Scaling behavior and positivity violation of the gluon propagator in full QCD

Bowman, Patrick O.; Heller, Urs M.; Leinweber, Derek B.; Parappilly, Maria; Sternbeck, André; Smekal, Lorenz von; Williams, Anthony G.; Zhang, Jianbo

doi:10.1103/physrevd.76.094505

Cited by 165 publications

(140 citation statements)

References 52 publications

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“…In this latter case we speak about positivity violation by the gluon. This violation of positivity has been observed both in lattice calculations [12,13,14] and for the solutions of the Schwinger-Dyson equations [10,15]. For completeness, in Fig.…”

Section: On the Gluon Propagatormentioning

confidence: 98%

Glueball spectral densities from the lattice

Oliveira¹,

Dudal²,

Silva³

2012

Proceedings of the 30th International Symposium on Lattice Field Theory — PoS(Lattice 2012)

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The propagator of a physical degree of freedom ought to obey a Källén-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) δ -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.

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Section: On the Gluon Propagatormentioning

confidence: 98%

Glueball spectral densities from the lattice

Oliveira¹,

Dudal²,

Silva³

2012

Proceedings of the 30th International Symposium on Lattice Field Theory — PoS(Lattice 2012)

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“…We hasten to emphasize that the aforementioned momentum configuration has been first considered in [21], in the context of the so-called "scaling" solutions [22]. Instead, our analysis will be carried out using an IR finite gluon propagator ∆ and ghost dressing function F , in conformity with the results obtained from a plethora of large-volume lattice simulations [23][24][25][26][27][28][29], as well as a variety of analytic approaches . Specifically, we will consider a simplified version of the so-called "one-loop dressed" approximation, where one computes the one-loop diagrams with fully dressed gluon and ghost propagators, but with tree-level (undressed) vertices (the case with dressed ghost-vertices only is also presented).…”

Section: Jhep09(2014)059mentioning

confidence: 99%

“…However, in order to get a sense of the general trend that one might expect from a general calculation, we may assume that the subtraction point lies sufficiently far in the UV. Then, for a representative large Euclidean momentum P , the qualitative behaviour of the form factor may be approximated by 24) so that, at P 2 = µ 2 R one obtains 25) JHEP09 (2014)059 and therefore, the value of V Γ (0) (0) gets renormalized to…”

Section: Jhep09(2014)059mentioning

confidence: 99%

Nonperturbative study of the four gluon vertex

Binosi

Ibañez

Papavassiliou

2014

J. High Energ. Phys.

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In this paper we study the nonperturbative structure of the SU(3) four-gluon vertex in the Landau gauge, concentrating on contributions quadratic in the metric. We employ an approximation scheme where "one-loop" diagrams are computed using fully dressed gluon and ghost propagators, and tree-level vertices. When a suitable kinematical configuration depending on a single momentum scale p is chosen, only two structures emerge: the tree-level four-gluon vertex, and a tensor orthogonal to it. A detailed numerical analysis reveals that the form factor associated with this latter tensor displays a change of sign (zero-crossing) in the deep infrared, and finally diverges logarithmically. The origin of this characteristic behavior is proven to be entirely due to the masslessness of the ghost propagators forming the corresponding ghost-loop diagram, in close analogy to a similar effect established for the three-gluon vertex. However, in the case at hand, and under the approximations employed, this particular divergence does not affect the form factor proportional to the tree-level tensor, which remains finite in the entire range of momenta, and deviates moderately from its naive tree-level value. It turns out that the kinematic configuration chosen is ideal for carrying out lattice simulations, because it eliminates from the connected Green's function all one-particle reducible contributions, projecting out the genuine one-particle irreducible vertex. Motivated by this possibility, we discuss in detail how a hypothetical lattice measurement of this quantity would compare to the results presented here, and the potential interference from an additional tensorial structure, allowed by Bose symmetry, but not encountered within our scheme.

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“…It is already known, from lattice simulations [4,5,6,7], that the Landau gauge gluon propagator displays a violation of spectral positivity. This implies that the gluon cannot appear as a free asymptotic S-matrix state and may be viewed as an indication of gluon confinement.…”

Section: Introductionmentioning

confidence: 99%

Spectral densities from the lattice

Silva¹,

Dudal²,

Oliveira³

2014

Proceedings of 31st International Symposium on Lattice Field Theory LATTICE 2013 — PoS(LATTICE 2013)

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We discuss a method to extract the Källén-Lehmann spectral density of a particle (be it elementary or bound state) propagator by means of 4d lattice data. We employ a linear regularization strategy, commonly known as the Tikhonov method with Morozov discrepancy principle. An important virtue over the popular maximum entropy method is the possibility to also probe unphysical spectral densities, as, for example, of a confined gluon. We apply our proposal to the SU(3) glue sector.

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Scaling behavior and positivity violation of the gluon propagator in full QCD

Cited by 165 publications

References 52 publications

Glueball spectral densities from the lattice

Glueball spectral densities from the lattice

Nonperturbative study of the four gluon vertex

Spectral densities from the lattice

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