Topological Properties Of QCD Research Articles

The topological properties of QCD at high temperature: problems and perspectives

Lattice computations are the only first principle method capable of quantitatively assessing the topological properties of QCD at high temperature, however the numerical determination of the topological properties of QCD, especially in the high temperature phase, is a notoriously difficult problem. We will discuss the difficulties encountered in such a computation and some strategies that have been proposed to avoid (or at least to alleviate) them.

Quark number holonomy and confinement-deconfinement transition

We propose a new quantity which describes the confinement-deconfinement transition based on topological properties of QCD. The quantity which we call the quark number holonomy is defined as the integral of the quark number susceptibility along the closed loop of $\theta$ where $\theta$ is the dimensionless imaginary chemical potential. Expected behavior of the quark number holonomy at finite temperature is discussed and its asymptotic behaviors are shown.

Gauge-dependent O.P.E. power corrections on the QCD coupling

The running coupling constant can be estimated by computing gluon two- and three-point Green functions from the lattice. Computing in lattice implies working in a fixed gauge sector (Landau). A source of systematic uncertainty is then the contribution of non gauge-invariant condensates, as 〈 A 2〉, generating power corrections that might still be important at very high energies. We study the impact of this gluon condensate on the analysis of lattice data and the estimate of Λ MS . We finally try the relationship of this condensate with topological properties of QCD through the instanton picture.

An instanton picture O.P.E.〈A 2〉 condensate?

Gluon two- and three-point Green Functions computed in Landau gauge from the lattice show the existence of power corrections to the purely perturbative expressions, that can be explained through an Operator Product Expansion as the influence of a non gauge invariant mass dimension two condensate. The relationship of this condensate with topological properties of QCD, namely instantons, will be studied, giving a first estimate of the contribution of instantons to this condensate based in the direct lattice measure, after a cooling process, of the instanton liquid properties.

Topological properties of QCD with two dynamical fermions

We investigate the topological susceptibility of the QCD vacuum with two flavours of dynamical staggered fermions on the lattice both at zero and finite temperature. At zero temperature we study the dependence of the signal on the fermion mass and at finite temperature we analyze the behaviour across the phase transition.

Topological properties of QCD with two dynamical fermions

Topological properties of QCD with two dynamical fermions

Symmetry and correlation functions in the high temperature phase of QCD

Simple group-theoretical arguments are used to demonstrate that in the high temperature (chirally restored) phase of QCD with N f massless flavours, all n-point correlation functions of quark bilinears are invariant under U(1) A transformations provided n < N f . In particular this implies that the two-point correlation function in the η′ channel is identical to that in the pion channel for N f > 2. Unlike previous work, this result does not depend on the topological properties of QCD and can be formulated without explicit reference to functional integrals.

Topological properties of the colour field in hard processes

Topological properties of the confining force field which is stretched between the outgoing quarks and gluons in hard processes are important for the distribution of final state hadrons. Different colour factors in the amplitudes obtained in perturbative QCD can be associated with different field configurations, and we discuss in detail some examples. It turns out that the amplitudes for different configurations are not always orthogonal. However it is possible that topological properties of QCD, not exhibited in perturbation theory, play a fundamental role and have to be included in order to completely specify a quantum mechanical state, in which case the interference terms would vanish. This question is important e.g. for the determination of αs and Λ from Υ decay.