Thermal imaginary part of a real-time static potential from classical lattice gauge theory simulations

Recently, a finite-temperature real-time static potential has been introduced via a Schr\"odinger-type equation satisfied by a certain heavy quarkonium Green's function. Furthermore, it has been pointed out that it possesses an imaginary part, which induces a finite width for the tip of the quarkonium peak in the thermal dilepton production rate. The imaginary part originates from Landau-damping of low-frequency gauge fields, which are essentially classical due to their high occupation number. Here we show how the imaginary part can be measured with classical lattice gauge theory simulations, accounting non-perturbatively for the infrared sector of finite-temperature field theory. We demonstrate that a non-vanishing imaginary part indeed exists non-perturbatively; and that its value agrees semi-quantitatively with that predicted by Hard Loop resummed perturbation theory.Comment: 18 pages. v2: clarifications and a reference added; published versio

Heavy Quark Thermalization in Classical Lattice Gauge Theory: Lessons for Strongly-Coupled QCD

Thermalization of a heavy quark near rest is controlled by the correlator of two electric fields along a temporal Wilson line. We address this correlator within real-time, classical lattice Yang-Mills theory, and elaborate on the analogies that exist with the dynamics of hot QCD. In the weak-coupling limit, it can be shown analytically that the dynamics on the two sides are closely related to each other. For intermediate couplings, we carry out non-perturbative simulations within the classical theory, showing that the leading term in the weak-coupling expansion significantly underestimates the heavy quark thermalization rate. Our analytic and numerical results also yield a general understanding concerning the overall shape of the spectral function corresponding to the electric field correlator, which may be helpful in subsequent efforts to reconstruct it from Euclidean lattice Monte Carlo simulations.Comment: 22 pages. v2: a reference and clarifications added; published versio

Real-time static potential in hot QCD

We derive a static potential for a heavy quark-antiquark pair propagating in Minkowski time at finite temperature, by defining a suitable gauge-invariant Green's function and computing it to first non-trivial order in Hard Thermal Loop resummed perturbation theory. The resulting Debye-screened potential could be used in models that attempt to describe the ``melting'' of heavy quarkonium at high temperatures. We show, in particular, that the potential develops an imaginary part, implying that thermal effects generate a finite width for the quarkonium peak in the dilepton production rate. For quarkonium with a very heavy constituent mass M, the width can be ignored for T \lsim g^2 M/12\pi, where g^2 is the strong gauge coupling; for a physical case like bottomonium, it could become important at temperatures as low as 250 MeV. Finally, we point out that the physics related to the finite width originates from the Landau-damping of low-frequency gauge fields, and could be studied non-perturbatively by making use of the classical approximation.Comment: 20 pages. v2: a number of clarifications and a few references added; published versio

The Sphaleron Rate in SU(N) Gauge Theory

The sphaleron rate is defined as the diffusion constant for topological number NCS = int g^2 F Fdual/32 pi^2. It establishes the rate of equilibration of axial light quark number in QCD and is of interest both in electroweak baryogenesis and possibly in heavy ion collisions. We calculate the weak-coupling behavior of the SU(3) sphaleron rate, as well as making the most sensible extrapolation towards intermediate coupling which we can. We also study the behavior of the sphaleron rate at weak coupling at large Nc.Comment: 18 pages with 3 figure

Estudo comparativo da sensibilidade nos pés de diabéticos com e sem úlceras utilizando o PSSD™ Comparative study of the sensitivity of diabetic lower extremities with and without ulcers using the PSSD™

INTRODUÇÃO: Determinar e comparar limiares de sensibilidade cutânea nos pés de pacientes diabéticos com úlcera em apenas um dos membros inferiores. MATERIAIS E MÉTODOS: 20 pacientes foram estudados, a média de idade e de conhecimento do diabetes foi 61,6 e 12,4 anos, respectivamente. Todos os pacientes foram previamente testados com o monofilamento de Semmes-Weinstein nº 5,07. A sensibilidade foi avaliada usando o teste de discriminação entre dois pontos e o PSSD&trade; (Pressure-Specified Sensory Device) para avaliar os limiares de sensibilidade de maneira quantitativa, em g/mm². Testadas três áreas da pele: polpa do hálux, dorso do pé e parte medial do calcâneo, incluindo-se quatro testes, um ponto estático, um ponto dinâmico, dois pontos estáticos e dois pontos dinâmicos. RESULTADOS: A distância média de discriminação de dois pontos em mm foi superior nos pés com úlceras, mas a diferença entre os membros inferiores teve significância estatística apenas para o hálux. Com o PSSD&trade;, todos os pacientes tiveram limiares de pressão superior nos pés com úlcera, em comparação com os pés sem úlcera, em todos os testes e com significância estatística. CONCLUSÃO: O PSSD&trade; foi capaz de diferenciar níveis de sensibilidade entre membros com e sem úlcera em pacientes diabéticos, com significância estatística.<br>INTRODUCTION: To determine and compare thresholds of cutaneous sensitivity of lower extremities in diabetic patients with an ulcer on only one lower extremity. METHODS AND MATERIALS: The study group included 20 patients with mean age of 61.6 and average time with diabetes of 12.4 years. All patients were previously tested using Semmes-Weinstein monofilament 5.07. Sensitivity was evaluated using the two point discrimination test and the PSSD&trade; (Pressure-Specified Sensory Device) in order to assess touch thresholds in a quantitative manner, in g/mm². Three skin areas were tested: hallux pulp, dorsum of foot and medial heel, including four tests: 1 point static, 1 point moving, 2 points static and 2 points moving. RESULTS: Mean 2 point discrimination distance in mm was higher in feet with ulcers, but the difference between extremities was only statistically significant for the hallux. With the PSSD&trade;, all patients had higher pressure thresholds in feet with ulcers when compared with feet without ulcers, in all tests, with statistical significance. CONCLUSION: The PSSD&trade; was able to differentiate levels of sensation between extremities with and without ulcers in diabetic patients, with statistical significance