Next-to-leading Order Calculation of the Color-Octet 3S1 Gluon Fragmentation Function for Heavy Quarkonium

The short-distance coefficients for the color-octet 3S1 term in the fragmentation function for a gluon to split into heavy quarkonium states is calculated to order alpha_s^2. The gauge-invariant definition of the fragmentation function by Collins and Soper is employed. Ultraviolet divergences are removed using the MS-bar renormalization procedure. The longitudinal term in the fragmentation function agrees with a previous calculation by Beneke and Rothstein. The next-to-leading order correction to the transverse term disagrees with a previous calculation.Comment: 17 pages, 4 figure

Universality in the physics of cold atoms with large scattering length

Effective field theories exploit a separation of scales in physical systems in order to perform systematically improvable, model-independent calculations. They are ideally suited to describe universal aspects of a wide range of physical systems. I will discuss recent applications of effective field theory to cold atomic and molecular few-body systems with large scattering length.Comment: Invited talk at Few-Body 17, June 2003, Durham, NC, USA, 5 pages, 3 figures, uses espcrc1.st

Color and Spin in Quarkonium Production

I describe the NRQCD factorization approach to the inclusive production of heavy quarkonium, contrasting it with the color-singlet and color evaporation models. These approaches differ dramatically in their assumptions about the roles played by color and spin in the production process. They also differ dramatically in their predictions for the production of charmonium at large transverse momentum.Comment: 17 pages, LATEX with style file sprocl.st

Few-Body Effects in Cold Atoms and Limit Cycles

Physical systems with a large scattering length have universal properties independent of the details of the interaction at short distances. Such systems can be realized in experiments with cold atoms close to a Feshbach resonance. They also occur in many other areas of physics such as nuclear and particle physics. The universal properties include a geometric spectrum of three-body bound states (so-called Efimov states) and log-periodic dependence of low-energy observables on the physical parameters of the system. This behavior is characteristic of a renormalization group limit cycle. We discuss universality in the three- and four-body sectors and give an overview of applications in cold atoms.Comment: 7 pages, 3 figures, plenary talk at the 18th International IUPAP Conference on Few-Body Problems in Physics (FB18), Santos, Brazil, August 200

Prompt Upsilon and Psi Production at LEP

Color-octet contributions to quarkonia production at LEP are studied herein. The short distance formation of heavy quark-antiquark pairs in color-octet configurations via gluon fragmentation processes is significantly enhanced relative to the creation of color-singlet pairs via heavy quark fragmentation. But the subsequent long distance hadronization of these colored pairs into physical quarkonium bound states is suppressed compared to the nonperturbative evolution of their colorless counterparts. We find that the overall LEP rates for gluon fragmentation into prompt Upsilon and Psi vector bosons exceed those from heavy quark fragmentation. Inclusion of the dominant color-octet quarkonium production channel eliminates sizable discrepancies between previous predictions and recent measurements of prompt Z \to \Jpsi+X, $Z \to \psi'+X$ and $Z \to \Upsilon+X$ branching fractions.Comment: 15 pages, harvmac, 3 uuencoded figure

Perturbative QCD and Tau Decay

Sufficiently inclusive observables in the decay of the tau lepton can be calculated using the methods of perturbative QCD. These include the asymmetry parameter $A_\tau$ that determines that angular distribution of the total hadron momentum in the decay of a polarized tau. It should be possible to measure $A_\tau$ accurately using existing data from LEP. Reliable estimates of theoretical errors are essential in order to determine whether a given observable is sufficiently inclusive to be calculated using perturbative methods. The theoretical uncertainties due to higher orders in $\alpha_s$ can be estimated using recent calculations to all orders in the large-$(33-2N_f)$ limit. These estimates indicate that tau decay data can be used to determine $\alpha_s(M_Z)$ to a precision of 2% or better.Comment: 9 pages, LaTeX with espcrc2.sty, invited talk presented at the TAU 96 Workshop, Estes Park, Colorado, in September 199

Thermalisation of Longitudinal Gluons

In the usual real-time finite-temperature gauge theory both the physical and the unphysical degrees of freedom are thermalised. We discuss the alternative approach where only the physical transverse components of the gauge field have bare thermal propagators, whereas the unphysical degrees of freedom are not heated. We show how pinch singularities are avoided: sometimes this requires resummation. If only the hard thermal loop is included in the resummation, the spatially-longitudinal component of the gauge field, which contains an extra collective plasmon mode, becomes fully thermalised, though the Faddeev-Popov ghost and the remaining unphysical component of the gauge field remain frozen.Comment: 10 pages, 1 figure appended as pictex-file, DAMTP 93-06, TUW-93-0

Gauge Dependence of the Resummed Thermal Gluon Self Energy

The gauge dependence of the hot gluon self energy is examined in the context of Pisarski's method for resumming hard thermal loops. Braaten and Pisarski have used the Ward identities satisfied by the hard corrections to the n-point functions to argue the gauge fixing independence of the leading order resummed QCD plasma damping rate in covariant and strict Coulomb gauges. We extend their analysis to include all linear gauges that preserve rotational invariance and display explicitly the conditions required for gauge fixing independence. It is shown that in covariant gauges the resummed damping constant is gauge fixing independent only if an infrared regulator is explicitly maintained throughout the calculation.Comment: 29 pages, report BI-TP 92/19, LPTHE-Orsay 92/32, WIN-TH-92/02 (June 1992

Tau Polarimetry with Inclusive Decays

The spin asymmetry parameter $A_\tau$ characterizing the angular distribution of the total hadron momentum in the decay of a polarized tau can be calculated rigorously using perturbative QCD and the operator product expansion. Perturbative QCD corrections to the free quark result $A_\tau = 1/3$ can be expressed as a power series in $\alpha_s(M_\tau)$ and nonperturbative QCD corrections can be expanded systematically in powers of $1/M_\tau^2$. The QCD prediction is $A_\tau = 0.41 \pm 0.02$. In the decay of a high energy tau into hadrons, the value of the hadronic energy distribution $dR_\tau/dz$ evaluated at the maximum hadronic energy fraction $z = 1$ can also be calculated rigorously from QCD.Comment: LateX, 11 pages, no figures, NUHEP-TH-93-

Hard photon production rate of a quark-gluon plasma at finite quark chemical potential

We compute the photon production rate of a quark-gluon plasma (QGP) at finite quark chemical potential $\mu$ using the Braaten-Pisarski method, thus continuing the work of Kapusta, Lichard, and Seibert who did the calculation for $\mu =0$.Comment: 9 pages, revtex, no figures, error in soft part corrected, figures available at ftp://theorie.physik.uni-giessen.de/usr/users/ftp/photon