A theoretical approach to low multiplicity diffractive dissociation

We investigate the dynamics of low mass inelastic diffractive production in the framework of the “1/N dual unitarization” scheme. The smallness of inelastic diffractive dissociation is explicitly demonstrated by incorporating a Deck type mechanism with the crucial planar bootstrap equation. Although both inelastic and elastic pomeron couplings are of the same order in 1/N, the origin for their smallness, however, is not identical. Our work further confirms the validity of the iterative procedure, where the elastic amplitude is first generated from only non-diffractive intermediate states (except possibly for central collisions). Using a previous study of the “Cylinder” strength, we present also a semi-quantitative results for the integrated cross-section for low multiplicity diffractive production and compare it with the elastic cross-section at very high energies.     

Isoscalar diffractive photoproduction: A source of gluonium

Data on diffractive photoproduction of isoscalar states appear to be anomalously large in a number of channels. Isoscalar diffractive photoproduction is studied in a model in which the pomeron is approximated by two gluons, and in which gluon intermediate states are allowed in the pomeron-meson interaction. It is shown that the model allows a resolution of the long-standing problem of the small (in vector meson dominance terms) diffractive θ photoproduction cross section. This sets the scale for the calculation, and it is then demonstrated that the model can explain the large isoscalar cross section if it is due primarily to the diffractive photoproduction of a system of gluons.     

Spin dependence of deep inelastic diffraction

Using a perturbative model for diffractive interactions, we derive an expression for the polarized diffractive structure function in the high energy limit. This structure function is given by the interference of diffractive amplitudes with polarized and unpolarized exchanges. For the polarized exchange we consider both two-gluon and quark-antiquark amplitudes. The polarized diffractive amplitude receives sizable contributions from non-strongly ordered regions in phase space, resulting in a double logarithmic enhancement at small x. The resummation of these double logarithmic terms is outlined. We also discuss the transition from our perturbative expression to the nonperturbative region. A first numerical estimate indicates that the perturbative contribution to the spin asymmetry is substantially larger than the nonperturbative one. Received: 7 July 1999 / Published online: 14 October 1999     

Diffraction and correlations at the LHC: definitions and observables

We note that the definition of diffractive events is a matter of convention. We discuss two possible “definitions”: one based on unitarity and the other on Large Rapidity Gaps (LRG) or Pomeron exchange. LRG can also arise from fluctuations and we quantify this effect and some of the related uncertainties. We find care must be taken in extracting the Pomeron contribution from LRG events. We show that long-range correlations in multiplicities can arise from the same multi-Pomeron diagrams that are responsible for LRG events, and we explain how early LHC data can illuminate our understanding of ‘soft’ interactions.     

Die Hartree-Fock-Theorie mit Zwischenzuständen: Klärung ihrer Struktur bei Zeitumkehrinvarianz und Anwendung auf das Kleinsche Rotations-Vibrationsmodell

In an earlier paper we have extended the new Tamm-Dancoff method to the “New Tamm-Dancoff method with intermediate states”. This extension makes it possible to treat the effect of nearby levels in many body systems with Green's functions. In addition to well-known approximations, such as the Hartree-Fock theory and the Hartree-Bogoliubov theory, we obtain a series of new approximations. The “Hartree-Fock theory with intermediate states”, which is the subject of the present investigation, is one of these. By using time reversal invariance we have succeeded in clarifying its structure, and we give the solution procedure. The exchange terms in theN-particle intermediate states can be represented by an additional potentialY, which (as is the case for the generalized density matrixρ) has to be determined selfconsistently. In this way we have overcome the difficulties, that Kerman and Klein met in their “generalized Hartree-Fock approximation”, which has some close similarities with our Hartree-Fock theory with intermediate states. We demonstrate our method for the exactly soluble rotational-vibrational model of Klein et al. Hereby we show how to treat conservation laws and the degeneracy of levels. The Hartree-Fock equations with three intermediate states turn out to give analytical expressions for the energies and the matrix elements. These agree excellently with the exact values in the rotational part of the spectrum.     

Forward pion-nucleon charge exchange reaction and Regge constraints

We present our recent study of pion-nucleon charge exchange amplitudes above 2 GeV. We analyze the forward pion-nucleon charge exchange reaction data in a Regge model and compare the resulting amplitudes with those from the Karlsruhe-Helsinki and George-Washington-University partial-wave analyses. We explore possible high-energy constraints for theoretical baryon resonance analyses in the energy region above 2 GeV. Our results show that for the pion-nucleon charge exchange reaction, the appropriate energy region for matching meson-nucleon dynamics to diffractive scattering should be around 3 GeV for the helicity flip amplitude.     

Equations from non-linear chiral transformations

In comparison with theWT chiral identity which is indispensable for renormalization theory, relations deduced from the non-linear chiral transformation have a totally different physical significance. We wish to show that non-linear chiral transformations are powerful tools to deduce useful integral equations for propagators. In contrast to the case of linear chiral transformations, identities derived from non-linear ones contain more involved radiative effects and are rich in physical content. To demonstrate this fact we apply the simplest non-linear chiral transformation to the Nambu-Jona-Lasinio model, and show how our identity is related to the Dyson-Schwinger equation and Bethe-Salpeter amplitudes of the Higgs and π. Unlike equations obtained from the effective potential, our resultant equation is exact and can be used for events beyond the LEP energy.     

Symplectic quantum mechanics

Using the notion of symplectic structure and Weyl (or star) product of non-commutative geometry, we construct unitary representations for the Galilei group and show how to rewrite the Schrödinger equation in phase space. This approach gives rise to a new procedure to derive Wigner functions without the use of the Liouville-von Neumann equation. Applications are presented by deriving the states of linear and nonlinear oscillators in terms of amplitudes of probability in phase space. The notion of coherent states is also discussed in this context.     

An eikonal perturbation theory having applications in hadron dynamics,I: Genesis

We develop a Lagrangian field-theoretic laboratory where one can rigorously investigate ideas and problems in high-energy hadronic interactions. In this paper (the first of a series) the general field-theoretic framework is outlined in the oversimplified model of a scalar-scalar Yukawa interaction. Functional methods are used to cast all Green's functions in an “operator eikonal” form. The eikonal approximations (EA's) in Lagrangian relativistic quantum mechanics are reviewed and discussed. We then derive an exact eikonal equation in quantum field theory. The perturbation theoretic solution of this equation leads to a new kind of eikonal perturbation theory (EPT) which generalizes simultaneously the EA's as well as the ordinary perturbation theory (OPT). Some salient features of Green's functions in the EPT are as follows: (i) the lowest-order EPT amplitudes correspond to a kind of semiclassical approximation; (ii) the lowest-order four-point amplitudes contain the high-energy part of the full radiatively corrected crossed ladder series, without vacuum polarization effects; (iii) for spin-one gluons, the latter amplitude develops diffractive behavior in the direct channel and, for spin-one and spin-zero gluons, Regge behavior in the crossed channel; (iv) for vanishing gluon mass, this amplitude develops poles, in the direct channel, corresponding to a positronium-like bound-state spectrum. Properties (i)–(iv) are generalized to EPT from EA's and are absent in OPT. Unlike in the case of EA's we also have that (v) the EPT is a quantum field theory, which properly includes selfinteraction effects; (vi) the EPT is an iterative perturbation theoretic scheme, which shares with OPT the properties of renormalizability.     

Diffractive scattering in the dual model

A method is suggested for calculating the elastic amplitude as the shadow of multiparticle processes. This does not require explicit formulae for the production amplitudes, but depends only on the following assumptions: (a) Regge behaviour, (b) semi-local duality, (c) exchange degeneracy. The system is multiperipheral in general structure but because of the assumption (a)-(c), it incorporates such features as the clustering of final particles and provides a proper treatment of quantum numbers, phases, and resonance spins. As a result, the unitarity sum separates automatically into two components corresponding respectively to pomeron and ordinary reggeon exchange, each of which is seen to have the correct qualitative dependence on the quantum numbers, the energy s, and the momentum transfer t. Quantitatively, the elastic amplitude is given in terms of a triple-Regge vertex, for which we suggest a simple parametization based on a detailed study of existing experiment and the Veneziano model. The method is then applied to calculate the elastic amplitudes for π^±p, K^±p and pp within the range 6 < s < 50 and 0 > t > ?0.5 GeV². Semi-quantitative agreement is obtained with experiment with essentially no free parameter. Although the investigation is restricted at present to elastic scattering as the shadow of only the non-diffractive component satisfying (a)-(c), the method is believed to apply also to other diffractive processes, and may be regarded as the first step in an iterative solution of the full unitarity equation.     

High-p jets in diffractive electroproduction

The diffractive production of high-p jets in deep-inelastic scattering is studied in the semiclassical approach. The p-spectra of and diffractive final states are found to be qualitatively different. For fina states, which are produced by ‘hard’ colour-singlet exchange, the p-spectrum is much softer than for final states, where the colour neutralization is ‘soft’. Furthermore, the two different final states can be clearly distinguished by their diffractive mass distributions.     

Geometric scaling as traveling waves

We show the relevance of the nonlinear Fisher and Kolmogorov-Petrovsky-Piscounov (KPP) equation to the problem of high energy evolution of the QCD amplitudes. We explain how the traveling wave solutions of this equation are related to geometric scaling, a phenomenon observed in deep-inelastic scattering experiments. Geometric scaling is for the first time shown to result from an exact solution of nonlinear QCD evolution equations. Using general results on the KPP equation, we compute the velocity of the wave front, which gives the full high energy dependence of the saturation scale.     

A method for the calculation of Coulomb interference and rescattering corrections to total cross sections in pure spin states

We propose a dispersion theoretic approach to the calculation of Coulomb interference and rescattering corrections to total cross sections in pure spin states. Both types of corrections can be carried out only if the real parts of the forward amplitudes are known, which in general is not the case. However, we show that under some assumptions the unknown real parts enter linearly, which together with analyticity leads to a uniquely solvable integral equation. Our approach is particularly useful in pp and pd scattering where corresponding measurements have been or will be performed. Some applications are discussed.     

Transferred cross-relaxation and cross-correlation in NMR: effects of intermediate exchange on the determination of the conformation of bound ligands

Exchange transferred effects in solution-state NMR experiments allow one to determine the conformation of ligands that are weakly bound to macromolecules. Exchange-transferred nuclear Overhauser effect spectroscopy ('TR-NOESY') provides information about internuclear distances in a ligand in the bound state. Recently the possibility of obtaining dihedral angle information from a ligand in the bound state by exchange-transferred cross-correlation spectroscopy ('TR-CCSY') has been reported. In both cases the analysis of the signal amplitudes is usually based on the assumption that rapid exchange occurs between the free and bound forms of the ligand. In this paper we show that the fast exchange condition is not easily attained for observing exchange-transferred cross-correlation effects even in systems where exchange-transferred NOE can be observed. Extensive simulations based on analytical expressions for signal intensities corresponding to fast, intermediate, and slow chemical exchange have been carried out on a test system to determine the exchange regimes in which the fast exchange condition can be fulfilled for successfully implementing TR-NOESY and TR-CCSY.     

The space-time picture of the Wee partons and the AGK cutting rules in perturbative QCD

We discuss the space-time picture of scattering amplitudes with single and double ladder exchange in perturbative QCD. Particular emphasis is given to the Abramovsky Gribov Kanchelli (AGK) rules which describe the relative contributions of the diffractive dissociation and processes with other multiplicities to the elastic scattering amplitude. Inside the Pomeron Pomeron interaction vertices we find a new matrix which describes the transition from one s-cut to another and which goes beyond the original AGK rules.     

Symmetries of Regge-Regge cuts

Regge-Regge cuts are shown to satisfy strong symmetry constraints in any model which incorporates Finkelstein's cut selection rule, SU(3) symmetry of Regge residues, and exchange degeneracy of trajectories and residues. These imply, amongst other things, the strong suppression of Regge-Regge cuts in pion-nucleon charge exchange, arising from a cancellation between ?-P′ and A₂-ω cuts. Therefore if Finkelstein's selection rule is valid, the πN change amplitudes cannot be understood by adding Regge-Regge cuts to an absorbed ? pole amplitude.     

Inelastic diffractive scattering in nonperturbative QCD

We examine diffractive proton-proton scattering and photo- and electroproduction of mesons , where X denotes a proton or a final state, into which the proton can go by diffractive dissociation. Using a functional integral approach we derive the scattering amplitudes, which are governed by the expectation values of light-like Wegner-Wilson loops, which are then evaluated using the model of the stochastic vacuum. For the proton, we assume a quark-diquark structure. From the scattering amplitudes we calculate total and differential cross sections for high centre of mass energy and small momentum transfer and compare with experiments. Furthermore we calculate isovector form factors for the proton and the pion within the same model. Received: 30 January 2001 / Revised version: 29 June 2001 / Published online: 3 August 2001     

Integrated diffractive optical mode converter for fiber-to-waveguide coupling

An integrated diffractive optical mode converter, which can be integrated into planar lightwave circuits (PLCs), consisting of a diffractive optical element (DOE) and a slab waveguide is presented for fiber-to-waveguide coupling. The DOE is designed using iterative phase retrieval algorithm. In the iterative algorithm, we introduce a new modification of far-field amplitude constraint to provide very high mode conversion quality. Compared with previously published mode converters, the scheme is more universal because it is applicable for any waveguide structure. In simulation, coupling losses lower than 0.12 dB have been reached for all the discussed waveguides. The converter is shown to be polarization-insensitive and applicable in multi-wavelength PLCs. And the tolerance on axis misalignment has been investigated.     

原子和离子间激光感生碰撞电荷交换的微扰理论

将激光感生碰撞电荷看作一个四体系统，发展了激光感生碰撞电荷电荷的微扰理论，以独立原子和离子的复合态波函数作为激光感生碰撞体系的基组函数，得到了体系态振幅的运动方程。利用激光感生碰撞电荷交换的微扰理论，对Ｃａ＾＋－Ｓｒ间激光感生碰撞电荷交换进行了数值计算，并与Ｇｒｅｅｎ等人的实验结果进行了比较。