Double Asymptotic Scaling '96

We review recent HERA data on the structure function F_2 at small x and large Q^2. We show that the salient features of the data are revealed by comparing them to the double asymptotic scaling behaviour which F_2 is predicted to satisfy in perturbative QCD.Comment: 5 pages, LaTeX with espcrc2.sty (included), 11 figures included by epsfi

Determination of alpha_s from F_2^p at HERA

We compute the proton structure function F_2^p at small x and large Q^2 at next-to-leading order in alpha_s(Q^2), including summations of all leading and subleading logarithms of Q^2 and 1/x in a way consistent with momentum conservation. We perform a detailed comparison to the 1993 HERA data, and show that they may be used to determine alpha_s(M_Z^2)=0.120 pm 0.005(exp) pm 0.009(th). The theoretical error is dominated by the renormalization and factorization scheme ambiguities.Comment: 24 pages, TeX with harvmac and epsf, 10 figures in compressed postscript. Final (published) versio

Small x Resummation with Quarks: Deep-Inelastic Scattering

We extend our previous results on small-x resummation in the pure Yang--Mills theory to full QCD with nf quark flavours, with a resummed two-by-two matrix of resummed quark and gluon splitting functions. We also construct the corresponding deep-inelastic coefficient functions, and show how these can be combined with parton densities to give fully resummed deep-inelastic structure functions F_2 and F_L at the next-to-leading logarithmic level. We discuss how this resummation can be performed in different factorization schemes, including the commonly used MSbar scheme. We study the importance of the resummation effects by comparison with fixed-order perturbative results, and we discuss the corresponding renormalization and factorization scale variation uncertainties. We find that for x below 0.01 the resummation effects are comparable in size to the fixed order NNLO corrections, but differ in shape. We finally discuss the phenomenological impact of the small-x resummation, specifically in the extraction of parton distribution from present day experiments and their extrapolation to the kinematics relevant for future colliders such as the LHCComment: 45 pages, 16 figures, plain TeX with harvma

Resummation of Hadroproduction Cross-sections at High Energy

We reconsider the high energy resummation of photoproduction, electroproduction and hadroproduction cross-sections, in the light of recent progress in the resummation of perturbative parton evolution to NLO in logarithms of Q^2 and x. We show in particular that the when the coupling runs the dramatic enhancements seen at fixed coupling, due to infrared singularities in the partonic cross-sections, are substantially reduced, to the extent that they are largely accounted for by the usual NLO and NNLO perturbative corrections. This leads to a novel explanation of the large K-factors commonly found in perturbative calculations of hadroproduction cross-sections. We give numerical estimates of high energy resummation effects for inclusive B-production, inclusive jets, Drell-Yan and vector boson production, along with their rapidity distributions. We find that resummation modifies the B-production cross-section at the LHC by at most 15%, but that the enhancement of gluonic W-production may be as large as 50% at large rapidities.Comment: 49 pages, 25 figures, version to be published in Nucl Phys

Quantitative constraints on the gluon distribution function in the proton from collider isolated-photon data

The impact of isolated-photon data from proton-(anti)proton collisions at RHIC, SppbarS, Tevatron and LHC energies, on the parton distribution functions of the proton is studied using a recently developed Bayesian reweighting method. The impact on the gluon density of the 35 existing isolated-gamma measurements is quantified using next-to-leading order (NLO) perturbative QCD calculations complemented with the NNPDF2.1 parton densities. The NLO predictions are found to describe well most of the datasets from 200 GeV up to 7 TeV centre-of-mass energies. The isolated-photon spectra recently measured at the LHC are precise enough to constrain the gluon distribution and lead to a moderate reduction (up to 20%) of its uncertainties around fractional momenta x~0.02. As a particular case, we show that the improved gluon density reduces the PDF uncertainty for the Higgs boson production cross section in the gluon-fusion channel by more than 20% at the LHC. We conclude that present and future isolated-photon measurements constitute an interesting addition to coming global PDF analyses.Comment: 30 pages, 20 figures. Few minor changes to match the published NPB versio

Unemployment in Latin America and the Caribbean

This study constructs a new data set on unemployment rates in Latin America and the Caribbean and then explores the determinants of unemployment. We compare different countries, finding that unemployment is influenced by the size of the rural population and that the effects of government regulations are generally weak. We also examine large, persistent increases in unemployment over time, finding that they are caused by contractions in aggregate demand. These demand contractions result from either disinflationary monetary policy or the defense of an exchange-rate peg in the face of capital flight. Our evidence supports hysteresis theories in which short-run changes in unemployment influence the natural rate.unemployment, hysteresis, monetary policy, Latin America and theCaribbean.

Asymptotically Free Partons at High Energy

We describe the application of renormalization group improved perturbative QCD to inelastic lepton-hadron scattering at high center-of-mass energy but comparatively low photon virtuality. We construct a high energy factorization theorem which complements the mass factorization theorem used for processes with high virtualities. From it we derive a renormalization group equation which resums all large logarithms at high energy, thereby extending to this regime asymptotic freedom and thus the full range of perturbative computational techniques. We discuss the solution of this equation in various limits, and in particular show that the high energy behaviour of physical cross-sections is consistent with phenomenological expectations and unitarity bounds.Comment: 16 pages, TeX with harvmac, 6 figures in encapsulated postscript, final versio

Resummation of Singlet Parton Evolution at Small x

We propose an improvement of the splitting functions at small x which overcomes the apparent problems encountered by the BFKL approach. We obtain a stable expansion for the x-evolution function chi(M) near M=0 by including in it a sequence of terms derived from the one- and two-loop anomalous dimension gamma. The requirement of momentum conservation is always satisfied. The residual ambiguity on the splitting functions is effectively parameterized in terms of the value of lambda, which fixes the small x asymptotic behaviour x^-lambda of the singlet parton distributions. We derive from this improved evolution function an expansion of the splitting function which leads to good apparent convergence, and to a description of scaling violations valid both at large and small x.Comment: 16 pages, 6 figures, LaTeX with epsfig; final version, to be published in Nucl. Phys. B. A few typos corrected for the recor

Unemployment in Latin America and the Caribbean

This study constructs a new data set on unemployment rates in Latin America and the Caribbean and then explores the determinants of unemployment. We compare different countries, finding that unemployment is influenced by the size of the rural population and that the effects of government regulations are generally weak. We also examine large, persistent increases in unemployment over time, finding that they are caused by contractions in aggregate demand. These demand contractions result from either disinflationary monetary policy or the defense of an exchange-rate peg in the face of capital flight. Our evidence supports hysteresis theories in which short-run changes in unemployment influence the natural rate.

de Branges-Rovnyak spaces: basics and theory

For $S$ a contractive analytic operator-valued function on the unit disk ${\mathbb D}$, de Branges and Rovnyak associate a Hilbert space of analytic functions ${\mathcal H}(S)$ and related extension space ${\mathcal D(S)}$ consisting of pairs of analytic functions on the unit disk ${\mathbb D}$. This survey describes three equivalent formulations (the original geometric de Branges-Rovnyak definition, the Toeplitz operator characterization, and the characterization as a reproducing kernel Hilbert space) of the de Branges-Rovnyak space ${\mathcal H}(S)$, as well as its role as the underlying Hilbert space for the modeling of completely non-isometric Hilbert-space contraction operators. Also examined is the extension of these ideas to handle the modeling of the more general class of completely nonunitary contraction operators, where the more general two-component de Branges-Rovnyak model space ${\mathcal D}(S)$ and associated overlapping spaces play key roles. Connections with other function theory problems and applications are also discussed. More recent applications to a variety of subsequent applications are given in a companion survey article