Ward identities of W∞ symmetry and higher-genus amplitudes in 2D string theory

The Ward identities of the W_∞ symmetry in two-dimensional string theory in the tachyon background are studied in the continuum approach. We consider amplitudes different from 2D string ones by the external leg factor and derive the recursion relations among them. The recursion relations have non-linear terms which give relations among the amplitudes defined on different genus. The solutions agree with the matrix model results even in higher genus. We also discuss the differences of the roles of the external leg factor between the c_M = 1 model and the c_m < 1 model.     

An intuitive approach to a generalized parton picture for high-energy lepton-hadron scattering

A generalized parton picture is developed, based on the impulse approximation. A parton is allowed to have non-point-like elastic form factors; inelastic current-parton scattering is taken into account explicitly. The amplitude of any exclusive channel of lepton-induced reactions is written down, with the parts containing the long-distance and the short-distance behavior of interaction dynamics clearly separated. Scaling violation is a natural feature of this picture. The inelastic structure functions, W₁ and νW₂, are studied in this scheme using various different theories; perturbative QCD, the scale-invariant parton model, the hadron bootstrap picture, and a phenomenological stripped-down hadron-parton model. The application of this picture to elastic lepton-hadron scattering and the problem of the selection of an infinite momentum frame are also discussed.     

A determination of sin2θ w and the lepton and quark electroweak couplings frome + e − data

Published data on lepton pair and quark pair final states ine ⁺ e ^? annihilation have been analysed in a self consistent way to yield values for the lepton and quark weak vector and axial vector couplings. Generation universality has been tested for the leptons and under the assumption of the standard model of the weak interaction, the parameter sin²θ _w has been determined separately for the lepton and quark sector. In the renormalisation scheme α,G _μ and sin²θ _w , the result for the lepton final states is sin²θ _w = 0.212±0.014 and for the hadron final states, sin²θ _w = 0.236±0.015. The combined result for this single parameter in the model is sin²θ _w = 0.223±0.011±0.007, corresponding tom _Z =93.0 _?1.8 ^+2.0 GeV.     

Tomography for amplitudes of hard exclusive processes

We discuss which part of information about hadron structure encoded in the Generalized Parton Distributions (GPDs) [part of total GPD image] can be restored from the known amplitude of a hard exclusive process. The physics content of this partial image is analyzed. Among other things, we show that this partial image contains direct information about how the target hadron responses to the (string) quark–antiquark operator of arbitrary spin J. Explicit equations relating physics content of the partial image of GPDs directly to the data are derived. Also some new results concerning the dual parametrization of GPDs are presented.     

Non-linear axisymmetric transient analysis of an orthotropic thin circular plate with an elastically restrained edge

Results are presented for the geometrically non-linear axisymmetric transient elastic stress and deflection responses of a cylindrically orthotropic thin circular plate with an elastically restrained edge, including both rotational and in-plane displacements. In the analysis the dynamic analogue of the von Kárman governing differential equations in terms of the normal displacement w and the stress function ψ are employed. The displacement w and stress function ψ are expanded in finite power series. The orthogonal point collocation method in the space domain and the Newmark-β scheme in the time domain are used. Four types of uniformly distributed transient loadings have been considered: step function, sinusoidal and N-shaped pulses, and exponentially decaying loads. The influence of the orthotropic parameter β and the elastic rotational and in-plane edge restraint parameters (K_b, K_i) on the large amplitude response has been investigated. The effect of a prescribed in-plane displacement on the non-linear transient response has also been studied.     

On an elaboration of M. Kac's theorem concerning eigenvalues of the Laplacian in a region with randomly distributed small obstacles

We removem-balls of centersw ₁,...,w _m with the same radius α/m from a bounded domain Ω inR ³ with smooth boundary γ. Let μ _k (α/m;w(m)) denote thek-th eigenvalue of the Laplacian in Ω/m-balls under the Dirichlet condition. We consider μ _k (α/m;w(m)) as a random variable on a probability space (w ₁,...,w _m)∈Ω × ... × Ω and we examine a precise behaviour of μ _k (α/m;w(m)) asm → ∞. We give an elaboration of. M. Kac's theorem.     

Quantumchromodynamic corrections for ΔF=2 processes in the presence of a heavy top quark

We calculate the QCD corrections to the ΔS=2 and ΔB=2 transition amplitudes for the casem _t ?m _w and extrapolate the results tom _t ?m _w , where they join smoothly with the low mass calculations,m _t ?m _w . We present explicit formulas for the corrections with numerical results summarized in tables and figures and compare them with earlier calculations. We arrive at a QCD corrected effective Hamiltonian which must hold for all ranges ofm _t .     

Nonperturbative contribution to the fermion propagator and dynamical electroweak symmetry breaking

We examine the field-theoretical contribution of fermion-antifermion condensates arising from a weak-SU(2) doublet of condensing fermions to electroweak vacuum polarization functions. For the custodial-SU(2) case of equal condensates and masses, we find that the condensate contributions to vacuum polarization functions uphold the electroweak signature relationm _w=m _zcosθ_w, and that these contributions are decoupled entirely from oblique radiative corrections. If only the upper member of the doublet forms a fermion-antifermion condensate, the relationm _w=m _zcosθ_w is again upheld in the limit that the mass of the lower member of the doublet is small compared to that of the upper member. For this case, the upper-member's fermion-antifermion condensate is shown to enter oblique radiative corrections. In the absense of an explicit Higgs mechanism, identification of this doublet with (t, b) is shown to be excluded by present empirical bounds onS, T, andU parameters. Further phenomenological consequences of fermion-antifermion condensate contributions to theW-Z mass matrix are discussed, both in the absense and in the presence of an explicit Higgs mechanism.     

Systematics of vector meson-proton scattering

The systematics of Vp scattering (V = ?, ω, φ, ψ) is studied using unitarity to relate the elastic and inelastic amplitudes. Assuming that φ and ψ are pure strange and charmed quark states, respectively, φp and ψp elastic amplitudes are shown, in the first approximation, to be generated by diffractive inelastic states. This leads to the relations B_ψ ≈ B_φ ≈ B_ω/2 ≈ B_?/2 for the elastic differential cross section slopes. The approximate m_V² is related to a similar suppression in inelastic Vp cross sections and, more speculatively, to the m_A² suppression of the hadronic production cross sections σ(pp → A).     

Influence of domain boundary width on the statics of 90° domains in epitaxial ferroelectric thin films

The influence of the domain boundary width on the statics of single 90° elastic domains (twins) in epitaxial ferroelectric tetragonal films grown on a cubic substrate is theoretically investigated. The inhomogeneous internal stresses arising in polydomain epitaxial systems are calculated by the effective dislocation method. The elastic energy stored in the heterostructure is determined. The equilibrium domain size is found and the stability diagram for single domains at different wall widths is constructed by minimizing the total internal energy of the system. It is demonstrated that, as the domain boundary width 2w increases, the stability region of 90° domains increases and qualitatively changes for ultrathin films when the parameter 2w exceeds the specific critical value 2w _cr. The equilibrium width 2w* of domain walls in thin films is predicted to be larger compared to the width 2w ₀ of domain boundaries in a macroscopic crystal.     

Behavior of the hadron potential at large distances and properties of the hadron spin-flip amplitude

The impact of the form of the hadron potential at large distances on the behavior of the hadron spin-flip amplitude at small angles is examined. The t-dependence of the spin-flip amplitude of high-energy hadron elastic scattering is analyzed under different assumptions on the hadron interaction. It is shown that the long tail of the nonGaussian form of the hadron potential of the hadron interaction in the impact parameter representation leads to a large value of the slope of the spin-flip amplitude (without the kinematical factor ) as compared with the slope of the spin-nonflip amplitude. This effect can explain the form of the differential cross-section and the analyzing power at small transfer momenta. The methods for the definition of the spin-dependent part of the hadron scattering amplitude are presented. A possibility to investigate the structure of the hadron spin-flip amplitude from the accurate measure of the differential cross-section and the spin correlation parameters is shown. Received: 14 December 2001 / Accepted: 17 January 2002     

From kaonic atoms to kaonic nuclei: A search for antikaon-mediated bound nuclear systems

Strong interaction processes were intensively studied at low energy with exotic atoms, touching one of the fundamental problems in hadron physic today — the still unsolved question of how hadron masses are generated. The question of the origin of the large hadron masses made up of light quarks, the current mass of the up (u) and down (d) quarks (m_u,d≈5 MeV) is two orders of magnitude smaller than a typical hadron mass of about 1 GeV, will be discussed in the context with the experimental work done in the field of exotic atoms expanded to exotic nuclei.An overview of the properties of exotic hydrogen atoms made of pions and kaons are presented, using high precision experiments unrevealing the nature of strong interaction physics at low energy. A new field which contributes to the understanding of the origin of the large hadron mass is the study of the mass modification in a nuclear medium. Antikaon mediated bound nuclear systems would be an ideal tool, if they exist, to look for chiral restoration at high density and zero temperature or even more exotic to look for phase transitions.     

Thermodynamical approach in high-energy scattering

A non-conventional thermodynamical approach earlier for high-energy collisions is considered in more detail. The approach provides a physical interpretation not only of the shape of the hadron form factor but also of the increase in its radius with energy . A precise analysis of experimental data on elastic scattering for is performed with the formulae derived. Predictions in the multi TeV range and comparison of results with recent data of the E 710 Collaboration for 1.8 TeV are made. Agreement occurs when the experimental t-distribution is scaled up by 11%.     

Physical pion-pion partial-wave equations based on three channel crossing symmetry

We present a set of closed systems of partial-wave equations for pion-pion scattering valid for ?28 m_π² ? s ? 125.31 m_π². These equations give the real part of a given partial-wave amplitude in terms of scattering lengths and a convergent series of integrals over the physical values of the absorptive parts of all partial waves. Our equations are extensions of relations previously derived from fixed-t dispersion relations. The new equations are rigorous consequences of axiomatic analyticity and three channel crossing symmetry. As an application, the effect of the f⁰-meson on the I = O S-wave is evaluated.     

Low momentum transfer theorem for two photon exchange in lepton hadron scattering

The two photon exchange contribution to lepton-hadron scattering is considered. Under the assumptions of Lorentz covariance, gauge invariance, unitarity and analyticity, we prove a low momentum transfer theorem for the relevant amplitudes. Fixed energy dispersion relations tell us that their nonanalytic part, in the neighbourhood of t = 0, is given by the contribution of the two photon cut in the t-channel. The t-channel absorptive parts are obtained from unitarity. Their calculation has as input the two amplitudes corresponding to Compton scattering on the hadron with a pole contribution, and the continuum controlled at low t by the electromagnetic polarizabilities. By means of the dispersion integral, one proves the expansion $\text{k}{}_1\text{(s)+k}{}_2\text{(s)}\text{?t}\text{+k}{}_3\text{(s)t}\text{log}\text{(?t)+O(t)}$ for the continuum contribution, where k₁(s) is the only unknown. Explicit expressions are obtained for the pole contribution as M → ∞, where M is the hadron mass, and for the continuum when (?t) <Λ and (?t) < 4m², where m is the muon mass and Λ is a characteristic parameter of the hadron structure.     

Depinning of a Discrete Elastic String from a Random Array of Weak Pinning Points with Finite Dimensions

In possible connection with dislocation pinning by foreign atoms in alloys and vortex pinning in type II superconductors, we compute the external force required to drag an elastic string along a discrete two-dimensional random array with finite dimensions. The obstacles, with a maximum pinning force f _m are distributed randomly on a rectangular lattice with square symmetry. The system dimensions are fixed by the total course of the elastic string L _x and the string length L _y . Our study shows that Larkin’s length is larger than L _y when f _m is less than a certain bound depending on the system size as well as on the obstacle density c _s . Below such a bound an analytical theory is developed to compute the depinning threshold. Some numerical simulations allow us to demonstrate the accuracy of the theory for an obstacle density ranging from 1 to 50% and for different geometries.     

Mass relations and neutrino oscillations in an SO(10) model

We present in detail a grand unified model based on SO(10) which naturally reproduces known fermion mass relations and mixing angles. It predicts m_νe ? m_νμ, m_ντ, and predominant ν_μ-ν_τ oscillations. Several other features of the model are analyzed in detail: construction of the Higgs potential, predictions for τ_p and sin²θ_w in a temporarily free model and a relation between the mass of the t-quark and the lifetime of the B meson.     

Soft π−p and pp elastic scattering in the energy range 30 to 345 GeV

Differential cross sections for π^?p and pp elastic scattering have been measured at incident momenta ranging from 30 to 345 GeV and in the t range 0.002 (GeV/c)² ? |t| ? 0.04 (GeV/c)². From the analysis of the data, the ratio ? (t = 0) of the real to the imaginary parts of the forward scattering amplitude was determined together with the logarithmic slope b of the diffraction cone.The results on the real parts confirm the validity of the forward dispersion relations at high energies. Using the dispersion relations, it was shown that the experimental data on ?_{π?p(t = 0)} require a continuous rise of the total πp cross sections, at least up to the energy of 2000 GeV, thus revealing a close similarity in high-energy behaviour of πp and pp interactions.The results on the slope parameters from this experiment together with the analysis of the available world data demonstrate that the existing experimental data are consistent with the hypothesis of a universal shrinkage of the hadronic diffraction cone at high energies. The value of the asymptotic shrinkage parameter α_p^′ was found to be independent of the kind of the incident hadron and of the momentum transfer in the t range |t| ? 0.2 (GeV/c)² : 2α_{p^′ = ± 3 (GeV/c)^?2}.