Hadron masses and power corrections to event shapes

It is widely believed that hadronisation leads to 1/Q corrections to e+e- event shapes. We show that there are further corrections, proportional to (ln Q)^A/Q with A=4C_A/beta_0~=1.6, associated with hadron masses and whose relative normalisations can be calculated from one observable to another. At today's energies these extra corrections can be of the same order of magnitude as `traditional' 1/Q corrections. They fall into two classes: universal and non-universal. The latter can be eliminated by suitable redefinitions of the observables

Geometric Scaling and QCD Dynamics in DIS

DIS data from HERA show a striking regularity as \sigma^{\gamma^* p} is a function of the ratio \tau=Q^2/Q_s^2(x) only. The scaling function shows a break at \tau ~ 1, which has been taken as an indication for saturation. However, besides saturation also the transition between dominance of k_t-ordered (DGLAP) and k_t-non-ordered (BFKL) evolution contributes to a break around this value of \tau, as well as the suppression for small Q^2 due to finite quark masses and confinement. In this paper we use a dipole cascade model based on Mueller's dipole model, which also includes energy conservation and pomeron mergins, to investigate the contributions of these different effects to the scaling behaviour. As a result we predict that the scaling function for \tau 1 GeV^2 become available. We also investigate the scaling properties of the charm contribution and the impact parameter dependence of the saturation scale.Comment: references added, figures 2, 7 and 8 updated v3: reference added, some misprints correcte

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

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

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

Energy Conservation and Saturation in Small-x Evolution

Important corrections to BFKL evolution are obtained from non-leading contributions and from non-linear effects due to unitarisation or saturation. It has been difficult to estimate the relative importance of these effects, as NLO effects are most easily accounted for in momentum space while unitarisation and saturation are easier in transverse coordinate space. An essential component of the NLO contributions is due to energy conservation effects, and in this paper we present a model for implementing such effects together with saturation in Mueller's dipole evolution formalism. We find that energy conservation severely dampens the small-x rise of the gluon density and, as a consequence, the onset of saturation is delayed. Using a simple model for the proton we obtain a reasonable qualitative description of the x-dependence of F2 at low Q^2 as measured at HERA even without saturation effects. We also give qualitative descriptions of the energy dependence of the cross section for gamma*-gamma* and gamma*-nucleus scattering

Accurate QCD predictions for heavy-quark jets at the Tevatron and LHC

Heavy-quark jets are important in many of today's collider studies and searches, yet predictions for them are subject to much larger uncertainties than for light jets. This is because of strong enhancements in higher orders from large logarithms, ln(p_t/m_Q). We propose a new definition of heavy-quark jets, which is free of final-state logarithms to all orders and such that all initial-state collinear logarithms can be resummed into the heavy-quark parton distributions. Heavy-jet spectra can then be calculated in the massless approximation, which is simpler than a massive calculation and reduces the theoretical uncertainties by a factor of three. This provides the first ever accurate predictions for inclusive b- and c-jets, and the latter have significant discriminatory power for the intrinsic charm content of the proton. The techniques introduced here could be used to obtain heavy-flavour jet results from existing massless next-to-leading order calculations for a wide range of processes. We also discuss the experimental applicability of our flavoured jet definition.Comment: 22 pages, 7 figure

Revisiting parton evolution and the large-x limit

This remark is part of an ongoing project to simplify the structure of the multi-loop anomalous dimensions for parton distributions and fragmentation functions. It answers the call for a "structural explanation" of a "very suggestive" relation found by Moch, Vermaseren and Vogt in the context of the x->1 behaviour of three-loop DIS anomalous dimensions. It also highlights further structure that remains to be fully explained.Comment: 6 pages, v2 corrects misprints and contains an additional referenc

Diffractive Excitation in DIS and pp Collisions

We have in earlier papers presented an extension of Mueller's dipole cascade model, which includes subleading effects from energy conservation and running coupling as well as colour suppressed effects from pomeron loops via a ``dipole swing''. The model was applied to describe the total cross sections in pp and gamma*p collisions. In this paper we present a number of improvements of the model, in particular related to the confinement mechanism. A consistent treatment of dipole evolution and dipole--dipole interactions is achieved by replacing the infinite range Coulomb potential by a screened potential, which further improves the frame-independence of the model. We then apply the model to elastic scattering and diffractive excitation, where we specifically study the effects of different sources for fluctuations. In our formalism we can take into account contributions from all different sources, from the dipole cascade evolution, the dipole--dipole scattering, from the impact-parameter dependence, and from the initial photon and proton wavefunctions. Good agreement is obtained with data from the Tevatron and from HERA, and we also present some predictions for the LHC.Comment: correction of titl

Power corrections and the interplay between perturbative and non-perturbative phenomena

We discuss the issue of interplay between perturbative and non-perturbative phenomena for power corrections to e+e- event shapes.Comment: 7 pages, to appear in the proceedings of QCD99 Euroconference, Montpellier, July 199