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Toward an understanding of discrete ambiguities in truncated partial-wave analyses
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Partial waves in B s * B ¯ s * production in e + e − annihilation near threshold
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Relativistic partial waves for celestial amplitudes
The formalism of relativistic partial wave expansion is developed for four-point celestial amplitudes of massless external particles. In particular, relativistic partial waves are found as eigenfunctions to the product representation of celestial Poincaré Casimir operators with appropriate eigenvalues. The requirement of hermiticity of Casimir operators is used to fix the corresponding integral inner product, and orthogonality of the obtained relativistic partial waves is verified explicitly. The completeness relation, as well as the relativistic partial wave expansion follow. Example celestial amplitudes of scalars, gluons, gravitons and open superstring gluons are expanded on the basis of relativistic partial waves for demonstration. A connection with the formulation of relativistic partial waves in the bulk of Minkowski space is made in appendices.
Direct Calculation of the Scattering Amplitude Without Partial Wave Decomposition: Inclusion of Correlation Effects - III
In the first two papers in this series, we developed a method for studying electron-hydrogen scattering that does not use partial wave analysis. We constructed an ansatz for the wave function in both the static and static exchange approximations and calculated the full scattering amplitude. Here we go beyond the static exchange approximation, and include correlation in the wave function via a modified polarized orbital. This correlation function provides a significant improvement over the static exchange approximation: the resultant elastic scattering amplitudes are in very good agreement with fully converged partial wave calculations for electron-hydrogen scattering. A fully variational modification of this approach is discussed in the conclusion of the article Popular summary of Direct calculation of the scattering amplitude without partial wave expansion. III ....." by J. Shertzer and A. Temkin. In this paper we continue the development of In this paper we continue the development of a new approach to the way in which researchers have traditionally used to calculate the scattering cross section of (low-energy) electrons from atoms. The basic mathematical problem is to solve the Schroedinger Equation (SE) corresponding the above physical process. Traditionally it was always the case that the SE was reduced to a sequence of one-dimensional (ordinary) differential equations - called partial waves which were solved and from the solutions "phase shifts" were extracted, from which the scattering cross section was calculated.
Dynamically-coupled partial-waves in ρπ isospin-2 scattering from lattice QCD
We present the first determination of ρπ scattering, incorporating dynamically-coupled partial-waves, using lattice QCD, a first-principles numerical approach to QCD. Considering the case of isospin-2 ρπ, we calculate partial-wave amplitudes with J ≤ 3 and determine the degree of dynamical mixing between the coupled S and D-wave channels with J P = 1 + . The analysis makes use of the relationship between scattering amplitudes and the discrete spectrum of states in the finite volume lattice. Constraints on the scattering amplitudes are provided by over one hundred energy levels computed on two lattice volumes at various overall momenta and in several irreducible representations of the relevant symmetry groups. The spectra follow from variational analyses of matrices of correlations functions computed with large bases of meson-meson operators. Calculations are performed with degenerate light and strange quarks tuned to the physical strange quark mass so that m π ~700 MeV, ensuring that the ρ is stable against strong decay. Furthermore, this work demonstrates the successful application of techniques, opening the door to calculations of scattering processes that incorporate the effects of dynamically-coupled partial-waves, including those involving resonances or bound states.
Relative partial wave theory of diatomic molecules
Relative partial wave theory used in investigating excited state of diatomic molecules
Partial wave calculation of the diatomic molecule
Partial wave calculation of diatomic divalent molecular /HeH/ ion
Correlations of π N partial waves for multireaction analyses
In the search for missing baryonic resonances, many analyses include data from a variety of pion- and photon-induced reactions. For elastic πN scattering, however, usually the partial waves of the SAID (Scattering Analysis Interactive Database) or other groups are fitted, instead of data. We provide the partial-wave covariance matrices needed to perform correlated χ 2 fits, in which the obtained χ 2 equals the actual χ 2 up to nonlinear and normalization corrections. For any analysis relying on partial waves extracted from elastic pion scattering, this is a prerequisite to assess the significance of resonance signals and to assign any uncertainty on results. Lastly, the influence of systematic errors is also considered.
Single-channel and single-energy partial-wave analysis with continuity improved through minimal phase constraints
Single-energy partial-wave analysis has often been applied as a way to fit data with minimal model dependence. However, remaining unconstrained, partial waves at neighboring energies will vary discontinuously because the overall amplitude phase cannot be determined through single-channel measurements. This problem can be mitigated through the use of a constraining penalty function based on an associated energy-dependent fit. However, the weight given to this constraint results in a biased fit to the data. In this paper, for the first time, we explore a constraining function which does not influence the fit to data. The constraint comes from the overall phase found in multichannel fits which, in the present study, are the Bonn-Gatchina and Jülich-Bonn multichannel analyses. The data are well reproduced and weighting of the penalty function does not influence the result. The method is applied to KΛ photoproduction data and all observables can be maximally well reproduced. While the employed multichannel analyses display very different multipole amplitudes, we show that the major difference between two sets of multipoles can be related to the different overall phases.
Exploring Resonance Structures in the Partial-Wave Analysis of ¿p0 Photoproduction at GlueX
This thesis studies what happens when a photon (¿) collides with a proton (p) and produces a neutral omega (¿) and pion (p0) pair, with a recoiling proton (p'), expressed as ¿p ¿ ¿p0p'. We study this and other reactions to better understand the strong nuclear force; one of the four fundamental forces that govern all the physics of the universe. This force is specifically responsible for the binding and decay of subatomic particles, such as the ones here. While we understand the ¿ and p0, what we are actually interested in is a short-lived unknown particle X that decays via X ¿ ¿p0. There are a multitude of possible particles X can be, and so our focus in this work is to find out what X is by determining its properties from the particles we measure. We do this via an intricate analysis procedure known as “partial-wave analysis”. By analogy, one can think of our particle detector as a buoy, and the particles we want to analyze (X) as pebbles hitting a pond. The waves created by the pebble will move our buoy, giving us information about the pebble that produced the wave. However, when multiple pebbles hit our pond, the waves overlap and interfere with each other. Our buoy only can measure the complicated interfering result of all the waves. To disentangle this, our partial-wave analysis works by modeling this interference pattern so that we may infer the properties of the pebbles (particles) we produced. In this thesis, we review the relevant experimental history in photoproduction and related production mechanisms, as well as the theoretical foundations that motivate our measurement. We describe the methods used to collect our data at the GlueX experiment stationed at the Jefferson Lab accelerator facility in Newport News, Virginia. We then detail the selections we apply to ensure our events are almost exclusively ¿p ¿ ¿p0p'. We cover the intensity model, how we verify its capabilities, and finally present our results together with systematic studies. Our primary result is the detection of a b1(1235) meson interfering with a wide JPC = 1-- vector state, measured via a mass-independent partial-wave analysis. It provides precise experimental results that can be used as input for theoretical models of the reaction, yielding conclusions about the procedures responsible for how our universe behaves at its most basic level.
Ambiguities in the partial-wave analysis of the photoproduction of pairs of pseudoscalar mesons
Applying the technique of partial-wave analysis, there are cases where more than one set of underlying complex-valued amplitudes can describe the measured observables. These ambiguities can sometimes be resolved using additional information, but assumptions are often required. It is known that the partial-wave analysis of two-pseudoscalar meson systems produced in photoproduction with a linearly polarized photon beam is free from discrete ambiguities stemming from the Barrelet zeros when the nucleon spin is ignored. In this article, we show that continuous ambiguities are possible for certain wave sets, even though the discrete ambiguities do not appear. We also explore ways to resolve these ambiguities and determine the maximal amount of information that can be obtained from analyses that suffer from these continuous ambiguities.
Partial-wave projection of relativistic three-body amplitudes
We derive the integral equations for partial-wave projected three-body scattering amplitudes, starting from the integral equations for three-body amplitudes developed for lattice QCD analyses. The results, which hold for generic three-body systems of spinless particles, build upon the recently derived partial-wave projected one-particle exchange, a primary component of the relativistic framework proven to satisfy 𝑆 matrix unitarity. We derive simplified expressions for factorizable short-distance interactions, 𝒦 3 , in two equivalent formalisms—one symmetric under particle interchange and one asymmetric. For the asymmetric case, we offer parametrizations useful for amplitude analysis. Finally, we examine toy models for 3𝜋 systems at unphysically heavy pion masses with total isospins 0, 1, and 2.
Partial-wave analyses of γ p → η p and γ n → η n using a multichannel framework
This paper introduces results from partial-wave analyses of the photoproduction reactions γp→ηp and γn→ηn. World data for the observables dσ/dΩ, Σ, T, P, F, and E were analyzed as part of this work. The dominant amplitude in the fitting range from threshold to a c.m. energy of 1900 MeV was found to be S 11 in both reactions, consistent with results of other groups. At c.m. energies above 1600 MeV, our solution deviates from published results, with this work finding higher-order partial waves becoming significant. Data off the proton imply that the higher-order terms contributing to the reaction include P 11 , P 13 , and F 15 . The final results also hint that F 17 is needed to fit double-polarization observables above 1900 MeV. Data off the neutron show a contribution from P 13 , as well as strong contributions from D 13 and D 15 .
Partial-wave projection of the one-particle exchange in three-body scattering amplitudes
As the study of three-hadron physics from lattice QCD matures, it is necessary to develop proper analysis tools in order to reliably study a variety of phenomena, including resonance spectroscopy and nuclear structure. Reconstructing the three-particle scattering amplitude requires solving integral equations, which can be written in terms of data-constrained dynamical functions and physical on shell quantities. The driving term in these equations is the so-called one-particle exchange, which leads to a kinematic divergence for particles on mass shell. A vital component in defining three-particle amplitudes with definite parity and total angular momentum, which are used in spectroscopic studies, is to project the one-particle exchange into definite partial waves. We present a general procedure to construct exact analytic partial-wave projections of the one-particle exchange contribution for any system composed of three spinless hadrons. Our result allows one full control over the analytic structure of the projection, which we explore for some low-lying partial waves with applications to three pions. Published by the American Physical Society 2024
Calculation of the Full Scattering Amplitude without Partial Wave Decomposition: Inclusion of Exchange - 2
The development of a practical method of accurately calculating the full scattering amplitude, without making a partial wave decomposition is continued. The method is developed in the context of electron-hydrogen scattering, and here exchange is dealt with by considering e-H scattering in the static exchange approximation. The Schroedinger equation in this approximation can be simplified to a set of coupled integro-differential equations. The equations are solved numerically for the full scattering wave function. The scattering amplitude can most accurately be calculated from an integral expression for the amplitude; that integral can be formally simplified, and then evaluated using the numerically determined wave function. The results are essentially identical to converged partial wave results.
Partial Wave Dispersion Relations: Application to Electron-Atom Scattering
In this Letter we propose the use of partial wave dispersion relations (DR's) as the way of solving the long-standing problem of correctly incorporating exchange in a valid DR for electron-atom scattering. In particular a method is given for effectively calculating the contribution of the discontinuity and/or poles of the partial wave amplitude which occur in the negative E plane. The method is successfully tested in three cases: (i) the analytically solvable exponential potential, (ii) the Hartree potential, and (iii) the S-wave exchange approximation for electron-hydrogen scattering.