Infrared Gluon and Ghost Propagators from Lattice QCD. Results from large asymmetric lattices

We report on the infrared limit of the quenched lattice Landau gauge gluon and ghost propagators as well as the strong coupling constant computed from large asymmetric lattices. The infrared lattice propagators are compared with the pure power law solutions from Dyson-Schwinger equations (DSE). For the gluon propagator, the lattice data is compatible with the DSE solution. The preferred measured gluon exponent being $\sim 0.52$, favouring a null zero momentum propagator. The lattice ghost propagator shows finite volume effects and, for the volumes considered, the propagator does not follow a pure power law. Furthermore, the strong coupling constant is computed and its infrared behaviour investigated.Comment: Talk given at QNP06; final version with improved english, accepted for publication at EPJ

A variational nonlinear Hausdorff-Young inequality in the discrete setting

Following the works of Lyons and Oberlin, Seeger, Tao, Thiele and Wright, we relate the variation of certain discrete curves on the Lie group $\text{SU}(1,1)$ to the corresponding variation of their linearized versions on the Lie algebra. Combining this with a discrete variational Menshov-Paley-Zygmund theorem, we establish a variational Hausdorff-Young inequality for a discrete version of the nonlinear Fourier transform on $\text{SU}(1,1)$.Comment: 16 page

Gribov copies, Lattice QCD and the gluon propagator

We address the problem of Gribov copies in lattice QCD. The gluon propagator is computed, in the Landau gauge, using 302 ($\beta = 5.8$) $12^4$ configurations gauge fixed to different copies. The results of the simulation shows that: i) the effect of Gribov copies is small (less than 10%); ii) Gribov copies change essentially the lowest momenta components ($q < 2.6$ GeV); iii) within the statistical accuracy of our simulation, the effect of Gribov copies is resolved if statistical errors are multiplied by a factor of two or three. Moreover, when modelling the gluon propagator, different sets of Gribov copies produce different sets of parameters not, necessarily, compatible within one standard deviation. Finally, our data supports a gluon propagator which, for large momenta, behaves like a massive gluon propagator with a mass of 1.1 GeV

The lattice Landau gauge gluon propagator: lattice spacing and volume dependence

The interplay between the finite volume and finite lattice spacing is investigated using lattice QCD simulations to compute the Landau gauge gluon propagator. Comparing several ensembles with different lattice spacings and physical volumes, we conclude that the dominant effects, in the infrared region, are associated with the use of a finite lattice spacing. The simulations show that decreasing the lattice spacing, while keeping the same physical volume, leads to an enhancement of the infrared gluon propagator. In this sense, the data from $\beta=5.7$ simulations, which uses an $a \approx 0.18$ fm, provides a lower bound for the infinite volume propagator.Comment: Final version to appear in Phys Rev

The Infrared Landau Gauge Gluon Propagator from Lattice QCD

The quenched Landau gauge gluon propagator is investigated in lattice QCD with large assimetric lattices, accessing momenta as low as $q \sim 100$ MeV or smaller. Our investigation focus on the IR limit of the gluon dressing function, testing the compatibility with recent solutions of the Dyson-Schwinger equations. In particular, the low energy parameters $\kappa$ and $\alpha (0)$ are measured.Comment: 3 pages, 1 figure. Talk given at Quark Confinement and the Hadron Spectrum VI 2004, Italy, 21-25 Sep. References correc