EXACT ESTIMATES FOR THE RATE OF CONVERGENCE OF THE s-STEP METHOD OF STEEPEST DESCENT

Zhuk, P.F. & Bondarenko, L.N. Ukr Math J (1997) 49: 1912. https://doi.org/10.1007/BF02513070We obtain exact (unimprovable) estimates for the rate of convergence of the s-step method of steepest descent for finding the least (greatest) eigenvalue of a linear bounded self-adjoint operator in a Hilbert space

On The Pomeron at Large 't Hooft Coupling

We begin the process of unitarizing the Pomeron at large 't Hooft coupling. We do so first in the conformal regime, which applies to good accuracy to a number of real and toy problems in QCD. We rewrite the conformal Pomeron in the $J$-plane and transverse position space, and then work out the eikonal approximation to multiple Pomeron exchange. This is done in the context of a more general treatment of the complex $J$-plane and the geometric consequences of conformal invariance. The methods required are direct generalizations of our previous work on single Pomeron exchange and on multiple graviton exchange in AdS space, and should form a starting point for other investigations. We consider unitarity and saturation in the conformal regime, noting elastic and absorptive effects, and exploring where different processes dominate. Our methods extend to confining theories and we briefly consider the Pomeron kernel in this context. Though there is important model dependence that requires detailed consideration, the eikonal approximation indicates that the Froissart bound is generically both satisfied and saturated.Comment: 63 pages, 7 figures; published version: references updated and several typos correcte

Calculation of the ultracold neutron upscattering loss probability in fluid walled storage bottles using experimental measurements of the thermomechanical properties of Fomblin

We present experimental measurements of the properties of a liquid "Fomblin" surface obtained by the quasielastic scattering of laser light. The properties include the surface tension and viscosity as a function of temperature. The results are compared to the measurements of the bulk fluid properties. We then calculate the upscattering rate of ultracold neutrons (UCN) from thermally excited surface capillary waves on the liquid surface and compare the results to experimental measurements of the UCN lifetime in Fomblin fluid-walled UCN storage bottles, and show that the excess loss rate for UCN energies near the Fomblin potential can be explained. The rapid temperature dependence of the Fomblin storage lifetime is explained by our analysis.Comment: 25 pages, 13 figures; 2nd version corrects several error

Regge Field Theory in zero transverse dimensions: loops versus "net" diagrams

Toy models of interacting Pomerons with triple and quaternary Pomeron vertices in zero transverse dimension are investigated. Numerical solutions for eigenvalues and eigenfunctions of the corresponding Hamiltonians are obtained, providing the quantum solution for the scattering amplitude in both models. The equations of motion for the Lagrangians of the theories are also considered and the classical solutions of the equations are found. Full two-point Green functions ("effective" Pomeron propagator) and amplitude of diffractive dissociation process are calculated in the framework of RFT-0 approach. The importance of the loops contribution in the amplitude at different values of the model parameters is discussed as well as the difference between the models with and without quaternary Pomeron vertex.Comment: 34 pages, 36 figure

Gas-liquid transition in the model of particles interacting at high energy

An application of the ideas of the inertial confinement fusion process in the case of particles interacting at high energy is investigated. A possibility of the gas-liquid transition in the gas is considered using different approaches. In particular, a shock wave description of interactions between particles is studied and a self-similar solution of Euler's equation is discussed. Additionally, Boltzmann equation is solved for self-consistent field (Vlasov's equation) in linear approximation for the case of a gas under external pressure and the corresponding change of Knudsen number of the system is calculated.Comment: 24 pages, 2 figur

Odderon in Gauge/String Duality

At high energies, elastic hadronic cross sections, such as $pp, \overline p p, \pi^{\pm} p$, are dominated by vacuum exchange, which in leading order of the $1/N_c$ expansion has been identified as the BFKL Pomeron or its strong AdS dual the closed string Reggeized graviton \cite{Brower:2006ea}. However the difference of particle anti-particle cross sections are given by a so-called Odderon, carrying C = -1 vacuum quantum numbers identified in weak coupling with odd numbers of exchanged gluons. Here we show that in the dual description the Odderon is the Reggeized Kalb-Ramond field ($B_{\mu\nu}$) in the Neveu-Schwartz sector of closed string theory. To first order in strong coupling, the high energy contribution of Odderon is evaluated for ${\cal N} = 4$ Super Yang-Mills by a generalization of the gravity dual analysis for Pomeron in Ref. \cite{Brower:2006ea}. The consequence of confinement on the Odderon are estimated in the confining QCD-like $AdS^5$ hardwall model of Polchinski and Strassler \cite{Polchinski:2001tt}.Comment: 69 pages, 6 figures. Title change to better reflect the content of the paper. More discussion added in the Comments section. To be published in JHE

The Pomeron and Gauge/String Duality

The traditional description of high-energy small-angle scattering in QCD has two components -- a soft Pomeron Regge pole for the tensor glueball, and a hard BFKL Pomeron in leading order at weak coupling. On the basis of gauge/string duality, we present a coherent treatment of the Pomeron. In large-N QCD-like theories, we use curved-space string-theory to describe simultaneously both the BFKL regime and the classic Regge regime. The problem reduces to finding the spectrum of a single j-plane Schrodinger operator. For ultraviolet-conformal theories, the spectrum exhibits a set of Regge trajectories at positive t, and a leading j-plane cut for negative t, the cross-over point being model-dependent. For theories with logarithmically-running couplings, one instead finds a discrete spectrum of poles at all t, where the Regge trajectories at positive t continuously become a set of slowly-varying and closely-spaced poles at negative t. Our results agree with expectations for the BFKL Pomeron at negative t, and with the expected glueball spectrum at positive t, but provide a framework in which they are unified. Effects beyond the single Pomeron exchange are briefly discussed.Comment: 68 pages, uses JHEP3.cls, utphys.bst; references added, typos corrected, and clarifying remarks adde

Pomeron loops in the perturbative QCD with Large N_c

The lowest order pomeron loop is calculated for the leading conformal weight with full dependence of the triple pomeron vertex on intermediate conformal weights. The loop is found to be convergent. Its contribution to the pomeron Green function begins to dominate already at rapidities 10$\div$15. The pomeron pole renormalization is found to be quite small due to a rapid fall of the triple pomeron vertex with rising conformal weights.Comment: 17 pages, 2 figure

A QCD motivated model for soft interactions at high energies

In this paper we develop an approach to soft scattering processes at high energies,which is based on two mechanisms: Good-Walker mechanism for low mass diffractionand multi-Pomeron interactions for high mass diffraction. The pricipal idea, that allows us to specify the theory for Pomeron interactions, is that the so called soft processes occur at rather short distances (r^2 \propto 1 /^2 \propto \alpha'_\pom \approx 0.01 GeV^{-2}), where perturbative QCD is valid. The value of the Pomeron slope \alpha'_\pom was obtained from the fit to experimental data. Using this theoretical approach we suggest a model that fits all soft data in the ISR-Tevatron energy range, the total, elastic, single and double diffractive cross sections, including $t$ dependence of the differential elastic cross section, and the mass dependence of single diffraction. In this model we calculate the survival probability of diffractive Higgs production, and obtained a value for this observable, which is smaller than 1% at the LHC energy range.Comment: 33pp,20 figures in eps file

Magnetic field - temperature phase diagram of quasi-two-dimensional organic superconductor lambda-(BETS)_2 GaCl_4 studied via thermal conductivity

The thermal conductivity kappa of the quasi-two-dimensional (Q2D) organic superconductor lambda-(BETS)_2 GaCl_4 was studied in the magnetic field H applied parallel to the Q2D plane. The phase diagram determined from this bulk measurement shows notable dependence on the sample quality. In dirty samples the upper critical field H_{c2} is consistent with the Pauli paramagnetic limiting, and a sharp change is observed in kappa(H) at H_{c2 parallel}. In contrast in clean samples H_{c2}(T) shows no saturation towards low temperatures and the feature in kappa(H) is replaced by two slope changes reminiscent of second-order transitions. The peculiarity was observed below ~ 0.33T_c and disappeared on field inclination to the plane when the orbital suppression of superconductivity became dominant. This behavior is consistent with the formation of a superconducting state with spatially modulated order parameter in clean samples.Comment: 10 pages, 8 figures, new figure (Fig.5) and references added, title change