Phenomenology of infrared finite gluon propagator and coupling constant

Natale, A. A.

doi:10.1590/s0103-97332007000200023

Cited by 14 publications

(16 citation statements)

References 33 publications

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“…13 Indeed, the RGZ tree-level gluon propagator describes well the numerical data in the SU(2) case [64,92], for d ¼ 3 and 4, and in the SU(3) case [93] with d ¼ 4. It is also interesting to note that the fitting values for the dimension-two condensates are very similar for the SU(2) and SU (3) gauge groups in the four-dimensional case.…”

Section: Introductionmentioning

confidence: 82%

“…3 These conditions can be given in terms of the value of the ghost dressing function F ðp 2 Þ ¼ p 2 Gðp 2 Þ at a given momentum scale p [22,31]. In particular, if one considers p ¼ 0, it is clear that 1=F ð0Þ ¼ 0 gives an IR-enhanced ghost propagator Gðp 2 Þ while 1=F ð0Þ > 0 yields a freelike behavior for Gðp 2 Þ at small momenta.…”

Section: Introductionmentioning

confidence: 99%

“…[27]. 3 The existence of different nonperturbative solutions for DSEs in relation to different boundary conditions has been discussed, for example, in Refs. [28,29] (see also Sec.…”

Section: Introductionmentioning

confidence: 99%

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No-pole condition in Landau gauge: Properties of the Gribov ghost form factor and a constraint on the2dgluon propagator

2012

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We study general properties of the Landau-gauge Gribov ghost form factor ðp 2 Þ for SUðN c Þ Yang-Mills theories in the d-dimensional case. We find a qualitatively different behavior for d ¼ 3, 4 with respect to the d ¼ 2 case. In particular, considering any (sufficiently regular) gluon propagator Dðp 2 Þ and the one-loop-corrected ghost propagator, we prove in the 2d case that the function ðp 2 Þ blows up in the infrared limit p ! 0 as ÀDð0Þ lnðp 2 Þ. Thus, for d ¼ 2, the no-pole condition ðp 2 Þ < 1 (for p 2 > 0) can be satisfied only if the gluon propagator vanishes at zero momentum, that is, Dð0Þ ¼ 0. On the contrary, in d ¼ 3 and 4, ðp 2 Þ is finite also if Dð0Þ > 0. The same results are obtained by evaluating the ghost propagator Gðp 2 Þ explicitly at one loop, using fitting forms for Dðp 2 Þ that describe well the numerical data of the gluon propagator in two, three and four space-time dimensions in the SU(2) case. These evaluations also show that, if one considers the coupling constant g 2 as a free parameter, the ghost propagator admits a one-parameter family of behaviors ( labeled by g 2 ), in agreement with previous works by Boucaud et al. In this case the condition ð0Þ 1 implies g 2 g 2 c , where g 2 c is a ''critical'' value. Moreover, a freelike ghost propagator in the infrared limit is obtained for any value of g 2 smaller than g 2 c , while for g 2 ¼ g 2 c one finds an infrared-enhanced ghost propagator. Finally, we analyze the Dyson-Schwinger equation for ðp 2 Þ and show that, for infrared-finite ghost-gluon vertices, one can bound the ghost form factor ðp 2 Þ. Using these bounds we find again that only in the d ¼ 2 case does one need to impose Dð0Þ ¼ 0 in order to satisfy the no-pole condition. The d ¼ 2 result is also supported by an analysis of the Dyson-Schwinger equation using a spectral representation for the ghost propagator. Thus, if the no-pole condition is imposed, solving the d ¼ 2 Dyson-Schwinger equations cannot lead to a massive behavior for the gluon propagator. These results apply to any Gribov copy inside the so-called first Gribov horizon; i.e., the 2d result Dð0Þ ¼ 0 is not affected by Gribov noise. These findings are also in agreement with lattice data.

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Section: Introductionmentioning

confidence: 82%

Section: Introductionmentioning

confidence: 99%

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No-pole condition in Landau gauge: Properties of the Gribov ghost form factor and a constraint on the2dgluon propagator

2012

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“…A discussion about the different solutions can be found in the introduction of Ref. [14], where the main references are also quoted. Only very recently it was claimed that a gauge invariant truncation of the QCD SDE can be obtained systematically [15].…”

Section: Introductionmentioning

confidence: 99%

Nonleptonic Annihilation Decays of B Meson With a Natural Infrared Cutoff

Natale

Zanetti

2009

Int. J. Mod. Phys. A

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Within the QCD factorization approach we compute the amplitudes for annihilation channels of B mesons decays into final states containing two pseudoscalar particles. These decays may be plagued by effects like non-perturbative physics or breaking of the factorization hypothesis and imply, at some extent, the introduction of an infrared cutoff in the calculation of amplitudes. We compute the decays with the help of infrared finite gluon propagators and coupling constants that were obtained in different solutions of the QCD Schwinger-Dyson equations. These solutions yield a natural cutoff for the amplitudes, and we argue that a systematic study of these B decays may provide a test for the QCD infrared behavior.

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“…A combination of analytical calculations, based on Dyson-Schwinger equations [1][2][3][4][5][6][7][8][9][10][11][12][13] and lattice gauge simulations , has given new insights into the behavior of QCD Green's functions. In particular, it has been found that in the Landau gauge at low momentum the ghost propagator is enhanced while the gluon propagator is suppressed.…”

Section: Introductionmentioning

confidence: 99%