arXiv subjects
Publications and source records attributed to J. R. Forshaw.
We study the high energy behaviour of elastic scattering amplitudes within the leading logarithm approximation. In particular, we cast the amplitude in a form which allows us to study the internal dynamics of the BFKL Pomeron for general momentum transfer. We demonstrate that the momentum transfer acts as an effective infrared cut-off which ensures that the dominant contribution arises from short distance physics.
In this paper we investigate the effect of introducing transverse momentum cutoffs on the BFKL equation. We present solutions in moment space for various models of the BFKL kernel for different combinations of these cutoffs. We improve on previous calculations by using the full BFKL kernel (rather than simplified analytic approximations). The significance of the next-to-leading or ``higher twist'' terms in the kernel are assessed. We find that, while these terms are negligible in the absence of cutoffs, introducing an infra-red cutoff markedly enhances their significance.
The high energy photoproduction of jets is being observed at the ep collider, HERA. It may be that the HERA centre-of-mass energy is sufficiently large that the production of more than one pair of jets per ep collision becomes possible, owing to the large number density of the probed gluons. We construct a Monte Carlo model of such multiparton interactions and study their effects on a wide range of physical observables. The conclusion is that multiple interactions could have very significant effects upon the photoproduction final state and that this would for example make extractions of the gluon density in the photon rather difficult. Total rates for the production of many (i.e. > 2) jets could provide direct evidence for the presence of multiple interactions, although parton showering and hadronization significantly affect low transverse energy jets.
At HERA, the large flux of almost real photons accompanying the electron beam leads to the copious photoproduction of jets. Regions of small momentum fractions $x$ of the incoming particles are explored, where the density of partons is high. As a result, the probability for more than one hard partonic scattering occurring in a single $γp$ collision could become significant. It is well known that this effect modifies the contribution of jets (minijets) to the total cross section. We discuss the latest HERA data on the total $γp$ cross section in this context. The possible effects of multiple hard interactions on event shapes and jet cross sections at HERA have been studied using Monte Carlo programs. We review some of the available results, which in general indicate that the effects of multiple interactions should be significant and may already be manifest in the existing HERA data.
The cross section for elastic vector meson production in photon-proton interactions at large $t$ is considered using the exact analytic solution of the BFKL equation in the azimuthally symmetric $n=0$ limit. We use a non-relativistic model for the vector meson production and find a small shrinkage in the $t$-distribution with increasing energy.
We propose a means of distinguishing between gluon- and quark-seeded systems that may in principle be measured in deep inelastic lepton scattering. As a particular application, we discuss those HERA data on deep inelastic $ep$ scattering which contain a large rapidity gap in the final state. It is standard to interpret these events as being due to ``pomeron" exchange, although precisely what is meant by this remains unclear. Guided by data, we make some rather general statements about these events and in particular we discuss the potential for discerning whether the exchanged colour singlet system can be interpreted as gluonic.
I discuss the theoretical status of the `soft' pomeron and its place in describing generic diffractive processes. The role of perturbative QCD (pQCD) corrections is considered, in particular in the context of quasi-elastic vector meson production at high $Q^2$. In those processes where short distances are dominant, the `hard' (pQCD) pomeron is expected to reveal itself, such a process may well be that of diffractive vector meson production at high-$t$ and I discuss this.
At $e^+e^-$ and $ep$ colliders, the large fluxes of almost on-shell photons accompanying the lepton beams lead to the photoproduction of jets. As the centre-of-mass energy is increased, regions of smaller $x$ in the parton densities are explored and these are regions of high parton density. As a result, the probability for more than one hard partonic scattering occurring in a single $γγ$ or $γp$ collision can become significant. This effect has been simulated using an eikonal prescription combined with the HERWIG Monte Carlo program. The possible effects of multiple hard interactions on event shapes and jet cross sections have been studied in this framework at a range of energies relevant to HERA and LEPII. The results indicate that the effects could be significant.
The unique nature of the photon can be investigated in hitherto unexplored kinematic regions at LEP2. We discuss the theoretical significance of deep inelastic measurements and present a prescription that allows a theoretically and experimentally sensible separation of the so-called `anomalous' and `hadronic' components of the target photon. We perform preliminary studies regarding the ability to reconstruct the $γ^* γ$ CM energy (and hence $x$) and the usefulness of the easier to measure electron structure function.
The diffractive process $γp\to V + X$ (where $V$ is a vector meson and $X$ results from the dissociation of the proton) is studied. In particular, we consider the region of large momentum transfer (i.e. $|t|\ggΛ_{QCD}^2$) and large centre-of-mass (CM) energy, $s$. The asymptotic $(s \to \infty, s/|t|\gg 1$) behaviour is derived from the BFKL equation and compared to that which is obtained in the Born approximation (two-gluon exchange). We also calculate the corrections to the Born graphs by iterating the BFKL kernel numerically. Improved convergence of the BFKL series is found by summing the logarithms which occur when an exchanged gluon goes nearly on shell. Importantly, we find evidence that the asymptotic solution to the BFKL equation is inappropriate over most of the HERA range and we provide more realistic predictions for the cross section. The predicted cross section is not too small and can be measured at HERA, up to momentum transfers $|t| \sim 10$GeV$^2$.
We outline a general method for obtaining the solution to the ($t=0$) BFKL equation in the presence of transverse momentum cutoffs. A lower cutoff allows one to avoid integration over nonperturbative momenta and an upper one is needed from energy-momentum conservation. Our method allows for the inclusion of an arbitrary number of poles in the kernel and is applicable to any input distribution. Taking Mellin transforms, we discuss the effect of introducing cutoffs by considering the singularity structure in the transform space. We present an improved calculation of the small-$x$ slope of the gluon density.
We investigate the coupling of the BFKL-Pomeron to quarks and to colorless states. Special emphasis is given to the effective quark-quark scattering amplitude of Mueller and Tang.
The validity of using QCD perturbation theory to generate dynamically the parton distribution functions of hadrons, starting from a valencelike input at low $Q^2$, is discussed. In particular, we consider the prescription of Barone {\em et al} who evolve from $Q^2 = 0$, and that of Glück {\em et al} who start evolution from $Q^2 \simeq (2Λ_{QCD})^2$.