Tackling the infrared problem of thermal QCD

Perturbative calculations of corrections to the behavior of an ideal gas of quarks and gluons, the limit that is formally realized at infinite temperature, are obstructed by severe infrared divergences. The limits to computability that the infrared problem poses can be overcome in the framework of dimensionally reduced effective theories. Here, we give details on the evaluation of the highest perturbative coefficient needed for this setup, in the continuum.Comment: 3 pages, Lattice2003(nonzero

Evading the Infrared Problem of Thermal QCD

Due to asymptotic freedom, QCD is guaranteed to be accessible to perturbative methods at asymptotically high temperatures. However, in 1979 Linde has pointed out the existence of an "infrared wall", beyond which an infinite number of Feynman diagrams contribute. Following a proposal by Braaten and Nieto, it is shown explicitly how the limits to computability that this infrared problem poses can be overcome in the framework of dimensionally reduced effective theories.Comment: To appear in the proceedings of SEWM04, Helsinki, Finland, 16-19 Jun 200

Loops for Hot QCD

In this talk we review the status concerning vacuum integrals needed in perturbative expansions of QCD at non-zero temperature. We will focus on the differences as compared to familiar zero-temperature techniques, and provide a list of known basic master integrals.Comment: 6 pages, to appear in the proceedings of the international conference on Loops and Legs in Quantum Field Theory, Sondershausen, 20-25 April 200

Two-loop QCD gauge coupling at high temperatures

We determine the 2-loop effective gauge coupling of QCD at high temperatures, defined as a matching coefficient appearing in the dimensionally reduced effective field theory. The result allows to improve on one of the classic non-perturbative probes for the convergence of the weak-coupling expansion at high temperatures, the comparison of full and effective theory determinations of an observable called the spatial string tension. We find surprisingly good agreement almost down to the critical temperature of the deconfinement phase transition. We also determine one new contribution of order O(g^6T^4) to the pressure of hot QCD.Comment: 17 page

Spatial string tension revisited

The spatial string tension, a classic non-perturbative probe for the convergence of the weak-coupling expansion at high temperatures, can be determined in full QCD as well as in a dimensionally reduced effective theory. Comparing both approaches, we find surprisingly good agreement almost down to the critical temperature of the deconfinement phase transition.Comment: 6 pages, 2 figures, talk given at Lattice 2005 (nonzero temperature and density

Constraints on the NMSSM from the oblique parameters

Electroweak precision measurements, encoded in the oblique parameters, give strong constraints on physics beyond the Standard Model. The oblique parameters S, T, U (V, W, X) are calculated in the next-to-minimal supersymmetric model (NMSSM). We outline the calculation of the oblique parameters in terms of one-loop gauge-boson selfenergies and find sensitive restrictions for the NMSSM parameter space.Comment: 11 pages, 7 figures, 1 tabl

Putting pressure on the spine : an osmoviscoelastic FE model of the intervertebral disc

Back pain is a frequently occurring complaint in adults, having a relatively large impact on the European economy due to the fact that it often partially incapacitates the patient. Intervertebral discs are believed to be a key element of back pain. Apart from providing flexibility to the spine, intervertebral discs have a mechanical role in absorbing and transmitting loads through the spine. As measurements in living humans are complex, finite element (FE) models have become an important tool to study load distribution in healthy and degenerated discs. The disc is subjected to a combination of elastic, viscous and osmotic forces, but the latter has mostly been neglected in previous 3D FE models. To illustrate, in the fiber-reinforced disc tissue, there is interdependency between swelling of its proteoglycan (PG) rich ground substance and the tensile stresses in its collagen structure, which has not been accounted for previously. Furthermore, the total amount of water in the tissue is divided into intrafibrillar water (IFW) and extrafibrillar water (EFW). IFW is present in the intrafibrillar space within the collagen fibers and is therefore not accessible to the PG’s that reside in the extrafibrillar compartment. Experimental results have shown that both gene expression of cells in the intervertebral disc and propagation of cracks are affected by changes in osmotic pressure which must be determined on the basis of the extrafibrillar water (EFW) only. Hence, quantification of intra- and extrafibrillar fluid exchange and its effect on osmolarity of disc tissue is important for determining the physical conditions of disc tissue and its role in disc degeneration and failure. In an initial osmoviscoelastic FE model (chapter 3), the interdependency of swelling and collagen pre-stressing was modeled. It predicted intradiscal pressures within unloaded discs to the order of 0.1-0.2MPa, which is in agreement with in vivo experimental measurements published by Wilke et al. In the initial model, a correction factor was used to account for the influence of IFW based on the seminal work of Urban and McMullin for tissue containing a low collagen content such as the nucleus pulposus. However, this was recently not shown to be the case for the annulus which has much higher collagen content. A study by Sivan et al. demonstrated that IFW was sensitive to the applied load which can alter significantly the fixed charged density. Consequently, the initial FE model of the disc in this thesis was extended to include the intra and extrafibrillar water differentiation (chapter 4) and exhibited that the intradiscal pressure profile was clearly influenced by the IFW content. Unfortunately, lack of experimental data to determine some of the model parameters limited the applicability of the model. In addition to osmotic effects, mechanical properties of the intervertebral disc are complex. The composite behavior of disc tissue is regulated by its biochemical composition and fiber-reinforced structure. The anisotropic, nonlinear behavior of a multicomponent material like the intervertebral disc can only be assessed through a variety of experiments. Hence, data from several different experiments was simultaneously fitted to a simple FE model to calculate the material law for the disc (chapter 5). As part of this study experimental data for the material properties of the disc published in literature, was complemented with further tensile tests on human annulus fibrosus. Furthermore, the existing data on compression of non-degenerated human annulus and nucleus tissue together with the new tensile data was used to tune the osmoviscoelastic material constitutive law. The osmoviscoelastic material law was implemented into the full 3D model. The bulging and creep behavior of the resulting disc model was confronted with experiments of whole discs from the literature. From this comparison, it appeared that a refinement of the osmoviscoelastic model was necessary. Thus, the simplified fiber structure from earlier studies was extended with a more complex secondary fiber structure, which reduced the deformability of the model, while maintaining a correct reproduction of the experiments in confined compression, relaxation and tensile stiffness. Furthermore, to ensure convergence of the highly non-linear simulations the shear stiffness of the elastic non-fibrillar matrix was increased slightly, which was still in reasonable agreement with the experimental data (chapter 6). The evaluated 3D disc model may now be used to explore the biomechanical implications of disc degeneration on its function and integrity as well as to explore therapeutic mechanisms for repair and regeneration. McNally et al. measured compressive stress profiles in human discs post mortem. The stresses in the nucleus were nearly constant, whereas high peaks of compressive stress were found on the posterior and anterior side of the annulus. The posterior side experienced the highest compressive stress peaks. These peaks may partly explain the prevalence of postero-lateral herniation in human intervertebral discs. The osmoviscoelastic disc model also predicted similar posterior and anterior stress peaks characterized by McNally et al. (chapter 7). The posterior peak was higher than the anterior peak, consistent with the experimental trend. Results of a primary sensitivity study showed that the development of these peaks depend partly on the amount of fixed charges, which influenced the swelling capacity of the disc tissue. Hence, an increase of the stress peaks was noticed when the swelling ability of the tissue was reduced; this indicated a load shift from nucleus towards the annulus. To further quantify parameters that influence the load distribution in the normal and degenerated disc, a degenerated human data set to describe the fiber and non-fiber properties is needed. Furthermore, the quantification of the stress and load distribution under different load cases (e.g. bending, torsion) is required

Four-loop lattice-regularized vacuum energy density of the three-dimensional SU(3) + adjoint Higgs theory

The pressure of QCD admits at high temperatures a factorization into purely perturbative contributions from "hard" thermal momenta, and slowly convergent as well as non-perturbative contributions from "soft" thermal momenta. The latter can be related to various effective gluon condensates in a dimensionally reduced effective field theory, and measured there through lattice simulations. Practical measurements of one of the relevant condensates have suffered, however, from difficulties in extrapolating convincingly to the continuum limit. In order to gain insight on this problem, we employ Numerical Stochastic Perturbation Theory to estimate the problematic condensate up to 4-loop order in lattice perturbation theory. Our results seem to confirm the presence of "large" discretization effects, going like $a\ln(1/a)$, where $a$ is the lattice spacing. For definite conclusions, however, it would be helpful to repeat the corresponding part of our study with standard lattice perturbation theory techniques.Comment: 35 pages. v2: minor corrections, published versio

Non-perturbative plaquette in 3d pure SU(3)

We present a determination of the elementary plaquette and, after the subsequent ultraviolet subtractions, of the finite part of the gluon condensate, in lattice regularization in three-dimensional pure SU(3) gauge theory. Through a change of regularization scheme to MSbar and a matching back to full four-dimensional QCD, this result determines the first non-perturbative contribution in the weak-coupling expansion of hot QCD pressure.Comment: 6 pages, 4 figures, talk presented at Lattice 2005 (Non-zero temperature and density