Dimensional renormalization: ladders to rainbows

Renormalization factors are most easily extracted by going to the massless limit of the quantum field theory and retaining only a single momentum scale. We derive factors and renormalized Green functions to all orders in perturbation theory for rainbow graphs and vertex (or scattering diagrams) at zero momentum transfer, in the context of dimensional renormalization, and we prove that the correct anomalous dimensions for those processes emerge in the limit D -> 4.Comment: RevTeX, no figure

Singlet Polarization Functions at O(\alpha_s^2)

We consider the three-loop singlet diagrams induced by axial-vector, scalar and pseudo-scalar currents. Expansions for small and large external momentum $q$ are presented. They are used in combination with conformal mapping and Pad\'e approximations in order to arrive at results for the polarization functions valid for all $q^2$. Results are presented for the imaginary parts which are directly related to physical quantities like the production of top quarks or the decay of scalar or pseudo-scalar Higgs bosons.Comment: LaTeX, 15 pages, 10 figures included as ps-files. The complete paper is also available via anonymous ftp at ftp://ttpux2.physik.uni-karlsruhe.de/ , or via www at http://www-ttp.physik.uni-karlsruhe.de/cgi-bin/preprints

Virtual Top-Quark Effects on the H->bb-bar Decay at Next-to-Leading Order in QCD

By means of a heavy-top-quark effective Lagrangian, we calculate the three-loop corrections of O(alpha_s^2 G_F M_t^2) to the H->bb-bar partial decay width of the standard-model Higgs boson with intermediate mass M_H<<2M_t. We take advantage of a soft-Higgs theorem to construct the relevant coefficient functions. We present our result both in the MS-bar and on-shell schemes of mass renormalization. The MS-bar formulation turns out to be favourable with regard to the convergence behaviour. We also test a recent idea concerning the naive non-abelianization of QCD.Comment: 8 pages (Latex), 5 figures (Postscript

Cloning Hubble Deep Fields I: A Model-Independent Measurement of Galaxy Evolution

We present a model-independent method of quantifying galaxy evolution in high-resolution images, which we apply to the Hubble Deep Field (HDF). Our procedure is to k-correct all pixels belonging to the images of a complete set of bright galaxies and then to replicate each galaxy image to higher redshift by the product of its space density, 1/V_{max}, and the cosmological volume. The set of bright galaxies is itself selected from the HDF, because presently the HDF provides the highest quality UV images of a redshift-complete sample of galaxies (31 galaxies with I<21.9, \bar{z}=0.5, and for which V/V_{max} is spread fairly). These galaxies are bright enough to permit accurate pixel-by-pixel k-corrections into the restframe UV (\sim 2000 A). We match the shot noise, spatial sampling and PSF smoothing of the HDF data, resulting in entirely empirical and parameter-free ``no-evolution'' deep fields of galaxies for direct comparison with the HDF. In addition, the overcounting rate and the level of incompleteness can be accurately quantified by this procedure. We obtain the following results. Faint HDF galaxies (I>24) are much smaller, more numerous, and less regular than our ``no-evolution'' extrapolation, for any interesting geometry. A higher proportion of HDF galaxies ``dropout'' in both U and B, indicating that some galaxies were brighter at higher redshifts than our ``cloned'' z\sim0.5 population.Comment: 51 pages, 23 figures, replacement includes figures not previously include

Detection of Evolved High-Redshift Galaxies in Deep NICMOS/VLT Images

A substantial population of high redshift early-type galaxies is detected in very deep UBVRIJHK images towards the HDF-South. Four elliptical profile galaxies are identified in the redshift range z=1-2, all with very red SEDs, implying ages of >2 Gyrs for standard passive evolution. We also find later type IR-luminous galaxies at similarly high redshift, (10 objects with z>1, H1 Gyr. The number and luminosity-densities of these galaxies are comparable with the local E/SO-Sbc populations for \Omega_m>0.2, and in the absence of a significant cosmological constant, we infer that the major fraction of luminous Hubble-sequence galaxies have evolved little since z~2. A highly complete photometric redshift distribution is constructed to H=25 (69 galaxies) showing a broad spread of redshift, peaking at z~1.5, in reasonable agreement with some analyses of the HDF. Five `dropout' galaxies are detected at z~3.8, which are compact in the IR, ~0.5 kpc/h at rest 3500\AA. No example of a blue IR luminous elliptical is found, restricting the star-formation epoch of ellipticals to z>10 for a standard IMF and modest extinction.Comment: 7 pages, 3 figures, accepted for publication in Astrophysical Journal Letters, discussion of clustering added, color image available at http://astro.berkeley.edu/~tjb/nic3.htm

The redshift of the gravitationally lensed radio source PKS1830-211

We report on the spectroscopic identification and the long awaited redshift measurement of the heavily obscured, gravitationally lensed radio source PKS 1830-211, which was first observed as a radio Einstein ring. The NE component of the doubly imaged core is identified, in our infrared spectrum covering the wavelength range 1.5-2.5 microns, as an impressively reddened quasar at z=2.507. Our redshift measurement, together with the recently measured time delay (Lovell et al.), means that we are a step closer to determining the Hubble constant from this lens. Converting the time delay into the Hubble constant by using existing models leads to high values for the Hubble constant. Since the lensing galaxy lies very close to the center of the lensed ring, improving the error bars on the Hubble constant will require not only a more precise time delay measurement, but also very precise astrometry of the whole system.Comment: 11 pages, 2 figures, Accepted ApJ

Lattice Green functions in all dimensions

We give a systematic treatment of lattice Green functions (LGF) on the $d$-dimensional diamond, simple cubic, body-centred cubic and face-centred cubic lattices for arbitrary dimensionality $d \ge 2$ for the first three lattices, and for $2 \le d \le 5$ for the hyper-fcc lattice. We show that there is a close connection between the LGF of the $d$-dimensional hypercubic lattice and that of the $(d-1)$-dimensional diamond lattice. We give constant-term formulations of LGFs for all lattices and dimensions. Through a still under-developed connection with Mahler measures, we point out an unexpected connection between the coefficients of the s.c., b.c.c. and diamond LGFs and some Ramanujan-type formulae for $1/\pi.$Comment: 30 page

An Old Cluster in NGC 6822

We present spectroscopy of two clusters in the dwarf irregular galaxy NGC 6822. From these we deduce an age for Cluster VII of 11 Gyr and [Fe/H] = -1.95 +/- 0.15 dex. Cluster VII appears to be an analog of the metal-poor galactic globular clusters. Cluster VI is found to be much younger and more metal rich, with an age of approximately 2 Gyr. Its derived metallicity, [Fe/H], of approximately -1.0 dex is comparable to that of the gas seen today in NGC 6822. The existence of a metal-poor old cluster in NGC 6822 rules out models for the chemical evolution of this galaxy with significant prompt initial enhancement. We find that a star formation rate which is constant with time and is within a factor of two of the present star formation rate can reproduce the two points on the age-metallicity relationship for NGC 6822 over the past 10 Gyr defined by these two clusters.Comment: 8 pages; accepted for publication in A

Matching QCD and HQET heavy--light currents at two loops and beyond

Heavy--light QCD currents are matched with HQET currents at two loops and leading order in $1/m$. A single formula applies to all current matchings. As a by--product, a master formula for the two--loop anomalous dimension of the QCD current $\bar{q}\gamma^{[\mu_1}\ldots\gamma^{\mu_n]}q$ is obtained, yielding a new result for the tensor current. The dependence of matching coefficients on $\gamma_5$ prescriptions is elucidated. Ratios of QCD matrix elements are obtained, independently of the three--loop anomalous dimension of HQET currents. The two--loop coefficient in $f_{{\rm B}^*}/f_{\rm B} =1-2\alpha_{\rm s}(m_b)/3\pi-K_b\alpha_{\rm s}^2/\pi^2 +{\rm O}(\alpha_{\rm s}^3,1/m_b)$ is $$K_b=\frac{83}{12}+\frac{4}{81}\pi^2+\frac{2}{27}\pi^2\log2-\frac19\zeta(3) -\frac{19}{54}N_l+\Delta_c=6.37+\Delta_c$$ with $N_l=4$ light flavours, and a correction, $\Delta_c=0.18\pm0.01$, that takes account of the non--zero ratio $m_c/m_b=0.28\pm0.03$. Fastest apparent convergence would entail $\alpha_{\rm s}(\mu)$ at $\mu=370$~MeV. ``Naive non--abelianization'' of large--$N_l$ results, via $N_l\to N_l-\frac{33}{2}$, gives reasonable approximations to exact two--loop results. All--order results for anomalous dimensions and matching coefficients are obtained at large $\beta_0=11-\frac23N_l$. Consistent cancellation between infrared-- and ultraviolet--renormalon ambiguities is demonstrated.Comment: 26 pages, preprint OUT-4102-52, LaTeX with epsf style option, uuencoded PostScript figure (compressed by gzip) appended at the en

Infrared renormalons and the relations between the Gross-Llewellyn Smith and the Bjorken polarized and unpolarized sum rules

It is demonstrated that the infrared renormalon calculus indicates that the QCD theoretical expressions for the Gross-Llewelln Smith sum rules and for the Bjorken polarized and unpolarized ones contain an identical negative twist-4 1/Q^2 correction. This observation is supported by the consideration of the results of calculations of the corresponding twist-4 matrix elements. Together with the indication of the similarity of perturbative QCD corrections to these three sum rules, this observation leads to simple new theoretical relations between the Gross-Llewellyn Smith and Bjorken polarized and unpolarized sum rules in the energy region $Q^2\geq 1 GeV^2$. The validity of this relation is checked using concrete experimental data for the Gross-Llewellyn Smith and Bjorken polarized sum rulesComment: 7 pages, LaTeX, minor misprints corrected, results unchanged, to be published in JETP Letters, vol 81, issue 1