Anomalies for Nonlocal Dirac Operators

The anomalies of a very general class of non local Dirac operators are computed using the $\zeta$-function definition of the fermionic determinant and an asymmetric version of the Wigner transformation. For the axial anomaly all new terms introduced by the non locality can be brought to the standard minimal Bardeen's form. Some extensions of the present techniques are also commented.Comment: (LaTeX) 10 pages, 1 figure. Talk given by E. R. A. at the International Workshop on Hadron Physics (Effective Theories of Low Energy QCD), Coimbra (Portugal), 10-15 September 1999. (To appear in the proceedings

The Powers of Deconfinement

The trace anomaly of gluodynamics encodes the breakdown of classical scale invariance due to interactions around the deconfinement phase transition. While it is expected that at high temperatures perturbation theory becomes applicable we show that current lattice calculations are far from the perturbative regime and are dominated instead by inverse even power corrections in the temperature, while the total perturbative contribution is estimated to be extremely small and compatible with zero within error bars. We provide an interpretation in terms of dimension-two gluon condensate of the dimensionally reduced theory which value agrees with a similar analysis of power corrections from available lattice data for the renormalized Polyakov loop and the heavy quark-antiquark free energy in the deconfined phase of QCD.Comment: To appear in the proceedings of 14th High-Energy Physics International Conference in Quantum Chromodynamics (QCD 08), Montpellier, France, 7-12 Jul 200

Heavy QˉQ{\bar Q}Q free energy from hadronic states

Within the spirit of the Hadron Resonance Gas model, we study a representation of the heavy $\bar{Q}Q$ free energy at temperatures below the phase transition in terms of the string and heavy-light hadrons. We discuss the string breaking phenomenon and the relevance of avoided crossings between the fundamental string and the hadron spectrum. Good agreement with lattice data is achieved.Comment: 5 pages, 5 figures. Talk given by E.Megias at the 18th International Conference in Quantum Chromodynamics (QCD 15), Montpellier, France, 29 Jun - 3 Jul 201

Thermal correlators in the hadron resonance gas: a dual Hagedorn distance

Fluctuations and correlations of conserved quantities in the confined phase of QCD are a viable way to characterize the existence of exotic and missing states with given quantum numbers in the hadronic spectrum. We study a realization of the Hadron Resonance Gas model in the light quark (uds) flavor sector of QCD to study the fluctuations and static correlators of electric charge, baryon number and strangeness. It is also conjectured an interesting duality between the correlators at zero temperature, and the fluctuations of integrated quantities at low temperatures, leading to the appearance of a dual Hagedorn distance for the former.Comment: 6 pages, 1 figure. Talk given by E.Megias at Excited QCD 2018, 11-15 March 2018, Kopaonik, Serbi

The Polyakov loop in various representations in the confined phase of QCD

We analyze the expectation value of the Polyakov loop in the fundamental and higher representations in the confined phase of QCD. We discuss a hadronic like representation, and find that the Polyakov loop corresponds to a partition function in the presence of a colored source, explaining its real and positive character. Saturating the sum rules to intermediate temperatures requires a large number of multipartonic excited states. By using constituent or bag models, we find detailed low temperature scaling rules which depart from the Casimir scaling and could be tested by lattice calculations.Comment: 40 pages, 27 figs. One figure and further discussion adde

Excited Hadrons, Heavy Quarks and QCD thermodynamics

We show how excited states in QCD can be profitably used to build up the Polyakov loop in the fundamental representation at temperatures below the hadron-quark-gluon crossover. The conditions under which a Hagedorn temperature for the Polyakov loop can be defined are analysed.Comment: 6 pages, 3 figures (minor corrections). Presented by ERA at Excited QCD 2013, 3-9 February 2013 Bjelasnica Mountain, Sarajevo, Bosnia-Herzegovin

Non-perturbative contribution to the Polyakov loop above the deconfinement phase transition

The Polyakov loop is an order parameter to the confinement-deconfinement phase transition in pure gluodynamics. Recently a simple phenomenological model has been proposed to describe the available lattice data for the renormalized Polyakov loop in the deconfinement phase (hep-ph/0505215). These data exhibit unequivocal inverse power temperature corrections driven by a dimension two gluon condensate. The heavy quark free energy is also studied and compared to lattice data.Comment: Talk given at Quark Matter 2005, 18th Internationl Conference on Nucleus-Nucleus Interactions, August 4-9, 2005, Budapest, Hungary, 4 pages, 3 figure

Trace Anomaly, Thermal Power Corrections and Dimension Two condensates in the deconfined phase

The trace anomaly of gluodynamics on the lattice shows clear fingerprints of a dimension two condensate above the phase transition. The condensate manifests itself through even powers of the inverse temperature while the total perturbative contribution corresponds to a mild temperature dependence and turns out to be compatible with zero within errors. We try several resummation methods based on a renormalization group improvement. The trace anomaly data are analyzed and compared with other determinations of the dimension two condensate based on the Polyakov loop and the heavy qq free energy, yielding roughly similar numerical values. The role of glueballs near the transition is also discussed.Comment: 15 pages, 7 figure

Heavy quark-antiquark free energy and thermodynamics of string-hadron avoided crossings

The correlation function between two Polyakov loops encodes the free-energy shift due to a pair of separated colour conjugated sources in the hot QCD medium. This is analyzed in terms of a novel K\"all\'en-Lehmann spectral representation for the separating distance, implying an increasing and concave free-energy at all temperatures. We express the heavy $\bar{Q} Q$ free-energy shift below the phase transition in QCD in terms of colour neutral purely hadronic states with no explicit reference to quarks and gluons. Good agreement with lattice data is achieved when considering the avoided crossing mechanism underlying string breaking and with standard quenched values of the string tension known from charmonium and bottomonium phenomenology. We also address the role of the corresponding entropy shift and its renormalization group properties.Comment: 14 pages, 6 figures. Section II.D corrected. To appear in Physical Review

New Improvements for Mie Scattering Calculations

New improvements to compute Mie scattering quantities are presented. They are based on a detailed analysis of the various sources of error in Mie computations and on mathematical justifications. The algorithm developed on these improvements proves to be reliable and efficient, without size ($x=2\pi R/\lambda$) nor refractive index ($m=m_R-{\rm i}m_I$) limitations, and the user has a choice to fix in advance the desired precision in the results. It also includes a new and efficient method to initiate the downward recurrences of Bessel functions.Comment: 17 pages, plain TEX, no figure