Polarized Structure Functions in QCD

We review the nucleon's polarized structure functions from the viewpoint of gauge invariant, nonlocal light-cone operators in QCD. We discuss a systematic treatment of the polarized structure functions and the corresponding parton distribution functions. We also address a question of what information on the structure of Nature will be obtained from the future polarized experiments. From this point of view, we will discuss the W gamma production at RHIC polarized experiment.Comment: 8 pages, 5 Postscript figures, Invited talk presented at the Workshop on Lepton Scattering, Hadrons and QCD, Adelaide, March 26 -- April 6, 200

Electroweak Sudakov at two loop level

We investigate the Sudakov double logarithmic corrections to the form factor of fermion in the SU(2)XU(1) electroweak theory. We adopt the familiar Feynman gauge and present explicit calculations at the two loop level. We show that the leading logarithmic corrections coming from the infrared singularities are consistent with the "postulated" exponentiated electroweak Sudakov form factor. The similarities and differences in the "soft" physics between the electroweak theory and the unbroken non-abelian gauge theory (QCD) will be clarified.Comment: 8 pages, 14 figure

Transversely Polarized Drell-Yan Process and Soft Gluon Resummation in QCD

We calculate the transverse-momentum $Q_T$ spectrum of the dilepton in the transversely polarized Drell-Yan process on the basis of the factorization theorem in QCD. We take into account universal logarithmically enhanced corrections in edge region of phase space by resumming multiple soft-gluon emissions to all orders in the small $Q_T$ region.Comment: 84 pages, 5 figures, Revised version published in Prog.Theor.Phy

Revisiting W gamma production at RHIC

We discuss W gamma production in polarized p p collisions at RHIC energy. We point out that the RHIC collider has two advantages over other hadron colliders to measure the characteristic feature of W gamma production: (1) the RHIC energy is not so high and (2) the polarized beams are available. We calculate the tree level cross section for W gamma production using a generic spin basis for W and discuss both the angular dependence and spin correlation.Comment: 14 pages, 15 Postscript figure

Galaxies Inside Stromgren Spheres of Luminous Quasars at z>6: Detection of The First Galaxies

The intrinsic Lyman-alpha emission lines of normal galaxies before reionization are much absorbed by the damping wing of the Gunn-Peterson trough, rendering their direct detection nearly impossible, if their intrinsic line widths are less than ~100km/s. High redshift luminous quasars prior to the completion of cosmological reionization at z~6, on the other hand, are capable of producing large HII regions around them (Stromgren spheres) to allow their intrinsic Lyman-alpha emission lines to be transmitted without overwhelming absorption (Cen & Haiman 2000). We suggest that targeted observations at the Stromgren spheres of known luminous quasars at z >= 6 would be able to detect Lyman-alpha emission lines of galaxies inside the Stromgren spheres largely unattenuated. A tunable, very narrowband filter of \Delta\lambda\over \lambda ~ 0.1% or a narrowband filter of \Delta\lambda\over \lambda ~1% with follow-up spectroscopic identifications will be required. Such observations could directly observe the sources of cosmological reionization including possibly the Pop III galaxies at z=6-20 by JWST. Possible applications include determinations of the ionization state of the intergalactic medium, the sizes of the Stromgren spheres, the ages of the quasars, the luminosity function of high redshift galaxies and its evolution, the spatial distribution of galaxies and its evolution, the biased distribution of galaxies around quasars and the anisotropy of quasar emission. Observations using Keck-class telescopes may already be made to enable a differentiation between a fully neutral and a 10% neutral intergalactic medium at z>6.Comment: Submitted to ApJ Letters, 10 page

The Major Sources of the Cosmic Reionizing Background at z ~ 6

In this paper, we address which sources contributed most of the reionizing photons. Our argument assumes that the reionization ended around z ~ 6 and that it was a relatively quick process, i.e., that there was a non-negligible fraction of neutral hydrogen in the Universe at somewhat earlier epochs. Starting from our earlier estimate of the luminosity function (LF) of galaxies at z ~ 6, we quantitatively show that the major sources of reionization are most likely galaxies with L < L*. Our approach allows us to put stronger constraints to the LF of galaxies at z ~ 6. To have the Universe completely ionized at this redshift, the faint-end slope of the LF should be steeper than $\alpha=-1.6$, which is the value measured at lower redshifts (z ~ 3), unless either the normalization (Phi*) of the LF or the clumping factor of the ionized hydrogen has been significantly underestimated. If Phi* is actually lower than what we assumed by a factor of two, a steep slope close to $\alpha=-2.0$ is required. Our LF predicts a total of 50 -- 80 z ~ 6 galaxies in the HST Ultra Deep Field (UDF) to a depth of AB=28.4 mag, which can be used to constraint both Phi* and $\alpha$. We conclude that the least luminous galaxies existing at this redshift should reach as low as some critical luminosity in order to accumulate the entire reionizing photon budget. On the other hand, the existence of significant amounts of neutral hydrogen at slightly earlier epochs, e.g. z ~ 7, requires that the least luminous galaxies should not be fainter than another critical value (i.e., the LF should cut-off at this point).Comment: ApJL in press (Jan 1, 2004 issue

Constraints on First-Light Ionizing Sources from Optical Depth of the Cosmic Microwave Background

We examine the constraints on high-redshift star formation, ultraviolet and X-ray pre-ionization, and the epoch of reionization at redshift z_r, inferred from the recent WMAP-5 measurement, tau_e = 0.084 +/- 0.016, of the electron scattering optical depth of the cosmic microwave background (CMB). Half of this scattering can be accounted for by the optical depth, tau_e = 0.04-0.05, of a fully ionized intergalactic medium (IGM) at z < z_GP = 6-7, consistent with Gunn-Peterson absorption in neutral hydrogen. The required additional optical depth, Delta-tau_e = 0.03 +/- 0.02 at z > z_GP, constrains the ionizing contributions of first light sources. WMAP-5 also measured a significant increase in small-scale power, which lowers the required efficiency of star formation and ionization from mini-halos. Early massive stars (UV radiation) and black holes (X-rays) can produce a partially ionized IGM, adding to the residual electrons left from incomplete recombination. Inaccuracies in computing the ionization history, x_e(z), and degeneracies in cosmological parameters (Omega_m, Omega_b, sigma_8, n_s) add systematic uncertainty to the measurement and modeling of $\tau_e$. From the additional optical depth from sources at z > z_GP, we limit the star-formation efficiency, the rate of ionizing photon production for Pop III and Pop II stars, and the photon escape fraction, using standard histories of baryon collapse, minihalo star formation, and black-hole X-ray preionization.Comment: Greatly revised version, based on WMAP-5 results and new models. Accepted for ApJ (2008

Extension of holomorphic functions and cohomology classes from non reduced analytic subvarieties

The goal of this survey is to describe some recent results concerning the L 2 extension of holomorphic sections or cohomology classes with values in vector bundles satisfying weak semi-positivity properties. The results presented here are generalized versions of the Ohsawa-Takegoshi extension theorem, and borrow many techniques from the long series of papers by T. Ohsawa. The recent achievement that we want to point out is that the surjectivity property holds true for restriction morphisms to non necessarily reduced subvarieties, provided these are defined as zero varieties of multiplier ideal sheaves. The new idea involved to approach the existence problem is to make use of L 2 approximation in the Bochner-Kodaira technique. The extension results hold under curvature conditions that look pretty optimal. However, a major unsolved problem is to obtain natural (and hopefully best possible) L 2 estimates for the extension in the case of non reduced subvarieties -- the case when Y has singularities or several irreducible components is also a substantial issue.Comment: arXiv admin note: text overlap with arXiv:1703.00292, arXiv:1510.0523

An Overdensity of Lyman-alpha Emitters at Redshift z=5.7 near the Hubble Ultra Deep Field

We have identified an obvious and strong large scale structure at redshift z=5.75 in a wide (31 by 33 arcminute) field, narrowband survey of the Chandra Deep Field South region. This structure is traced by 17 candidate Lyman alpha emitters, among which 12 are found in an 823nm filter (corresponding to Lyman alpha at z=5.77 +- 0.03) and 5 in an 815nm image (z=5.70 +- 0.03). The Lyman alpha emitters in both redshift bins are concentrated in one quadrant of the field. The Hubble Ultra Deep Field, Chandra Deep Field South, and GOODS-South fields all lie near the edge of this overdense region. Our results are consistent with reports of an overdensity in the UDF region at z=5.9. This structure is the highest redshift overdensity found so far.Comment: 12 pages, AASTeX. Submitted to ApJ Letters, and revised in response to referee's comment