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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.
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.
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
Amplitude reconstruction from complete photoproduction experiments and truncated partial-wave expansions
Here, we compare the methods of amplitude reconstruction, for a complete experiment and a truncated partial-wave analysis, applied to the photoproduction of pseudoscalar mesons. The approach is pedagogical, showing in detail how the amplitude reconstruction (observables measured at a single energy and angle) is related to a truncated partial-wave analysis (observables measured at a single energy and a number of angles).
A new scintillation hodoscope for CLAS12 and partial wave analysis of the channel yp → pK + K -
This thesis consists of two parts that have contributed to a new meson spectroscopy program, MesonEx, which is currently taking place in Hall B of the upgraded Thomas Jefferson National Accelerator Facility (JLab) in the USA. The first, hardware part, presents design, testing, construction and calibration of a fast-timing scintillation Hodoscope for a new Forward Tagger detector, that has been installed inside the upgraded CEBAF Large Acceptance Spectrometer (CLAS12) which is situated in the Hall B of JLab. The Forward Tagger is a key apparatus for measurement of quasi-real photoproduction of mesons in the MesonEx, and a necessary device for other new hadron spectroscopy programs. The second, software and analysis part, presents contributions to the general HAdron SPEctroscopy CenTre (HASPECT) analysis framework, that has been developed in preparation for the MesonEx data analysis. The software contribution consists of finalizing HASPECT simulation and analysis chains in a model-independent way, and developing a mass-independent partial wave analysis procedure. This procedure has been tested via analysis of the γ p → pK + K - channel from the g 11 a CLAS data, in the photon energy range E γ = 3.0-3.8 GeV and momentum transfer squared range -t = 0.6 - 0.7 (GeV/c 2 ) 2 . The first result of this analysis is the differential cross section for the ϕ(1020) resonance photoproduction. This result has been compared with a previous analysis result, and a good agreement has validated the developed analysis procedure. Furthermore, S , P and D partial waves have been extracted from the data set, using the same procedure, and ambiguous solutions for these partial waves have been calculated, using the method of Barrelet zeros which is for the first time applied to photoproduction of the K + and K - mesons on the proton. Distributions of the calculated solutions have been compared with the fit results. It is found that the physical solution contains contributions of the ϕ(1020) in the P -wave and the a 2(1320) in the D -wave.
The exact discontinuity of a partial wave along the left-hand cut and the exact N∕D method in non-relativistic scattering
We first deduce the analytical continuation in the complex planes of the initial and final three-momenta of the Lippmann–Schwinger equation in coupled or uncoupled partial-wave amplitudes. This result allows us to deduce a master equation whose solution is the exact discontinuity of the on-shell partial-wave amplitudes along the left-hand cut. This equation is always a linear non-singular integral equation whose solution is fixed exclusively by the knowledge of the potential, applicable to either regular or singular potentials. The capability of calculating exactly this discontinuity allows one to settle the exact N∕D method in two-body non-relativistic scattering for coupled and uncoupled waves. We exemplify this new advance in scattering theory by explicitly checking the agreement between the Lippmann–Schwinger equation with the corresponding solutions of the exact N∕D method for some examples that involve regular and singular potentials, either attractive or repulsive.
Symmetrizing relativistic three-body partial wave amplitudes
S matrix principles and symmetries impose constraints on three-particle scattering amplitudes, which can be formulated as a class of integral equations for their partial wave projections. However, these amplitudes are typically expressed in an asymmetric basis, where one of the initial and final state particles is singled out, and all quantum numbers are defined relative to this spectator. In this work, we show how to construct symmetric partial wave amplitudes, which have been symmetrized over all possible spectator combinations, using their asymmetric counterparts and sets of recoupling coefficients. We derive these recoupling coefficients for arbitrary angular momentum and isospin for arbitrary systems of spinless particles with SU(2) flavor symmetry. We propose a simple intensity observable suitable for visualizing the structure of three-body dynamics in Dalitz distributions. Finally, we provide some numerical examples of Dalitz distributions relevant for future lattice QCD calculations of 3𝜋 systems and provide numerical evidence that the symmetrization procedure is consistent with expected symmetries of Dalitz plots.
Secondary γ-ray decays from the partial-wave $\textit{T}$ matrix with an $\textit{R}$-matrix application to 15 N($p, α_1γ$) 12 C
The secondary γ rays emitted following a nuclear reaction are frequently relatively straightforward to detect experimentally. Despite the large volume of such data, a practical formalism for describing these γ rays in terms of partial-wave $\textit{T}$-matrix elements has never been given. The partial-wave formalism is applicable when $\textit{R}$-matrix methods are used to describe the reaction in question. This paper supplies the needed framework, and it is demonstrated by the application to the 15 N($p, α_1γ$) 12 C reaction.