Discovery of a Kiloparsec Scale X-ray/Radio Jet in the z=4.72 Quasar GB 1428+4217

We report the discovery of a one-sided 3.6" (24 kpc, projected) long jet in the high-redshift, z=4.72, quasar GB 1428+4217 in new Chandra X-ray and VLA radio observations. This is the highest redshift kiloparsec-scale X-ray/radio jet known. Analysis of archival VLBI 2.3 and 8.6 GHz data reveal a faint one-sided jet extending out to ~200 parsecs and aligned to within ~30 deg of the Chandra/VLA emission. The 3.6" distant knot is not detected in an archival HST image, and its broad-band spectral energy distribution is consistent with an origin from inverse Compton scattering of cosmic microwave background photons for the X-rays. Assuming also equipartition between the radiating particles and magnetic field, the implied jet Lorentz factor is ~5. This is similar to the other two known z ~ 4 kpc-scale X-ray jet cases and smaller than typically inferred in lower-redshift cases. Although there are still but a few such very high-redshift quasar X-ray jets known, for an inverse Compton origin, the present data suggest that they are less relativistic on large-scales than their lower-redshift counterparts.Comment: ApJL, accepted, 5 pages, 3 figure

Recent Progress on Perturbative QCD Fragmentation Functions

The recent development of perturbative QCD (PQCD) fragmentation functions has strong impact on quarkonium production. I shall summarize $B_c$ meson production based on these PQCD fragmentation functions, as well as, the highlights of some recent activities on applying these PQCD fragmentation functions to explain anomalous $J/\psi$ and $\psi'$ production at the Tevatron. Finally, I discuss a fragmentation model based on the PQCD fragmentation functions for heavy quarks fragmenting into heavy-light mesons.Comment: 13 pages and 6 Postscript figures, Standard LaTeX. Complete Postscript version can be found at http://www.ph.utexas.edu/~cheung/paper/hopkin/hopkin-hep.ps.gz Invited talk at PASCOS/HOPKINS 1995 Symposium, Johns Hopkins University, Baltimore, Maryland, March 22--25, 199

Chiral differential operators on supermanifolds

The first part of this paper provides a new formulation of chiral differential operators (CDOs) in terms of global geometric quantities. The main result is a recipe to define all sheaves of CDOs on a smooth cs-manifold; its ingredients consist of an affine connection and an even 3-form that trivializes the first Pontrjagin form. With the connection fixed, two suitable 3-forms define isomorphic sheaves of CDOs if and only if their difference is exact. Moreover, conformal structures are in one-to-one correspondence with even 1-forms that trivialize the first Chern form. Applying our work in the first part, we construct what may be called "chiral Dolbeault complexes" of a complex manifold M, and analyze conditions under which these differential vertex superalgebras admit compatible conformal structures or extra gradings (fermion numbers). When M is compact, their cohomology computes (in various cases) the Witten genus, the two-variable elliptic genus and a spin-c version of the Witten genus. This part contains some new results as well as provides a geometric formulation of certain known facts from the study of holomorphic CDOs and sigma models.Comment: much simplified calculations in section 3, making full use of the formulation from section 2; improved notation