Diffraction at HERA and the Confinement Problem

We discuss HERA data on the high energy behavior of the total gamma*p cross section and on diffraction in deep inelastic scattering. We outline their novelty in comparison with diffraction in high energy hadron hadron scattering. As a physical picture, we propose an interpretation in terms of QCD radiation at small and large distances: a careful study of the transition between the two extremes represents a new approach to the QCD confinement problem.Comment: 30 pages. Some references adde

Quark-Antiquark-Gluon Jets in DIS Diffractive Dissociation

We study the diffractive production of $q\bar{q}g$ jets with large transverse momenta in the region of large diffractive masses (small $\beta$). Cross sections for transverse and longitudinal photons are obtained in the leading log 1/x_{\fP} and log $1/\beta$ approximation, keeping all powers in log $k_t^2/Q^2$. We perform a numerical study and illustrate the angular distribution of the three jets. We also estimate the integrated diffractive three jet cross section and compare with the dijet cross section obtained before.Comment: 28 pages (Latex), 20 figures (Postscript

Massive c\bar c g - Calculation in Diffractive DIS and Diffractive D^* - Production at HERA

We calculate the cross section for $c\bar{c}g$-production in diffractive DIS with finite quark masses at zero momentum transfer $t$. The calculation is done in the leading log(1/$x_{P}$) approximation and is valid in the region of high diffractive masses $M$ (small $\beta$). We apply our cross section formula including both $c{\bar c}$- and $c\bar{c}g$ in a Monte Carlo simulation to diffractive $D^{*\pm}$ meson production at HERA. We compare our predictions to results of H1 using three parameterizations for the unintegrated gluon density.Comment: 11 pages, 5 figure

The BFKL-Pomeron In Deep Inelastic Diffractive Dissociation near t=0

The small-$t$ behaviour of the deep inelastic diffractive dissociation cross section in the triple Regge region is investigated, using the BFKL approximation in perturbative QCD. We show that the cross section is finite at $t=0$, but the diffusion in $\ln{k_t^2}$ leads to a large contribution of small momenta at the triple Pomeron vertex. We study the dependence upon the total energy and the invariant mass. At $t=0$, there is a decoupling of the three BFKL singularities which is a consequence of the conservation of the conformal dimension. For large invariant masses, the four gluon state in the upper t-channel plays an important role and cannot be neglected.Comment: 43 pages, LaTex , 11 ps-figures (uuencoded) appende

Unconditional stability of semi-implicit discretizations of singular flows

A popular and efficient discretization of evolutions involving the singular $p$-Laplace operator is based on a factorization of the differential operator into a linear part which is treated implicitly and a regularized singular factor which is treated explicitly. It is shown that an unconditional energy stability property for this semi-implicit time stepping strategy holds. Related error estimates depend critically on a required regularization parameter. Numerical experiments reveal reduced experimental convergence rates for smaller regularization parameters and thereby confirm that this dependence cannot be avoided in general.Comment: 21 pages, 8 figure