Renormalization Group Summation and the Free Energy of Hot QCD

Using an approach developed in the context of zero-temperature QCD to systematically sum higher order effects whose form is fixed by the renormalization group equation, we sum to all orders the leading log (LL) and next-to-leading log (NLL) contributions to the thermodynamic free energy in hot QCD. While the result varies considerably less with changes in the renormalization scale than does the purely perturbative result, a novel ambiguity arises which reflects the strong scheme dependence of thermal perturbation theory.Comment: 7 pages REVTEX4, 2 figures; v2: typos correcte

The Equation of State for Dense QCD and Quark Stars

We calculate the equation of state for degenerate quark matter to leading order in hard-dense-loop (HDL) perturbation theory. We solve the Tolman-Oppenheimer-Volkov equations to obtain the mass-radius relation for dense quark stars. Both the perturbative QCD and the HDL equations of state have a large variation with respect to the renormalization scale for quark chemical potential below 1 GeV which leads to large theoretical uncertainties in the quark star mass-radius relation.Comment: 7 pages, 3 figure

An adaptive inelastic magnetic mirror for Bose-Einstein condensates

We report the reflection and focussing of a Bose-Einstein condensate by a new pulsed magnetic mirror. The mirror is adaptive, inelastic, and of extremely high optical quality. The deviations from specularity are less than 0.5 mrad rms, making this the best atomic mirror demonstrated to date. We have also used the mirror to realize the analog of a beam-expander, producing an ultra-cold collimated fountain of matter wavesComment: 4 pages, 4 figure

Coupled-mode equations and gap solitons in a two-dimensional nonlinear elliptic problem with a separable periodic potential

We address a two-dimensional nonlinear elliptic problem with a finite-amplitude periodic potential. For a class of separable symmetric potentials, we study the bifurcation of the first band gap in the spectrum of the linear Schr\"{o}dinger operator and the relevant coupled-mode equations to describe this bifurcation. The coupled-mode equations are derived by the rigorous analysis based on the Fourier--Bloch decomposition and the Implicit Function Theorem in the space of bounded continuous functions vanishing at infinity. Persistence of reversible localized solutions, called gap solitons, beyond the coupled-mode equations is proved under a non-degeneracy assumption on the kernel of the linearization operator. Various branches of reversible localized solutions are classified numerically in the framework of the coupled-mode equations and convergence of the approximation error is verified. Error estimates on the time-dependent solutions of the Gross--Pitaevskii equation and the coupled-mode equations are obtained for a finite-time interval.Comment: 32 pages, 16 figure

Denominators of Eisenstein cohomology classes for GL_2 over imaginary quadratic fields

We study the arithmetic of Eisenstein cohomology classes (in the sense of G. Harder) for symmetric spaces associated to GL_2 over imaginary quadratic fields. We prove in many cases a lower bound on their denominator in terms of a special L-value of a Hecke character providing evidence for a conjecture of Harder that the denominator is given by this L-value. We also prove under some additional assumptions that the restriction of the classes to the boundary of the Borel-Serre compactification of the spaces is integral. Such classes are interesting for their use in congruences with cuspidal classes to prove connections between the special L-value and the size of the Selmer group of the Hecke character.Comment: 37 pages; strengthened integrality result (Proposition 16), corrected statement of Theorem 3, and revised introductio

Femto-Photography of Protons to Nuclei with Deeply Virtual Compton Scattering

Developments in deeply virtual Compton scattering allow the direct measurements of scattering amplitudes for exchange of a highly virtual photon with fine spatial resolution. Real-space images of the target can be obtained from this information. Spatial resolution is determined by the momentum transfer rather than the wavelength of the detected photon. Quantum photographs of the proton, nuclei, and other elementary particles with resolution on the scale of a fraction of a femtometer is feasible with existing experimental technology.Comment: To be published in Physical Review D. Replaces previous version with minor changes in presentatio

Description and evaluation of tropospheric chemistry and aerosols in the Community Earth System Model (CESM1.2)

The Community Atmosphere Model (CAM), version 5, is now coupled to extensive tropospheric and stratospheric chemistry, called CAM5-chem, and is available in addition to CAM4-chem in the Community Earth System Model (CESM) version 1.2. The main focus of this paper is to compare the performance of configurations with internally derived "free running" (FR) meteorology and "specified dynamics" (SD) against observations from surface, aircraft, and satellite, as well as understand the origin of the identified differences. We focus on the representation of aerosols and chemistry. All model configurations reproduce tropospheric ozone for most regions based on in situ and satellite observations. However, shortcomings exist in the representation of ozone precursors and aerosols. Tropospheric ozone in all model configurations agrees for the most part with ozonesondes and satellite observations in the tropics and the Northern Hemisphere within the variability of the observations. Southern hemispheric tropospheric ozone is consistently underestimated by up to 25%. Differences in convection and stratosphere to troposphere exchange processes are mostly responsible for differences in ozone in the different model configurations. Carbon monoxide (CO) and other volatile organic compounds are largely underestimated in Northern Hemisphere mid-latitudes based on satellite and aircraft observations. Nitrogen oxides (NOx) are biased low in the free tropical troposphere, whereas peroxyacetyl nitrate (PAN) is overestimated in particular in high northern latitudes. The present-day methane lifetime estimates are compared among the different model configurations. These range between 7.8 years in the SD configuration of CAM5-chem and 8.8 years in the FR configuration of CAM4-chem and are therefore underestimated compared to observational estimations. We find that differences in tropospheric aerosol surface area between CAM4 and CAM5 play an important role in controlling the burden of the tropical tropospheric hydroxyl radical (OH), which causes differences in tropical methane lifetime of about half a year between CAM4-chem and CAM5-chem. In addition, different distributions of NOx from lightning explain about half of the difference between SD and FR model versions in both CAM4-chem and CAM5-chem. Remaining differences in the tropical OH burden are due to enhanced tropical ozone burden in SD configurations compared to the FR versions, which are not only caused by differences in chemical production or loss but also by transport and mixing. For future studies, we recommend the use of CAM5-chem configurations, due to improved aerosol description and inclusion of aerosol–cloud interactions. However, smaller tropospheric surface area density in the current version of CAM5-chem compared to CAM4-chem results in larger oxidizing capacity in the troposphere and therefore a shorter methane lifetime

Joint resummation in electroweak boson production

We present a phenomenological application of the joint resummation formalism to electroweak annihilation processes at measured boson momentum Q_T. This formalism simultaneously resums at next-to-leading logarithmic accuracy large threshold and recoil corrections to partonic scattering. We invert the impact parameter transform using a previously described analytic continuation procedure. This leads to a well-defined, resummed perturbative cross section for all nonzero Q_T, which can be compared to resummation carried out directly in Q_T space. From the structure of the resummed expressions, we also determine the form of nonperturbative corrections to the cross section and implement these into our analysis. We obtain a good description of the transverse momentum distribution of Z bosons produced at the Tevatron collider.Comment: 27 pages, LaTeX, 8 figures as eps files. Some additions to earlier version, this version as published in Phys. Rev. D66 (2002) 01401

Trace Anomaly and Quasi-Particles in Finite Temperature SU(N) Gauge Theory

We consider deconfined matter in SU(N) gauge theory as an ideal gas of transversely polarized quasi-particle modes having a temperature-dependent mass m(T). Just above the transition temperature, the mass is assumed to be determined by the critical behavior of the energy density and the screening length in the medium. At high temperature, it becomes proportional to T as the only remaining scale. The resulting (trace anomaly based) interaction measure Delta=(e - 3P)/T^4 and energy density are found to agree well with finite temperature SU(3) lattice calculations.Comment: 13 pages, 13 figures; references added for version

Angular Conditions,Relations between Breit and Light-Front Frames, and Subleading Power Corrections

We analyze the current matrix elements in the general collinear (Breit) frames and find the relation between the ordinary (or canonical) helicity amplitudes and the light-front helicity amplitudes. Using the conservation of angular momentum, we derive a general angular condition which should be satisfied by the light-front helicity amplitudes for any spin system. In addition, we obtain the light-front parity and time-reversal relations for the light-front helicity amplitudes. Applying these relations to the spin-1 form factor analysis, we note that the general angular condition relating the five helicity amplitudes is reduced to the usual angular condition relating the four helicity amplitudes due to the light-front time-reversal condition. We make some comments on the consequences of the angular condition for the analysis of the high-$Q^2$ deuteron electromagnetic form factors, and we further apply the general angular condition to the electromagnetic transition between spin-1/2 and spin-3/2 systems and find a relation useful for the analysis of the N-$\Delta$ transition form factors. We also discuss the scaling law and the subleading power corrections in the Breit and light-front frames.Comment: 24 pages,2 figure