On the critical point of the Random Walk Pinning Model in dimension d=3

We consider the Random Walk Pinning Model studied in [3,2]: this is a random walk X on Z^d, whose law is modified by the exponential of \beta times L_N(X,Y), the collision local time up to time N with the (quenched) trajectory Y of another d-dimensional random walk. If \beta exceeds a certain critical value \beta_c, the two walks stick together for typical Y realizations (localized phase). A natural question is whether the disorder is relevant or not, that is whether the quenched and annealed systems have the same critical behavior. Birkner and Sun proved that \beta_c coincides with the critical point of the annealed Random Walk Pinning Model if the space dimension is d=1 or d=2, and that it differs from it in dimension d\ge4 (for d\ge 5, the result was proven also in [2]). Here, we consider the open case of the marginal dimension d=3, and we prove non-coincidence of the critical points.Comment: 23 pages; v2: added reference [4], where a result similar to Th. 2.8 is proven independently for the continuous-time mode

Bootstrapping One-Loop QCD Amplitudes

We review the recently developed bootstrap method for the computation of high-multiplicity QCD amplitudes at one loop. We illustrate the general algorithm step by step with a six-point example. The method combines (generalized) unitarity with on-shell recursion relations to determine the not cut-constructible, rational terms of these amplitudes. Our bootstrap approach works for arbitrary configurations of gluon helicities and arbitrary numbers of external legs.Comment: 18 pages, 9 figures; extended version of talks given at the 7th Workshop On Continuous Advances In QCD, 11-14 May 2006, Minneapolis, Minnesota; at SUSY06: 14th International Conference On Supersymmetry And The Unification Of Fundamental Interactions, 12-17 Jun 2006, Irvine, California; at the LoopFest V: Radiative Corrections For The International Linear Collider: Multi-Loops And Multi-Legs, 19-21 Jun 2006, SLAC, Menlo Park, California; and at the Vancouver Linear Colliders Workshop (ALCPG 2006), 19-22 Jul 2006, Vancouver, British Columbi

Power Corrections to e+e- Dijet Event Shapes

We discuss a class of event shapes for e+e- dijet events that include the thrust as a special case. Large logarithmic corrections to the corresponding cross sections can be resummed to all logarithmic orders at leading power. However, irrespective of the order up to which the perturbative expansion is calculated, it has to be supplemented by nonperturbative corrections due to its at best asymptotic nature. We find that the leading power corrections are universal for the class of event shapes discussed here. Based on these findings, we provide sample numerical predictions for the distributions of the new event shapes.Comment: 3 pages, 1 figure; presented by C.F. Berger at the International Europhysics Conference on High-Energy Physics (HEP 2003), Aachen, Germany, 17-23 July 200

Hard exclusive photoproduction of Φ\Phi and J/ΨJ/\Psi mesons

We present predictions for differential cross sections for the reaction $\gamma p \to \Phi p$ and give an outlook to which extent our calculations may be generalized to the photoproduction of $J/\Psi$ mesons. Our results are obtained within perturbative QCD treating the proton as a quark-diquark system.Comment: 4 pages, 1 figure, uses Elsevier style espcrc1.st

Effective Polynomial Ballisticity Condition for Random Walk in Random Environment

The conditions $(T)_\gamma,$ $\gamma \in (0,1),$ which have been introduced by Sznitman in 2002, have had a significant impact on research in random walk in random environment. Among others, these conditions entail a ballistic behaviour as well as an invariance principle. They require the stretched exponential decay of certain slab exit probabilities for the random walk under the averaged measure and are asymptotic in nature. The main goal of this paper is to show that in all relevant dimensions (i.e., $d \ge 2$), in order to establish the conditions $(T)_\gamma$, it is actually enough to check a corresponding condition $(\mathcal{P})$ of polynomial type. In addition to only requiring an a priori weaker decay of the corresponding slab exit probabilities than $(T)_\gamma,$ another advantage of the condition $(\mathcal{P})$ is that it is effective in the sense that it can be checked on finite boxes. In particular, this extends the conjectured equivalence of the conditions $(T)_\gamma,$ $\gamma \in (0,1),$ to all relevant dimensions.Comment: 21 pages, 2 figures; followed referee's and readers' comments, corrected minor errors; to appear in Comm. Pure Appl. Mat

Exclusive Decuplet-Baryon Pair Production in Two-Photon Collisions

This work extends our previous studies of two-photon annihilation into baryon-antibaryon pairs from spin-1/2 octet to spin-3/2 decuplet baryons. Our approach is based on perturbative QCD and treats baryons as quark-diquark systems. Using the same model parameters as in our previous work, supplemented by QCD sum-rule results for decuplet baryon wave functions, we are able to give absolute predictions for decuplet baryon cross sections without introducing new parameters. We find that the $\Delta^{++}$ cross section is of the same order of magnitude as the proton cross section, well within experimental bounds.Comment: 14 pages, 2 figure