Linear Symmetries of Scattering Amplitudes

If we define, roughly, linear symmetries as those symmetries which lead to linear relationships among scattering amplitudes, we are then faced with the question whether we already know all possible types of linear symmetries or whether there are new types of symmetries which we can yet discover. We argue that for an important class of these symmetries there can be no new types of symmetries, except for one which we call scaling symmetry. We also attempt to point out all types of symmetries which other classes have. In analyzing the above question we are led to a simple and consistent formalism for describing linear symmetries which takes linearity as the starting point for dealing with these symmetries. In this approach all linear symmetries are formally treated on an equal footing. General results on linear symmetries are derived: These symmetries are then classified into three main classes, and an effort is made to discover the characteristic properties of the individual classes.     

Holomorphic Factorization of Superstring Scattering Amplitudes

The holomorphic factorization of the superstring partition function is verified at arbitrary genus. The evaluation of scattering amplitudes and the implications of genus-dependent estimates on the string coupling are given.     

Integral Relations for Multichannel Reactions

Multichannel scattering reactions can be described through two integral relations based on the Kohn variational principle. When used in combination with the hyperspherical adiabatic expansion method the pattern of convergence of the corresponding ${{\mathcal K}}$ -matrix is similar to the one found when applied to obtain bound states.     

Invariant Spinors and their Use for Expansions of Scattering Amplitudes

A general covariant scheme is proposed for the kinematical analysis of arbitrary reactions. By this scheme the problem of finding invariant amplitudes and corresponding kinematical covariants can be solved systematically. The amplitudes are labelled by two invariant indices for each particle related to spin and parity. The method provides a tool for exploiting the symmetries of the M-function, including crossing symmetry and the Pauli principle. Amplitudes free from kinematical singularities can easily be constructed.     

The Vanishing of Two-Point Functions for Three-Loop Superstring Scattering Amplitudes

In this paper we show that the two-point function for the three-loop chiral superstring measure ansatz proposed by Cacciatori, Dalla Piazza, and van Geemen [2] vanishes. Our proof uses the reformulation of the ansatz given in [8], theta functions, and specifically the theory of the Γ₀₀ linear system, introduced by van Geemen and van der Geer [6], on Jacobians. At the two-loop level, where the amplitudes were computed by D’Hoker and Phong [11–14, 17, 18], we give a new proof of the vanishing of the two-point function (which was proven by them). We also discuss the possible approaches to proving the vanishing of the two-point function for the proposed ansatz in higher genera [3, 8, 25].     

An Infrared-Finite Algorithm for Rayleigh Scattering Amplitudes,and Bohr's Frequency Condition

In this paper, we rigorously justify Bohr’s frequency condition in atomic spectroscopy. Moreover, we construct an algorithm enabling us to calculate the transition amplitudes for Rayleigh scattering of light at an atom, up to a remainder term of arbitrarily high order in the finestructure constant. Our algorithm is constructive and circumvents the infrared divergences that invalidate standard perturbation theory.     

Reaction Mechanisms in a Multichannel Scattering Theory for Identical Particles

Exchange effects in rearrangement reactions are studied in the framework of a general algebraic theory of identical-particle scattering. An algebraic definition of reaction mechanisms proposed previously is used to distinguish the contributions to scattering amplitudes made by different exchange processes. Previous statements concerning the number of possible exchange mechanisms and their relative weight factors are rigorously proved. The results of this paper differ from those obtained in previous studies, as here identical clusters of particles are also treated as indistinguishable. Received March 31, 1994; revised Juli 22, 1994; accepted for publication September 29, 1994     

Vacuum Polarization Bubble Effects on the Triangle Relations for B Meson Charmless Decay Amplitudes

Assuming that factorization is valid and that contributions of the exchange, annihilation, and penguin-annihilation diagrams are negligible, we study the effects of the QCD vacuum polarization bubbles on the decay amplitudes of some B meson charmless decays into two light pseudoscalars. The bubbles have much less effects on B⁰→π⁺π^-, π^-K⁺, π⁰K⁰ than on B⁰→π⁰π⁰ thus the triangle relation √2A(B⁺→π⁺π⁰) = A(B⁰→π^-K⁺)/R_u+√2A(B⁰→π⁰K⁰)/R_u is changed slightly while √2A(B⁺→π⁺π⁰)=√2A(B⁰→π⁰π⁰)+A(B⁰→π⁺π^-) is altered significantly. This may indicate that in order to test or use these triangle relations other higher order QCD corrections should also be carefully taken into consideration.     

Partial Wave Crossing Relations for Meson-Baryon Scattering

Three different types of relations for meson-baryon partial wave amplitudes following from the s ↔ u crossing symmetry of the invariant amplitudes are investigated: i) the partial wave crossing relations directly derived from the s ↔ u crossing symmetry and the partial wave projection, ii) the partial wave crossing relations following from a combined use of s ↔ u crossing symmetry and analyticity, and iii) the crossing sum rules, which are a direct consequence of the s ↔ u crossing symmetry. The kernels entering the crossing relations i) and ii) are given in an analytic form, valid for arbitrary angular momentum. Their properties are studied in detail. By means of the partial wave crossing relations ii) it is demonstrated that u-channel exchange of a resonance leads to a resonance-like behaviour of the partial wave amplitudes on the crossed physical cut. This phenomenon is described in terms of “pseudoresonances”. Finally the crossing sum rules iii) and their practical use are thoroughly discussed, and they are compared with the partial wave crossing relations i) and ii). Special attention is paid to the crossing symmetry constraints on the S-wave amplitudes. As a result of these investigations we present a crossing symmetric ansatz for these amplitudes which gives a more reliable parametrization than the usual effective range approximation.     

Phenomenological Dispersion Theory of KN Scattering

A survey is given of the present state of experimental and theoretical knowledge of the kaonnucleon interaction, with special attention to recent applications of phenomenological dispersion theory in elucidating this interaction. Various alternative methods of analyzing the data are compared and contrasted. The topics covered include the low-energy parameters, dispersion relation calculations of the real parts of the forward scattering amplitudes and the KNY coupling constants, analyses of the data by recently developed analytic continuation techniques, and high-energy phenomenology.     

Dispersion Relations for Proton Relaxation in Solid Dielectrics

Russian Physics Journal - Frequency-temperature spectra of the complex permittivity are studied for proton semiconductors and dielectrics using the methods of a quasi-classical kinetic theory of...     

Regge Models and Dispersion Relations for Partial Waves

The asymptotic behaviour of partial wave amplitudes is calculated supposing various Regge models for the total scattering amplitude A(s, t, u). The high energy partial wave behaviour obtained is combined with the validity of partial wave dispersion relations. It is shown that consistency of these assumptions can only be achieved by demanding. 1) a definite asymptotic behaviour of the discontinuity of the left hand cut of partial wave amplitudes. 2) the validity of partial wave sum rules of similar kind as the well-known finite energy sum rules for the total amplitude. All steps of the derivation shall first be demonstrated for elastic scattering of identical scalar particles. Then within the helicity formalism the results are generalized for particles with arbitrary spin and different masses. Finally the question is studied whether the sum rules can be employed to determine unknown CDD-pole parameters in an N/D approach for the I = J = 1/2 state in πN scattering. It is shown that the sum rules of highest order are able to do that.     

Scattering Amplitudes Interpolating Between Instant Form and Front Form of Relativistic Dynamics

Among the three forms of relativistic Hamiltonian dynamics proposed by Dirac in 1949, the front form has the largest number of kinematic generators. This distinction provides useful consequences in the analysis of physical observables in hadron physics. Using the method of interpolation between the instant form and the front form, we introduce the interpolating scattering amplitude that links the corresponding time-ordered amplitudes between the two forms of dynamics and provide the physical meaning of the kinematic transformations as they allow the invariance of each individual time-ordered amplitude for an arbitrary interpolation angle. We discuss the rationale for using front form dynamics, nowadays known as light-front dynamics (LFD), and present a few explicit examples of hadron phenomenology that LFD uniquely can offer from first-principles quantum chromodynamics. In particular, model-independent constraints are provided for the analyses of deuteron form factors and the N Δ transition form factors at large momentum transfer squared Q ². The swap of helicity amplitudes between the collinear and non-collinear kinematics is also discussed in deeply virtual Compton scattering.     

Experimental Knowledge of the Real Parts of the K±p Forward Scattering Amplitudes

A compilation of experimentally determined values of the real parts of the K^±p forward scattering amplitudes is given in a form in which these data may be used directly in analyses of forward dispersion relations. The methods of determining these real parts from experimental data are briefly reviewed and a survey of K^±p low-energy parametrizations and phase shift analyses is given. A summary is given of the theoretical determinations of the real parts.     

Angular Dispersion and Deflection Function for Heavy Ion Elastic Scattering

The differential cross sections for elastic scattering products of ^17F on ^208Pb have been measured. The angular dispersion plots of ln（dσ/dθ） versus θ^2 are obtained from the angular distribution of the elastic scattering differential cross sections. Systematical analysis on the angular dispersion for the available experimental data indicates that there is an angular dispersion turning angle at forward angular range within the grazing angle. This turning angle can be clarified as nucleal rainbow in classical deflection function. The exotic behaviour of the nuclear rainbow angle offers a new probe to investigate the halo and skin phenomena.     

Evidence of Dispersion Relations for the Nonlinear Response of the Lorenz 63 System

Along the lines of the nonlinear response theory developed by Ruelle, in a previous paper we have proved under rather general conditions that Kramers-Kronig dispersion relations and sum rules apply for a class of susceptibilities describing at any order of perturbation the response of Axiom A non equilibrium steady state systems to weak monochromatic forcings. We present here the first evidence of the validity of these integral relations for the linear and the second harmonic response for the perturbed Lorenz 63 system, by showing that numerical simulations agree up to high degree of accuracy with the theoretical predictions. Some new theoretical results, showing how to derive asymptotic behaviors and how to obtain recursively harmonic generation susceptibilities for general observables, are also presented. Our findings confirm the conceptual validity of the nonlinear response theory, suggest that the theory can be extended for more general non equilibrium steady state systems, and shed new light on the applicability of very general tools, based only upon the principle of causality, for diagnosing the behavior of perturbed chaotic systems and reconstructing their output signals, in situations where the fluctuation-dissipation relation is not of great help.     

Dispersion Relations for Isothermal Plasma around the Horizon of Reissner-Nordstroem-de Sitter Black Hole

We formulate the general relativistic magnetohydrodynamic equations for isothermal plasma in spatially fiat Reissner-Nordstroem-de Sitter metric by using 3＋1 split of spacetime. Respective perturbed equations are linearized for rotating magnetized surroundings. These are then Fourier analyzed and the corresponding dispersion relations are obtained. These relations are discussed both analytically and numerically in order to investigate the nature of waves with positive angular frequency around the horizon.     

Compton散射下激光等离子体纵波色散特性

应用电子与多光子集团非线性Compton散射模型,研究了Compton散射下激光等离子体纵波色散特性.结果表明:长波支纵色散曲线由解析上的长波、数值计算结果和短波组成,长波支和短波支纵色散均随相对论正负电子对特征温度的增大而增大,随Compton散射引起的频率的增量的增大而降低,且单温激光等离子体的色散曲线与散射前的双温等离子体的色散曲线相似.