Large multiplicity fluctuations and saturation effects in onium collisions

This paper studies two related questions in high energy onium-onium scattering: the probability of producing an unusually large number of particles in a collision, where it is found that the cross section for producing a central multiplicity proportional to $k$ should decrease exponentially in $\sqrt{k}$. Secondly, the nature of gluon (dipole) evolution when dipole densities become so high that saturation effects due to dipole-dipole interactions become important: measures of saturation are developed to help understand when saturation becomes important, and further information is obtained by exploiting changes of frame, which interchange unitarity and saturation corrections.Comment: 30 pages LaTeX2e, 11 figures included using epsfig. Compressed postscript of whole paper also available at http://www.hep.phy.cam.ac.uk/theory/papers

OEDIPUS: Onium Evolution, Dipole Interaction and Perturbative Unitarisation Simulation

A Monte Carlo simulation program is presented which can be used to determine the small-$x$ evolution of a heavy onium using Mueller's colour dipole formulation, giving the full distribution of dipoles in rapidity and impact parameter. Routines are also provided which calculate onium-onium scattering amplitudes between individual pairs of onium configurations, making it possible to establish the contribution of multiple pomeron exchange terms to onium-onium scattering (the unitarisation corrections).Comment: 21 pages LaTeX2e. Postscript available from http://www.hep.phy.cam.ac.uk/theory/papers and program available from ftp://axpf.hep.phy.cam.ac.uk/pub/theory/oedipus.tar.g

Ultra-High Energy Neutrinos: A Review of Theoretical and Phenomenological Issues

We review the phenomenology of ultra-high energy (UHE) neutrino detection. The motivations for looking for such neutrinos stemming from observational evidence and the potential for new physics discoveries are enumerated, and their expected sources and fluxes are given. Cross-sections with nucleons all the way upto neutrino energies of 10^20 eV, and the attenuation of the fluxes in the earth are discussed. Finally, sample event-rates for existing and future Water/Ice Cerenkov detectors are provided.Comment: Invited Talk at Neutrino 2000, XIX International Conference on Neutrino Physics and Astrophysics, Sudbury, Canada, June 16-21, 2000. 12 pages. References updated; minor changes to tex

Studies of Unitarity at Small~xx Using the Dipole Formulation

Mueller's dipole formulation of onium-onium scattering is used to study unitarity corrections to the BFKL power growth at high energies. After a short discussion of the spatial distribution of colour dipoles in a heavy quarkonium and the associated fluctuations, results are presented showing that the one and two-pomeron contributions to the total cross section are the same at a rapidity $Y \simeq 14$. Above this rapidity the large fluctuations in the onium wave function cause the multiple pomeron series to diverge. Resumming the series allows one to show that unitarity corrections set in gradually for the total cross section, which is dominated by rare, large, configurations of the onia. The elastic cross section comes mostly from much smaller impact parameters and has significant unitarity corrections starting at a rapidity $Y\simeq 8$.Comment: 30 pages LaTeX2e with 12 figures as appended as uuencoded eps. Uses epsfig. Postscript file for complete paper available from http://www.hep.phy.cam.ac.uk/theory/papers/index.htm

Instanton-induced Effects in QCD High-Energy Scattering

We evaluate a number of new instanton-induced phenomena in QCD, starting with static dipole-dipole potentials, and proceeding to quark-quark and dipole-dipole scattering at high energy. We use a non-perturbative formulation of the scattering amplitude in terms of a correlator of two Wilson-lines (quarks) or Wilson-loops (dipoles) and analyze the Euclidean amplitudes with both perturbative gluons and instantons. The results are analytically continued to Minkowski geometry, by interpreting the angle between the Wilson lines as rapidity. We discuss the relevance of our results for the phenomenology of near-forward hadronic processes at high energy, especially for processes with multiple color exchanges

The Gluon Impact Factors

We calculate in the next-to-leading approximation the non-forward gluon impact factors for arbitrary color state in the $t$-channel. In the case of the octet state we check the so-called "second bootstrap condition" for the gluon Reggeization in QCD, using the integral representation for the impact factors. The condition is fulfilled in the general case of an arbitrary space-time dimension and massive quark flavors for both helicity conserving and non-conserving parts.Comment: 32 pages, LaTeX, 1 EPS figure, uses epsf.sty and axodraw.st

NLO BFKL Equation, Running Coupling and Renormalization Scales

I examine the solution of the BFKL equation with NLO corrections relevant for deep inelastic scattering. Particular emphasis is placed on the part played by the running of the coupling. It is shown that the solution factorizes into a part describing the evolution in Q^2, and a constant part describing the input distribution. The latter is infrared dominated, being described by a coupling which grows as x decreases, and thus being contaminated by infrared renormalons. Hence, for this part we agree with previous assertions that predictive power breaks down for small enough x at any Q^2. However, the former is ultraviolet dominated, being described by a coupling which falls like 1/(\ln(Q^2/\Lambda^2) + A(\bar\alpha_s(Q^2)\ln(1/x))^1/2)with decreasing x, and thus is perturbatively calculable at all x. Therefore, although the BFKL equation is unable to predict the input for a structure function for small x, it is able to predict its evolution in Q^2, as we would expect from the factorization theory. The evolution at small x has no true powerlike behaviour due to the fall of the coupling, but does have significant differences from that predicted from a standard NLO in alpha_s treatment. Application of the resummed splitting functions with the appropriate coupling constant to an analysis of data, i.e. a global fit, is very successful.Comment: Tex file, including a modification of Harvmac, 46 pages, 8 figures as .ps files. Correction of typos, updating of references, very minor corrections to text and fig.

Probing Nucleon Spin Structure

One of the important questions in high energy physics is the relation of quark and gluon spin to that of the nucleons which they comprise. Polarization experiments provide a mechanism to probe the spin properties of elementary particles and provide crucial tests of Quantum Chromodynamics (QCD). The theoretical and experimental status of this fundamental question will be reviewed in this paper.Comment: 65 pages, 3 Postscript figures, LaTeX. To be published in "Progress in Particle and Nuclear Physics

Particle Production in a Hadron Collider Rapidity Gap: The Higgs Case

Production of rare particles within rapidity gaps has been proposed as a background-free signal for the detection of new physics at hadron colliders. No complete formalism accounts for such processes yet. We study a simple lowest-order QCD model for their description. Concentrating on Higgs production, we show that the calculation of the cross section pp -> pp H can be embedded into existing models which successfully account for diffractive data. We extend those models to take into account single and double diffractive cross sections pp -> H X1 X2 with a gap between the fragments X1 and X2. Using conservative scenarios, we evaluate the uncertainties in our calculation, and study the dependence of the cross section on the gap width. We predict that Higgs production within a gap of 4 units of rapidity is about 0.3 pb for a 100 GeV Higgs at the Tevatron, and almost 2 pb for a 400 GeV Higgs within a gap of 6 units at the LHC with 14 TeV beams.Comment: LaTeX file, 30 pages, 12 figures and psfig.sty included in a second uufile. The full ready-to-print postscript manuscript is available by anonymous ftp at ftp://lpsvsh.lps.umontreal.ca/ in theorie/hep-ph/Rapidity.ps (it's a VAX so you'll have to use the format theorie.hep-ph if you change by more than one directory at a time

A Consistent Next-to-Leading-Order QCD Calculation of Hadronic Diffractive Scattering

We calculate the order alpha_s^2 and order alpha_s^3 QCD contributions to colour-singlet exchange in the leading log s approximation. We implement the resulting amplitude at the hadronic level and thus construct the QCD pomeron and odderon to this order of perturbation theory. We show that the structure of the hadronic form factors provides a natural mechanism through which the odderon gets suppressed at t=0 whereas it dominates the elastic cross section at large t. We also demonstrate that the inclusion of nonperturbative effects through a modification of the gluon propagator accelerates greatly the convergence of the log s expansion, although not enough to provide agreement with the data.Comment: 26 pages, McGill/93-2