Modeling the gluon propagator in Landau gauge: Lattice estimates of pole masses and dimension-two condensates

We present an analytic description of numerical results for the Landau-gauge SU(2) gluon propagator D(p(2)), 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(p(2)) 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(p(2)). 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.

No-pole condition in Landau gauge: Properties of the Gribov ghost form factor and a constraint on the 2d gluon propagator

We study general properties of the Landau-gauge Gribov ghost form factor sigma(p(2)) for SU(N-c) Yang-Mills theories in the d-dimensional case. We find a qualitatively different behavior for d = 3, 4 with respect to the d = 2 case. In particular, considering any (sufficiently regular) gluon propagator D(p(2)) and the one-loop-corrected ghost propagator, we prove in the 2d case that the function sigma(p(2)) blows up in the infrared limit p -> 0 as -D(0) ln(p(2)). Thus, for d = 2, the no-pole condition sigma(p(2)) < 1 (for p(2) > 0) can be satisfied only if the gluon propagator vanishes at zero momentum, that is, D(0) = 0. On the contrary, in d = 3 and 4, sigma(p(2)) is finite also if D(0) > 0. The same results are obtained by evaluating the ghost propagator G(p(2)) explicitly at one loop, using fitting forms for D(p(2)) 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 sigma(0) <= 1 implies g(2) <= g(c)(2), where g(c)(2) is a "critical" value. Moreover, a freelike ghost propagator in the infrared limit is obtained for any value of g(2) smaller than g(c)(2), while for g(2) = g(c)(2) one finds an infrared-enhanced ghost propagator. Finally, we analyze the Dyson-Schwinger equation for sigma(p(2)) and show that, for infrared-finite ghost-gluon vertices, one can bound the ghost form factor sigma(p(2)). Using these bounds we find again that only in the d = 2 case does one need to impose D(0) = 0 in order to satisfy the no-pole condition. The d = 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 = 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 D(0) = 0 is not affected by Gribov noise. These findings are also in agreement with lattice data.

Tectonic implications of the 1419 Ma Nova Guarita mafic intrusives paleomagnetic pole (Amazonian Craton) on the longevity of Nuna

The Nuna supercontinent was probably assembled in the Paleoproterozoic, but its paleogeography and the timing for its demise are stills matter of debate. A paleomagnetic and geochronological study carried out on the Mesoproterozoic Nova Guarita dyke swarm (northern Mato Grosso State, SW Amazonian Craton) provides additional constraints on the duration of this supercontinent. Paleomagnetic AF and thermal treatment revealed south/southwest (northeast) magnetic directions with downward (upward) inclinations for 19 analyzed sites. These directions are carried by PSD magnetite with high unblocking temperatures as indicated by additional magnetic tests, including thermomagnetic curves, hysteresis loops and the progressive acquisition of isothermal remanence in selected samples. A positive contact test with the host granite in one of the studied dykes further attests to the primary origin of the characteristic magnetic component. A mean site direction was calculated at D-m = 220.5 degrees, I-m = 45.9 degrees (alpha(95) = 6.5 degrees, K = 27.7), which yielded a paleomagnetic pole located at 245.9 degrees E, 47.9 degrees S (A(95) = 7.0 degrees). Ar-40/Ar-39 dating carried out on biotites from four analyzed dykes yielded well-defined plateau ages with a mean of 1418.5 +/- 3.5 Ma. The Nova Guarita pole precludes a long-lived Nuna configuration in which Laurentia, Baltica, North China, and Amazonia formed a long and continuous block as previously proposed for the Paleoproterozoic. It is nevertheless fully compatible with a SAMBA (Amazonia-Baltica) link at Mesoproterozoic times. (C) 2011 Elsevier B.V. All rights reserved.