Total scattering cross-section and extraction of low energy parameters of Σ±p scattering

The lowest momentum at which the total scattering cross-section data are available for Σ⁺ p and Σ⁻ p scattering is 145 MeV/c and 142.5 MeV/c respectively. Thus extracting low energy parameters amounts to extrapolating the data to still lower energies. Using the analytic structure of foward scattering amplitude to advantage a parameterization of theσ _T is presented which is hoped to be more reliable and stable for deriving results through extrapolation. The scattering lengths and effective ranges for the Σ⁺ p and Σ⁻ p are also estimated.     

Spin waves in the block checkerboard antiferromagnetic phase

Motivated by the discovery of a new family of 122 iron-based superconductors, we present the theoretical results on the ground state phase diagram, spin wave, and dynamic structure factor obtained from the extended J₁-J₂ Heisenberg model. In the reasonable physical parameter region of K₂Fe₄Se₅, we find that the block checkerboard antiferromagnetic order phase is stable. There are two acoustic spin wave branches and six optical spin wave branches in the block checkerboard antiferromagnetic phase, which have analytic expressions at the high-symmetry points. To further compare the experimental data on neutron scattering, we investigate the saddlepoint structure of the magnetic excitation spectrum and the inelastic neutron scattering pattern based on linear spin wave theory.     

Resonance properties from a coupled channel meson exchange model

In this talk, I present the results on the pole structure of pion-nucleon scattering in an analytic model based on meson exchange. The analytic properties of scattering amplitudes provide important informa-tion. Besides the cuts, the poles and zeros on the different Riemann sheets determine the global behavior of the amplitude on the physical axis. Pole positions and residues allow for a parameterization of resonances in a well-defined way, free of assumptions for the background and energy dependence of the resonance part. This is a necessary condition to relate resonance contributions in different reactions.     

Factorization and infrared properties of non-perturbative contributions to DIS structure functions

In this paper we present a new derivation of QCD factorization. We deduce the k _T and collinear factorizations for the DIS structure functions by consecutive reductions of a more general theoretical construction. We begin by studying the amplitude of forward Compton scattering off a hadron target, representing this amplitude as a set of convolutions of two blobs connected by the simplest, two-parton intermediate states. Each blob in the convolutions can contain both the perturbative and non-perturbative contributions. We formulate conditions for separating the perturbative and non-perturbative contributions and attributing them to the different blobs. After that the convolutions correspond to QCD factorization. Then we reduce this totally unintegrated (basic) factorization first to k _T -factorization and finally to collinear factorization. In order to yield a finite expression for the Compton amplitude, the integration over the loop momentum in the basic factorization must be free of both ultraviolet and infrared singularities. This obvious mathematical requirement leads to theoretical restrictions on the non-perturbative contributions (parton distributions) to the Compton amplitude and the DIS structure functions related to the Compton amplitude through the Optical Theorem. In particular, our analysis excludes the use of the singular factors x ^−a (with a>0) in the fits for the quark and gluon distributions because such factors contradict the integrability of the basic convolutions for the Compton amplitude. This restriction is valid for all DIS structure functions in the framework of both k _T -factorization and collinear factorization if we attribute the perturbative contributions only to the upper blob. The restrictions on the non-perturbative contributions obtained in the present paper can easily be extended to other QCD processes where the factorization is exploited.     

Asymptotics of the S-matrix and unitarisation

The manner in which the elastic scattering amplitude obeys unitarity, how it enters the circle of unitarity, and what its asymptotic limit is, remains a problem for models which include terms that rise fast with s. We have checked that the features of cross sections which come from unitarisation are present for most unitarisation schemes, e.g. those that saturate the profile function or those that describe multiple exchanges via an analytic formula. We have also obtained a scheme which interpolates between different classes of the unitarisation and found corresponding non-linear equations. Considering different forms of energy dependence of the scattering amplitude, and a variety of unitarisation schemes, we show that, in order to reproduce the data, the fits choose an amplitude that corresponds to an asymptotic value S = 0.     

Unitary amplitudes with cut-plane analyticity from given scattering data

We continue the study of constructing the scattering amplitude for scalar particles from elastic scattering data at a given energy. Here we require the scattering amplitude, f (z), to be analytic in a suitably cut z-plane; (z is the cosine of the scattering angle). We find that, in the elastic domain, the unitarity constraint is satisfied by a continuum of amplitudes, all corresponding to the same elastic scattering data. This continuum ambiguity in determination of f (z), which was noted earlier in formulations based on a smaller domain on analyticity, is associated with lack of knowledge of the contribution to unitarity from inelastic channels. We discuss the problem of incorporating smooth energy dependence in the determination of the scattering amplitude over some range of energy, and show that, under certain restrictions on the scattering data, there is a continuum of amplitudes having smooth energy dependence.     

Two-photon multiterm nonadiabatic transitions

The resonance Raman scattering phenomenon via the predissociated state is described in the four crossing terms A-(1, 2)-B model when terms 1 and 2 strongly interact. The Green's function closed representation for the coupled intermediate electronic terms 1 and 2 is obtained. The transition amplitude I _{A-(1, 2)-B} is found in the WKB approximation. The resonance Raman scattering via the predissociated ³Π_Ou ⁺ state of the interhalogen molecules is treated in detail.     

Microlocalization of Resonant States and Estimates of the Residue of the Scattering Amplitude

We obtain some microlocal estimates of the resonant states associated to a resonance z₀ of an h-differential operator. More precisely, we show that the normalized resonant states are outside the set of trapped trajectories and are in the incoming area of the phase space. As an application, we show that the residue of the scattering amplitude of a Schrödinger operator is small in some directions under an estimate of the norm of the spectral projector. Finally we prove such a bound in some examples.     

Phase shift analysis of pion-4He scattering by optimal polynomial expansion

A novel method of phase shift analysis for the scattering of charged pion from⁴He nuclei is proposed. The nuclear amplitudef _N (ϑ) has been parametrized in terms of a polynomial expansion in a conformally mapped variable, which is obtained by optimally exploiting the analytic property off _N . The method exhibits a significant reduction in the number of free parameters required for the fixed energy phase shift analysis of the differential cross-section data. The nuclear amplitude thus constructed is then used to obtain phase shifts and inelastic parameters of all possible orders. Reliable values of the real and imaginary parts of the forward amplitude are also obtained.     

Unitarized Chiral Perturbation Theory in a finite volume: Scalar meson sector

We develop a scheme for the extraction of the properties of the scalar mesons f ₀(600) , f ₀(980) , and a ₀(980) from lattice QCD data. This scheme is based on a two-channel chiral unitary approach with fully relativistic propagators in a finite volume. In order to discuss the feasibility of finding the mass and width of the scalar resonances, we analyze synthetic lattice data with a fixed error assigned, and show that the framework can be indeed used for an accurate determination of resonance pole positions in the multichannel scattering.     

Optical absorption by quasiparticles in superconducting multilayers

The absorption of photons by quasiparticles in the Bloch bands of multilayers, formed by alternating normal (N) and superconducting (S) regions, is computed for the vector of the oscillating electric field being perpendicular to the N-S interfaces. The absorption spectrum extends down to frequencies below the gap of the S-layers, and its structure results from the combined effects of Andreev scattering and conventional scattering at the N-S interfaces. For not too different Fermi energies ?_FS and ?_FN in the S and N layers there is one prominent resonance peak. With increasing temperature low frequency absorption goes up. For ?_FS ? ?_FN, on the other hand, a sharp multipeak structure at low frequencies is found.     

<Emphasis Type="Italic">Q</Emphasis><Superscript>2</Superscript> evolution of parton densities at smal-<Emphasis Type="Italic">x</Emphasis> values

In the leading twist approximation of the Wilson operator product expansion with “frozen” and analytic strong coupling constants we show that Bessel-inspired behavior of the structure function F ₂ at small x, obtained for a flat initial condition in the DGLAP evolution equations, leads to good agreement with the deep-inelastic scattering experimental data from HERA.     

Allowing for Coulomb effects in the effective range expansion for two coupled channels

A Coulomb-modified matrix of scattering amplitudes (an [(F)\tilde]\tilde F matrix) is considered for the case of two coupled channels of elastic scattering of charged particles with different orbital angular momenta (l ₁ and l ₂ = l ₁ + 2). Matrix elements of the [(F)\tilde]\tilde F matrix are expressed in terms of the matrix elements of a [(K)\tilde] ^{- 1}\tilde K^{ - 1} matrix inverse to a modified reaction K matrix. The elements of the [(K)\tilde] ^{- 1}\tilde K^{ - 1} matrix are written as expansions that are generalizations of single-channel effective range expansion with allowance for the Coulomb interaction. If a system of colliding particles involves a bound state, the analytic continuation of these expansions into the region of negative energies makes it possible to obtain both the position of the pole corresponding to the bound state and the scattering amplitude residues in this pole, in terms of which the corresponding vertex constants and asymptotic normalization coefficients are expressed.     

Unitarity structure of scattering amplitudes

As a first step towards constructing scattering amplitudes satisfying unitarity, analyticity and crossing symmetry, we derive a linear non-singular integral equation for the total scattering amplitude which is equivalent to the unitarity condition. For this purpose we use the partial-waveN/D representation (with inelasticity) and the convolution theorem for Legendre transforms. We also discuss briefly the choice of two functionsN(s, cos Θ),C(s, cos Θ) which determine the unitary scattering amplitude through the integral equation. These functions may hopefully be chosen so that the analyticity and crossing symmetry requirements are satisfied.

     

Resonance scattering of electrons from orientated O2 physisorbed on graphite

We have studied inelastic electron scattering from a saturated monolayer of O₂ physisorbed on graphite at 25K. The cross-section for excitation of the v = 0–1 vibrational transition in O₂ peaks at 8.5–9eV, and is attributed to the ⁴Σ_u negative ion resonance. The angular distribution of electrons inelastically ejected out of the resonance orbital has been measured, and is found to peak at 15° from the normal to the crystal for several different incident electron beam angles, in accord with the theory of resonant electron scattering by an orientated molecule. We discuss the implications of this measurement for a determination of the orientation of the O₂ molecule on the surface, taking account of possible multiple scattering effects.     

Isospin breaking in <Emphasis Type="BoldItalic">K</Emphasis><Subscript><Emphasis Type="BoldItalic">l4</Emphasis></Subscript> decays

Data on K _e4 decays allow one to extract experimental information on the elastic π π scattering amplitude near threshold, and to confront the outcome of the analysis with predictions made in the framework of QCD. These predictions concern an isospin symmetric world, while experiments are carried out in the real world, where isospin-breaking effects—generated by electromagnetic interactions and by the mass difference of the up and down quarks—are always present. We discuss the corrections required to account for these, so that a meaningful comparison with the predictions becomes possible. In particular, we note that there is a spectacular isospin-breaking effect in K _e4 decays. Once it is taken into account, the previous discrepancy between NA48/2 data on K _e4 decays and the prediction of π π scattering lengths disappears.     

Features of pion-nucleon scattering with nucleons as chiral solitons

We show that after simultaneous quantization of the rotational and translational collective degrees of freedom of chiral solitons, the p-wave pion-nucleon scattering amplitude can be generated in close analogy with the phenomenologically successful Δ-isobar model. In particular, the Δ-decay width arises naturally. We also comment on the usual background scattering method and find that the absence of the Δ resonance in this approach is closely related to the fact that the value of the axial vector coupling constant g_A comes out too small. We discuss this in the context of the Adler-Weisberger sum rule. We also comment on some problems in s-wave πN scattering.     

The Three-Boson System at Next-to-Next-to-Leading Order

We discuss effective field-theory treatments of the problem of three particles interacting via short-range forces (range R ≪ a ₂, with a ₂ the two-body scattering length). We show that forming a once-subtracted scattering equation yields a scattering amplitude whose low-momentum part is renormalization-group invariant up to corrections of O(R ³/a ₂ ³). Since corrections of O(R/a ₂) and O(R ²/a ₂ ²) can be straightforwardly included in the integral equation’s kernel, a unique solution for 1 + 2 scattering phase shifts and three-body bound-state energies can be obtained up to this accuracy. We use our equation to calculate the correlation between the binding energies of Helium-4 trimers and the atom-dimer scattering length. Our results are in excellent agreement with recent three-dimensional Faddeev calculations that used phenomenological inter-atomic potentials.     

Small-x behavior of the structure function and its slope for “frozen” and analytic strong-coupling constants

Using the leading-twist approximation of the Wilson operator product expansion with “frozen” and analytic versions of the strong-coupling constant, we show that the Bessel-inspired behavior of the structure function F₂ and its slope ∂lnF₂/∂ln(1/x) at small values of x, obtained for a flat initial condition in the DGLAP evolution equations, leads to good agreement with experimental data of deep-inelastic scattering at DESY HERA.