure of QCD propagators in Minkowski space

Siringo, Fabio

doi:10.1103/physrevd.94.114036

Cited by 72 publications

(111 citation statements)

References 88 publications

(244 reference statements)

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“…Recently, a more pragmatic approach was taken in [16,37,38], or in other works like [39][40][41]. Instead of a model justified from first principles, the observations obtained from lattice simulations were used as a guiding principle.…”

Section: Introductionmentioning

confidence: 99%

Some remarks on the spectral functions of the Abelian Higgs model

et al. 2019

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We consider the unitary Abelian Higgs model and investigate its spectral functions at one-loop order. This analysis allows to disentangle what is physical and what is not at the level of the elementary particle propagators, in conjunction with the Nielsen identities. We highlight the role of the tadpole graphs and the gauge choices to get sensible results. We also introduce an Abelian Curci-Ferrari action coupled to a scalar field to model a massive photon which, like the non-Abelian Curci-Ferarri model, is left invariant by a modified non-nilpotent BRST symmetry. We clearly illustrate its non-unitary nature directly from the spectral function viewpoint. This provides a functional analogue of the Ojima observation in the canonical formalism: there are ghost states with nonzero norm in the BRST-invariant states of the Curci-Ferrari model. * david.dudal@kuleuven.be †

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Section: Introductionmentioning

confidence: 99%

Some remarks on the spectral functions of the Abelian Higgs model

et al. 2019

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“…More takes on the analytic structure of gluon and/or quark propagators can be found in e.g. [43][44][45][46][47][48][49][50][51]. Although these rational function fits never capture the renormalization group-controlled logarithmic tails, we explained how our construct is insensitive to these structures anyhow.…”

Section: Discussionmentioning

confidence: 98%

Extracting topological information from momentum space propagators

et al. 2019

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A new topological invariant quantity, sensitive to the analytic structure of both fermionic and bosonic propagators, is proposed. The gauge invariance of our construct is guaranteed for at least small gauge transformations. A generalization compatible with the presence of complex poles is introduced and applied to the classification of propagators typically emerging from nonperturbative considerations. We present partial evidence that the topological number can be used to detect chiral symmetry breaking or deconfinement. *

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“…Several comments are in order. First, let us mention a comparison with a similar approach [38,39], where the analytic structures of gluon and quark propagators are investigated with a massivetype model in light of the variational principle and optimization. In there, the gluon propagator has two pairs of complex conjugate poles, while the quark propagator has a physical pole and no complex poles in N F = 2 QCD.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…Considerable efforts have been devoted to reconstructing the spectral functions from the Euclidean data based on the Källén-Lehmann spectral representation, e.g., [31,32]. On the other hand, several models of Yang-Mills theory [14,[33][34][35][36][37][38][39], including the (pure) massive Yang-Mills model [40,41], and a way of the reconstruction from the Euclidean data [42] predict complex poles in the gluon propagator that invalidate the Källén-Lehmann spectral representation. The existence of complex poles of the propagators of the confined particles is a controversial issue, e.g., [43].…”

Section: Introductionmentioning

confidence: 99%

Complex poles and spectral functions of Landau gauge QCD and QCD-like theories

Hayashi

Kondo

2020

Phys. Rev. D

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In view of the expectation that the existence of complex poles is a signal of confinement, we investigate the analytic structure of gluon, quark, and ghost propagators in the Landau gauge QCD and QCD-like theories by employing an effective model of Yang-Mills theory with a gluon mass term, which we call the massive Yang-Mills model. In this model, we particularly investigate the number of complex poles in the parameter space of the model consisting of gauge coupling constant, gluon mass, and quark mass for the gauge group SU (3) and various numbers of quark flavors NF within the asymptotic free region. This investigation extends the previous result obtained for the pure Yang-Mills theory with no flavor of quarks NF = 0 that the gluon propagator has a pair of complex conjugate poles and the negative spectral function while the ghost propagator has no complex pole. The gluon and quark propagators at the best-fit parameters for NF = 2 QCD have one pair of complex conjugate poles as in the zero flavor case. By increasing quark flavors, we find a new region in which the gluon propagator has two pairs of complex conjugate poles for light quarks with the intermediate number of flavors 4 N f < 10. However, the gluon propagator has no complex poles if very light quarks have many flavors N f ≥ 10 or both of the gauge coupling and quark mass are small. In the other regions, the gluon propagator has one pair of complex conjugate poles. Moreover, as a general feature, we argue that the gluon spectral function of this model with nonzero quark mass is negative in the infrared limit. In sharp contrast to gluons, the quark and ghost propagators are insensitive to the number of quark flavors within the current approximations adopted in this paper. These results suggest that details of the confinement mechanism may depend on the number of quark flavors and quark mass.

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Analytic structure of QCD propagators in Minkowski space

Cited by 72 publications

References 88 publications

Some remarks on the spectral functions of the Abelian Higgs model

Some remarks on the spectral functions of the Abelian Higgs model

Extracting topological information from momentum space propagators

Complex poles and spectral functions of Landau gauge QCD and QCD-like theories

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