Heavy quark diffusion in perturbative QCD at next-to-leading order

We compute the momentum diffusion coefficient of a nonrelativistic heavy quark in a hot QCD plasma, to next-to-leading order in the weak coupling expansion. Corrections arise at O(g); physically they represent interference between overlapping scatterings, as well as soft, electric scale ($p\sim gT$) gauge field physics, which we treat using the hard thermal loop (HTL) effective theory. In 3-color, 3-flavor QCD, the momentum diffusion constant of a fundamental representation heavy quark at NLO is $\kappa = \frac{16\pi}{3} \alpha_s^2 T^3 (\ln \frac{1}{g} + 0.07428 + 1.8869 g)$. The convergence of the weak coupling expansion is poor.Comment: 4 pages, 3 figure

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

A way to estimate the heavy quark thermalization rate from the lattice

The thermalization rate of a heavy quark is related to its momentum diffusion coefficient. Starting from a Kubo relation and using the framework of the heavy quark effective theory, we argue that in the large-mass limit the momentum diffusion coefficient can be defined through a certain Euclidean correlation function, involving color-electric fields along a Polyakov loop. Furthermore, carrying out a perturbative computation, we demonstrate that the spectral function corresponding to this correlator is relatively flat at small frequencies. Therefore, unlike in the case of several other transport coefficients, for which the narrowness of the transport peak makes analytic continuation from Euclidean lattice data susceptible to severe systematic uncertainties, it appears that the determination of the heavy quark thermalization rate could be relatively well under control.Comment: 17 pages. v2: clarifications and references added, published versio

Demography of the George River Caribou Herd: Evidence of Population Regulation by Forage Exploitation and Range Expansion

The George River caribou herd in northern Quebec/Labrador increased from about 5000 animals in 1954 to 472,200 (or 1.1 caribou/km) prior to the 1984 calving season. The range used by the herd expanded from 160,000 to 442,000 sq km for the period 1971-84. The exponential rate of increase (r) was estimated at 0.11 in the 1970s. Calf:female ratio in autumn was relatively constant (x=0.52) from 1973 to 1983, but decreased to about 0.39 in 1984-86. The harvest rate was relatively low in the 1970s (about 3%/y), but seemingly increased in the mid-1980s to 5-7% as a result of more liberal regulations and a greater impetus to exploit caribou for subsistence. The cumulative impact of lower calf recruitment and more intensive hunting may have appreciably depressed the growth rate of the herd in 1984-86. A greater year-round competition for food resources and a greater energy expenditure associated with range expansion are presented as probable regulatory factors for the George River herd. It is argued that the nature of caribou-habitat interactions in continental regions generate long-term fluctuations in caribou numbers if human exploitation remains low. At present, wolf predation does not appear to be an important mortality factor capable of regulating the George River herd.Key words: caribou, population regulation, food limitation, northem Quebec, Labrador, wolf predationMots clés: caribou, régulation de la population, limitation de la nourriture, nord du Québec, Labrador, prédation des loup

Heavy quark diffusion in QCD and N=4 SYM at next-to-leading order

We present the full details of a calculation at next-to-leading order of the momentum diffusion coefficient of a heavy quark in a hot, weakly coupled, QCD plasma. Corrections arise at O(g_s); physically they represent interference between overlapping scatterings, as well as soft, electric scale (p ~ gT) gauge field physics, which we treat using the hard thermal loop (HTL) effective theory. In 3-color, 3-flavor QCD, the momentum diffusion constant of a fundamental representation heavy quark at NLO is kappa = (16\pi/3) alpha_s^2 T^3 (log(1/g) + 0.07428 + 1.9026 g). We extend the computation to a heavy fundamental representation ``probe'' quark in large N_c, N=4 Super Yang-Mills theory, where the result is kappa^{SYM}= (lambda^2 T^3)(6\pi) (log(1/\sqrt{\lambda}) + 0.4304 + 0.8010 \sqrt{lambda}) (where lambda=g_s^2 N_c is the t'Hooft coupling). In the absence of some resummation technique, the convergence of perturbation theory is poor.Comment: 40 pages, 14 figure

Colour-electric spectral function at next-to-leading order

The spectral function related to the correlator of two colour-electric fields along a Polyakov loop determines the momentum diffusion coefficient of a heavy quark near rest with respect to a heat bath. We compute this spectral function at next-to-leading order, O(alpha_s^2), in the weak-coupling expansion. The high-frequency part of our result (omega >> T), which is shown to be temperature-independent, is accurately determined thanks to asymptotic freedom; the low-frequency part of our result (omega << T), in which Hard Thermal Loop resummation is needed in order to cure infrared divergences, agrees with a previously determined expression. Our result may help to calibrate the overall normalization of a lattice-extracted spectral function in a perturbative frequency domain T << omega << 1/a, paving the way for a non-perturbative estimate of the momentum diffusion coefficient at omega -> 0. We also evaluate the colour-electric Euclidean correlator, which could be directly compared with lattice simulations. As an aside we determine the Euclidean correlator in the lattice strong-coupling expansion, showing that through a limiting procedure it can in principle be defined also in the confined phase of pure Yang-Mills theory, even if a practical measurement could be very noisy there.Comment: 38 page

Aerial surveys vs hunting statistics to monitor deer density : the example of Anticosti Island (Québec, Canada)

Cervid densities have recently increased in many parts of North America and Europe. To design sustainable harvesting strategies, a good understanding of deer population dynamics and reliable estimates of population densities are required. This is especially true on Anticosti Island, Québec, Canada, where sport hunting is the main source of income, and where long-lasting impacts of white-tailed deer Odocoileus virginianus on the forest ecosystem have been reported due to high deer densities. We compared white-tailed deer densities estimated in 2001 on the basis of an extensive aerial survey of 512 plots, each 3.5 km long by 60 m wide, with indices based on hunting statistics in 24 hunting zones on the island. We found a positive correlation between the number of deer seen per hunter day and the density of deer estimated by the aerial survey, but this correlation was highly influenced by the four locations with the highest densities of deer. We detected no significant correlation between deer density estimated by the aerial survey within each hunting zone and the number of deer harvested per hunter day. Our results underline the need for comparative studies addressing the validity of density indices based on hunting statistics to monitor variations in cervid population numbers

Contribution of picoplankton to the total particulate organic carbon concentration in the eastern South Pacific

International audienceProchlorococcus, Synechococcus, picophytoeukaryotes and bacterioplankton abundances and contributions to the total particulate organic carbon concentration, derived from the total particle beam attenuation coefficient (cp), were determined across the eastern South Pacific between the Marquesas Islands and the coast of Chile. All flow cytometrically derived abundances decreased towards the hyper-oligotrophic centre of the gyre and were highest at the coast, except for Prochlorococcus, which was not detected under eutrophic conditions. Temperature and nutrient availability appeared important in modulating picophytoplankton abundance, according to the prevailing trophic conditions. Although the non-vegetal particles tended to dominate the cp signal everywhere along the transect (50 to 83%), this dominance seemed to weaken from oligo- to eutrophic conditions, the contributions by vegetal and non-vegetal particles being about equal under mature upwelling conditions. Spatial variability in the vegetal compartment was more important than the non-vegetal one in shaping the water column particle beam attenuation coefficient. Spatial variability in picophytoplankton biomass could be traced by changes in both total chlorophyll a (i.e. mono + divinyl chlorophyll a) concentration and cp. Finally, picophytoeukaryotes contributed ~38% on average to the total integrated phytoplankton carbon biomass or vegetal attenuation signal along the transect, as determined by size measurements (i.e. equivalent spherical diameter) on cells sorted by flow cytometry and optical theory. Although there are some uncertainties associated with these estimates, the new approach used in this work further supports the idea that picophytoeukaryotes play a dominant role in carbon cycling in the upper open ocean, even under hyper-oligotrophic conditions

Contribution of picoplankton to the total particulate organic carbon (POC) concentration in the eastern South Pacific

International audienceProchlorococcus, Synechococcus, picophytoeukaryotes and bacterioplankton abundances and contributions to the total particulate organic carbon concentration (POC), derived from the total particle beam attenuation coefficient (cp), were determined across the eastern South Pacific between the Marquesas Islands and the coast of Chile. All flow cytometrically derived abundances decreased towards the hyper-oligotrophic centre of the gyre and were highest at the coast, except for Prochlorococcus, which is not detected under eutrophic conditions. Temperature and nutrient availability appeared important in modulating picophytoplankton abundance, according to the prevailing trophic conditions. Although the non-vegetal particles tended to dominate the cp signal everywhere along the transect (50 to 83%), this dominance seemed to weaken from oligo- to eutrophic conditions, the contributions by vegetal and non-vegetal particles being about equal under mature upwelling conditions. Spatial variability in the vegetal compartment was more important than the non-vegetal one in shaping the water column particulate attenuation coefficient. Spatial variability in picophytoplankton biomass could be traced by changes in both Tchla and cp. Finally, picophytoeukaryotes contributed with ~38% on average to the total integrated phytoplankton carbon biomass or vegetal attenuation signal along the transect, as determined by direct size measurements on cells sorted by flow cytometry and optical theory. The role of picophytoeukaryotes in carbon and energy flow would therefore be very important, even under hyper-oligotrophic conditions