Total and diffractive cross sections in enhanced Pomeron scheme

For the first time, a systematic analysis of the high energy behavior of total and diffractive proton-proton cross sections is performed within the Reggeon Field Theory framework, based on the resummation of all significant contributions of enhanced Pomeron diagrams to all orders with respect to the triple-Pomeron coupling. The importance of different classes of enhanced graphs is investigated and it is demonstrated that absorptive corrections due to "net"-like enhanced diagrams and due to Pomeron "loops" are both significant and none of those classes can be neglected at high energies. A comparison with other approaches based on partial resummations of enhanced diagrams is performed. In particular, important differences are found concerning the predicted high energy behavior of total and single high mass diffraction proton-proton cross sections, with our values of $\sigma_{pp}^{{\rm tot}}$ at $\sqrt{s}=14$ TeV being some $25\div40$% higher and with the energy rise of $\sigma_{{\rm HM}}^{{\rm SD}}$ saturating well below the LHC energy. The main causes for those differences are analyzed and explained

Minimal Obstructions for Partial Representations of Interval Graphs

Interval graphs are intersection graphs of closed intervals. A generalization of recognition called partial representation extension was introduced recently. The input gives an interval graph with a partial representation specifying some pre-drawn intervals. We ask whether the remaining intervals can be added to create an extending representation. Two linear-time algorithms are known for solving this problem. In this paper, we characterize the minimal obstructions which make partial representations non-extendible. This generalizes Lekkerkerker and Boland's characterization of the minimal forbidden induced subgraphs of interval graphs. Each minimal obstruction consists of a forbidden induced subgraph together with at most four pre-drawn intervals. A Helly-type result follows: A partial representation is extendible if and only if every quadruple of pre-drawn intervals is extendible by itself. Our characterization leads to a linear-time certifying algorithm for partial representation extension

Diffractive dissociation including pomeron loops in zero transverse dimensions

We have recently studied the QCD pomeron loop evolution equations in zero transverse dimensions [Shoshi:2005pf]. Using the techniques developed in [Shoshi:2005pf] together with the AGK cutting rules, we present a calculation of single, double and central diffractive cross sections (for large diffractive masses and large rapidity gaps) in zero transverse dimensions in which all dominant pomeron loop graphs are consistently summed. We find that the diffractive cross sections unitarise at asymptotic energies and that they are suppressed by powers of alpha_s. Our calculation is expected to expose some of the diffractive physics in hadron-hadron collisions at high energy.Comment: 14 pages, 5 figures; numerous explanations added, matches the published versio

Monte Carlo treatment of hadronic interactions in enhanced Pomeron scheme: I. QGSJET-II model

The construction of a Monte Carlo generator for high energy hadronic and nuclear collisions is discussed in detail. Interactions are treated in the framework of the Reggeon Field Theory, taking into consideration enhanced Pomeron diagrams which are resummed to all orders in the triple-Pomeron coupling. Soft and "semihard" contributions to the underlying parton dynamics are accounted for within the "semihard Pomeron" approach. The structure of cut enhanced diagrams is analyzed; they are regrouped into a number of subclasses characterized by positively defined contributions which define partial weights for various "macro-configurations" of hadronic final states. An iterative procedure for a Monte Carlo generation of the structure of final states is described. The model results for hadronic cross sections and for particle production are compared to experimental data

Model Checking Lower Bounds for Simple Graphs

A well-known result by Frick and Grohe shows that deciding FO logic on trees involves a parameter dependence that is a tower of exponentials. Though this lower bound is tight for Courcelle's theorem, it has been evaded by a series of recent meta-theorems for other graph classes. Here we provide some additional non-elementary lower bound results, which are in some senses stronger. Our goal is to explain common traits in these recent meta-theorems and identify barriers to further progress. More specifically, first, we show that on the class of threshold graphs, and therefore also on any union and complement-closed class, there is no model-checking algorithm with elementary parameter dependence even for FO logic. Second, we show that there is no model-checking algorithm with elementary parameter dependence for MSO logic even restricted to paths (or equivalently to unary strings), unless E=NE. As a corollary, we resolve an open problem on the complexity of MSO model-checking on graphs of bounded max-leaf number. Finally, we look at MSO on the class of colored trees of depth d. We show that, assuming the ETH, for every fixed d>=1 at least d+1 levels of exponentiation are necessary for this problem, thus showing that the (d+1)-fold exponential algorithm recently given by Gajarsk\`{y} and Hlin\u{e}n\`{y} is essentially optimal

Helicity amplitudes for high-energy scattering

We present a prescription to calculate manifestly gauge invariant tree-level helicity amplitudes for arbitrary scattering processes with off-shell initial-state gluons within the kinematics of high-energy scattering. We show that it is equivalent to Lipatov's effective action approach, and show its computational potential through numerical calculations for scattering processes with several particles in the final state.Comment: 27 pages, reference adde