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-

Fragmentation Functions for Lepton Pairs

We calculate the fragmentation function for a light quark to decay into a lepton pair to leading order in the QCD coupling constant. In the formal definition of the fragmentation function, a QED phase must be included in the eikonal factor to guarantee QED gauge invariance. We find that the longitudinal polarization fraction is a decreasing function of the factorization scale, in accord with the intuitive expectation that the virtual photon should behave more and more like a real photon as the transverse momomentum of the fragmenting quark increases.Comment: 13 pages, 4 figures, normalization corrected, text abbreviate

The Massive Thermal Basketball Diagram

The "basketball diagram" is a three-loop vacuum diagram for a scalar field theory that cannot be expressed in terms of one-loop diagrams. We calculate this diagram for a massive scalar field at nonzero temperature, reducing it to expressions involving three-dimensional integrals that can be easily evaluated numerically. We use this result to calculate the free energy for a massive scalar field with a phi^4 interaction to three-loop order.Comment: 19 pages, 3 figure

Parton Model Calculation of Inclusive Charm Production by a Low-energy Antiproton Beam

The cross section for inclusive charm production by a low-energy antiproton beam is calculated using the parton model and next-to-leading order perturbative QCD. For an antiproton beam with a momentum of 15 GeV, the charm cross section at next-to-leading order in the QCD coupling constant changes by more than an order of magnitude as the charm quark mass is varied from 1.3 to 1.7 GeV. The variations can be reduced by demanding that the same value of the charm quark mass give the measured charm cross sections for fixed-target experiments with a proton beam. The resulting estimate for the charm cross section from a low-energy antiproton beam is large enough to allow the study of charm meson mixing.Comment: 9 pages, 4 figure

Color-Octet Fragmentation and the psi' Surplus at the Tevatron

The production rate of prompt $\psi'$'s at large transverse momentum at the Tevatron is larger than theoretical expectations by about a factor of 30. As a solution to this puzzle, we suggest that the dominant $\psi'$ production mechanism is the fragmentation of a gluon into a $c \bar c$ pair in a pointlike color-octet S-wave state, which subsequently evolves nonperturbatively into a $\psi'$ plus light hadrons. The contribution to the fragmentation function from this process is enhanced by a short-distance factor of $1/\alpha_s^2$ relative to the conventional color-singlet contribution. This may compensate for the suppression by $v^4$, where $v$ is the relative momentum of the charm quark in the $\psi'$. If this is indeed the dominant production mechanism at large $p_T$, then the prompt $\psi'$'s that are observed at the Tevatron should almost always be associated with a jet of light hadrons.Comment: 9 pages, LaTe

Damping Rate of a Yukawa Fermion at Finite Temperature

The damping of a massless fermion coupled to a massless scalar particle at finite temperature is considered using the Braaten-Pisarski resummation technique. First the hard thermal loop diagrams of this theory are extracted and effective Green's functions are constructed. Using these effective Green's functions the damping rate of a soft Yukawa fermion is calculated. This rate provides the most simple example for the damping of a soft particle. To leading order it is proportional to $g^2T$, whereas the one of a hard fermion is of higher order.Comment: 5 pages, REVTEX, postscript figures appended, UGI-94-0

The neutrino emission due to plasmon decay and neutrino luminosity of white dwarfs

One of the effective mechanisms of neutrino energy losses in red giants, presupernovae and in the cores of white dwarfs is the emission of neutrino-antineutrino pairs in the process of plasmon decay. In this paper, we numerically calculate the emissivity due to plasmon decay in a wide range of temperatures (10^7-10^11) K and densities (200-10^14) g cm^-3. Numerical results are approximated by convenient analytical expressions. We also calculate and approximate by analytical expressions the neutrino luminosity of white dwarfs due to plasmon decay, as a function of their mass and internal temperature. This neutrino luminosity depends on the chemical composition of white dwarfs only through the parameter mu_e (the net number of baryons per electron) and is the dominant neutrino luminosity in all white dwarfs at the neutrino cooling stage.Comment: 19 pages, 3 figures, accepted for publication in MNRA

Comment on ``Damping of energetic gluons and quarks in high-temperature QCD''

Burgess and Marini have recently pointed out that the leading contribution to the damping rate of energetic gluons and quarks in the QCD plasma, given by $\gamma=c g^2\ln(1/g)T$, can be obtained by simple arguments obviating the need of a fully resummed perturbation theory as developed by Braaten and Pisarski. Their calculation confirmed previous results of Braaten and Pisarski, but contradicted those proposed by Lebedev and Smilga. While agreeing with the general considerations made by Burgess and Marini, I correct their actual calculation of the damping rates, which is based on a wrong expression for the static limit of the resummed gluon propagator. The effect of this, however, turns out to be cancelled fortuitously by another mistake, so as to leave all of their conclusions unchanged. I also verify the gauge independence of the results, which in the corrected calculation arises in a less obvious manner.Comment: 5 page

Hard Thermal Loops, Gauged WZNW Action and the Energy of Hot Quark-Gluon Plasma

The generating functional for hard thermal loops in QCD is rewritten in terms of a gauged WZNW action by introducing an auxiliary field. This shows in a simple way that the contribution of hard thermal loops to the energy of the quark-gluon plasma is positive.Comment: 9 pages, CU-TP 60