Pion Form Factor Phase, PIon Pion Elasticity and New Electron-Positron Data

New precise data on the low energy electron-positron annihilation into hadrons from Novosibirsk are used to obtain bounds on the elasticity parameter and the difference between the phase of the pion form factor and that of pion pion scatteringComment: 9 pages, 4 figures, submitted to Physics Letters

Colored Spin Systems, BKP Evolution and finite N_c effects

Even within the framework of the leading logarithmic approximation the eigenvalues of the BKP kernel for states of more than three reggeized gluons are unknown in general, contrary to the planar limit case where the problem becomes integrable. We consider a 4-gluon kernel for a finite number of colors and define some simple toy models for the configuration space dynamics, which are directly solvable with group theoretical methods. Then we study the dependence of the spectrum of these models with respect to the number of colors and make comparisons with the large limit case.Comment: 17 pages, 4 figures, references update, to appear on EPJ

Reggeon exchange from gauge/gravity duality

We perform the analysis of quark-antiquark Reggeon exchange in meson-meson scattering, in the framework of the gauge/gravity correspondence in a confining background. On the gauge theory side, Reggeon exchange is described as quark-antiquark exchange in the t channel between fast projectiles. The corresponding amplitude is represented in terms of Wilson loops running along the trajectories of the constituent quarks and antiquarks. The paths of the exchanged fermions are integrated over, while the "spectator" fermions are dealt with in an eikonal approximation. On the gravity side, we follow a previously proposed approach, and we evaluate the Wilson-loop expectation value by making use of gauge/gravity duality for a generic confining gauge theory. The amplitude is obtained in a saddle-point approximation through the determination near the confining horizon of a Euclidean "minimal surface with floating boundaries", i.e., by fixing the trajectories of the exchanged quark and antiquark by means of a minimisation procedure, which involves both area and length terms. After discussing, as a warm-up exercise, a simpler problem on a plane involving a soap film with floating boundaries, we solve the variational problem relevant to Reggeon exchange, in which the basic geometry is that of a helicoid. A compact expression for the Reggeon-exchange amplitude, including the effects of a small fermion mass, is then obtained through analytic continuation from Euclidean to Minkowski space-time. We find in particular a linear Regge trajectory, corresponding to a Regge-pole singularity supplemented by a logarithmic cut induced by the non-zero quark mass. The analytic continuation leads also to companion contributions, corresponding to the convolution of the same Reggeon-exchange amplitude with multiple elastic rescattering interactions between the colliding mesons.Comment: 60+1 pages, 14 figure

The spin dependence of high energy proton scattering

Motivated by the need for an absolute polarimeter to determine the beam polarization for the forthcoming RHIC spin program, we study the spin dependence of the proton-proton elastic scattering amplitudes at high energy and small momentum transfer.We examine experimental evidence for the existence of an asymptotic part of the helicity-flip amplitude phi_5 which is not negligible relative to the largely imaginary average non-flip amplitude phi_+. We discuss theoretical estimates of r_5, essentially the ratio of phi_5 to phi_+, based upon extrapolation of low and medium energy Regge phenomenological results to high energies, models based on a hybrid of perturbative QCD and non-relativistic quark models, and models based on eikonalization techniques. We also apply the model-independent methods of analyticity and unitarity.The preponderence of evidence at available energy indicates that r_5 is small, probably less than 10%. The best available experimental limit comes from Fermilab E704:those data indicate that |r_5|<15%. These bounds are important because rigorous methods allow much larger values. In contradiction to a widely-held prejudice that r_5 decreases with energy, general principles allow it to grow as fast as ln(s) asymptotically, and some models show an even faster growth in the RHIC range. One needs a more precise measurement of r_5 or to bound it to be smaller than 5% in order to use the classical Coulomb-nuclear interference technique for RHIC polarimetry. As part of this study, we demonstrate the surprising result that proton-proton elastic scattering is self-analysing, in the sense that all the helicity amplitudes can, in principle, be determined experimentally at small momentum transfer without a knowledge of the magnitude of the beam and target polarization

Instantons and the infrared behavior of the fermion propagator in the Schwinger Model

Fermion propagator of the Schwinger Model is revisited from the point of view of its infrared behavior. The values of anomalous dimensions are found in arbitrary covariant gauge and in all contributing instanton sectors. In the case of a gauge invariant, but path dependent propagator, the exponential dependence, instead of power law one, is established for the special case when the path is a straight line. The leading behavior is almost identical in any sector, differing only by the slowly varying, algebraic prefactors. The other kind of the gauge invariant function, which is the amplitude of the dressed Dirac fermions, may be reduced, by the appropriate choice of the dressing, to the gauge variant one, if Landau gauge is imposed.Comment: 9 pages, in REVTE

Temporality in ranked models

W zbiorze danych określony jest pewien porządek czasowy dla wybranych obiektów. Poprzez model rangowy rozumiemy taką liniową transformację, która zachowuje w najlepszym możliwym stopniu wiedzę a priori o uporządkowaniu obiektów. W artykule przedstawiono koncepcję budowy modelu rangowego opierając się na minimalizacji wypukłej i odcinkowo-liniowej (CPL) funkcji kryterialnej. Zagadnienie zostało sprowadzone do problemu znalezienia optymalnej hiperpłaszczyzny rozdzielającej zbiory zbudowane z elementów powstałych z różnic arytmetycznych wektorów cech tworzących pary, dla których określony jest porządek czasowy.A known temporal order between selected objects in a data set is given. We assume the ranked model is such a linear transformation, which preserve in the most possible manner the a priori knowledge of the order between objects. The procedure of the ranked models design which is based on the minimisation of the convex and piecewise linear (CPL) criterion functions is presented in the paper. The task of the ranked model design is boiled down to the problem of searching an optimal hyperplane separated the sets constructed on the basis of the elements created from the arithmetic substractions of the vectors - the pairs with the given temporal order

Scheduling based on ranked regression models

Zagadnienia szeregowania zadań pojawiają się między innymi w kontekście problemów realizowalności dużych procesów obliczeniowych i ich optymalizacji. Przy rozstrzyganiu tego typu problemów można wykorzystywać metody regresji rangowej. Do celów konstrukcji modeli regresji rangowej poszczególne zadania obliczeniowe charakteryzowane są poprzez wielowymiarowe wektory zależności. Wektory zależności pozwalają stwierdzić czy określone zadanie może być zrealizowane tylko wtedy, gdy zostaną wcześniej zrealizowane pewne inne zadania. Regresja rangowa obejmuje konstrukcję takich odwzorowań liniowych z wielowymiarowej przestrzeni zalżności na przestrzeń jednowymiarową (linię czasu), która odzwierciedla w możliwie dużym stopniu zależności pomiędzy zadaniami.The issues of scheduling of tasks are found, among other things, in connection with the problems of realizeable of big computing processes and optimisation of them. The ranked regresion methods can be used to determine of this kind of problems. Separate computing tasks are characterized by multidimensional vectors of dependences in order to form the ranked regresion models . The vectors of dependences allow to state whether particular task can be realised only when certain other tasks have realised before. The ranked regresion includes the designing of such linear transformations from the multidimensional space of dependences to unidimensional space (time line), which reflect the dependences beetwen task as well as possible