The discrete ambiguities appearing in the complete experiment problem for single pseudoscalar meson photoproduction within truncated partial-wave analysis are discussed. It is shown that, in addition to the double ambiguity known from previous works, it is always necessary to take into account another ambiguity arising when truncation in total angular momentum is employed.
Ambiguities in pseudoscalar-meson photoproduction, arising from incomplete experimental data, have analogs in pion-nucleon scattering. Amplitude ambiguities have important implications for the problems of amplitude extraction and resonance identification in partial-wave analysis. The effect of these ambiguities on observables is described. We compare our results with those found in earlier studies.
We consider the problem of determining amplitudes from observables for the case of pseudoscalar meson photoproduction. We find a number of surprisingly simple constraints which give necessary conditions for a complete set of measurements. These results contradict one of the selection rules derived previously.
The complete experiment problem for photoproduction of single pseudoscalar mesons is reviewed briefly. If this problem is investigated in the context of a truncated partial wave analysis, the chance emerges to obtain a unique multipole solution measuring less polarization observables than demanded by the classical solution of the problem that is formulated in terms of spin amplitudes.
The role of dynamics in spin observables for pseudoscalar meson photoproduction is investigated using a density matrix approach in a multipole truncated framework. Extraction of novel rules for $γp \rightarrow π^+ n,~ K^+ Λ$ and $ηp$ reactions based on resonance dominance, and on other broad and reasonable dynamical assumptions, are discussed. Observables that are particularly sensitive to missing nucleonic resonances predicted by quark-based approaches, are singled out.
The amplitudes for photoproduction of two pseudoscalars on a nucleon are expanded in the overall c.m. frame in a model independent way with respect to the contribution of the final state partial wave of total angular momentum $J$ and its projection on the normal to the plane spanned by the momenta of the final particles. The expansion coefficients which are analogues to the multipole amplitudes for single meson photoproduction contain the complete information about the reaction dynamics. Results of an explicit evaluation are presented for the moments $W_{jm}$ of the inclusive angular distribut…
For photoproduction reactions with final states consisting of two pseudoscalar mesons and a spin-1/2 baryon, 8 complex amplitudes need to be determined uniquely. A modified version of Moravcsik's theorem is employed for these reactions, resulting in slightly over-complete sets of polarization observables that are able to determine the amplitudes uniquely. Further steps were taken to reduce the found sets to minimal complete sets. As a final result, multiple minimal complete sets without any remaining ambiguities are presented for the first time. These sets consist of $2N=16$ observables, conta…
Pseudoscalar-meson photoproduction is characterized by four complex reaction amplitudes. A complete set is a minimum theoretical set of observables that allow to determine these amplitudes unambiguously. It is studied whether complete sets remain complete when experimental uncertainty is involved. To this end, data from the GRAAL Collaboration and simulated data from a realistic model, both for the $γp \to K^+ Λ$ reaction, are analyzed in the transversity representation of the reaction amplitudes. It is found that only the moduli of the transversity amplitudes can be determined without ambigui…
The problem of extracting photoproduction amplitudes uniquely from so called complete experiments is discussed. This problem can be considered either for the extraction of full production amplitudes, or for the determination of multipoles. Both cases are treated briefly. Preliminary results for the fitting of multipoles, as well as the determination of their error, from recent polarization measurements in the $Δ$-region are described in more detail.
The problem of determining completely the spin amplitudes of photoproduction of two pseudoscalar mesons on a nucleon from observables is studied. The procedure of reconstruction of the scattering matrix elements from a complete set of observables is based on the expressions of all observables as quadratic hermitean forms in the reaction matrix elements which are derived explicitly. Their inversion allows one to find explicit solutions for the reaction matrix elements in terms of observables. Two methods for finding a complete set of observables are presented. In particular, one set was found, …
A complete set for pseudoscalar-meson photoproduction is a minimum set of observables from which one can determine the underlying reaction amplitudes unambiguously. The complete sets considered in this work involve single- and double-polarization observables. It is argued that for extracting amplitudes from data, the transversity representation of the reaction amplitudes offers advantages over alternate representations. It is shown that with the available single-polarization data for the p(γ,K^+)Λreaction, the energy and angular dependence of the moduli of the normalized transversity amplitude…
A truncated partial wave analysis for the photoproduction of two pseudoscalar mesons on a nucleon is discussed with respect to the determination of a complete set of observables. For the selection of such a set we have applied a criterion previously developed for photo- and electrodisintegration of a deuteron, which allows one to find a 'minimal' set of observables for determining the partial wave amplitudes up to possible discrete ambiguities. The question of resolving the remaining ambiguities by invoking additional observables is discussed for the simplest case, when the partial wave expans…
The subject of this doctoral study is the pseudoscalar meson photoproduction from nuclei. Two types of processes are investigated in this regard: coherent and quasifree processes. In the case of the coherent process, we study it for the photoproduction of pion and eta mesons. We place special emphasis on the various sources that put into question earlier nonrelativistic-impulse-approximation calculations. These include: final-state interactions, relativistic effects, off-shell ambiguities, and violations to the impulse approximation. By far the largest uncertainty emerges from the ambiguity in…
The question of pseudovector versus pseudoscalar coupling schemes for the kaon-hyperon-nucleon interaction is re-examined for the reaction $γp\to K^+ Λ$ in several isobaric models. These models typically include Born terms, $K^*$- and $K_1$-exchange in the t-channel, and a few different combinations of spin-1/2 baryon resonances in the $s$- and $u$-channels. The coupling constants are obtained by fitting to a large data set. We find that both pseudoscalar and pseudovector couplings can allow for a satisfactory description of the present database. The resulting coupling constants, $g_{KΛN}$ and…
The number and type of measurements needed to ascertain the amplitudes for pseudoscalar meson photoproduction are analyzed in this paper. It is found that 8 carefully selected measurements can determine the four transversity amplitudes without discrete ambiguities. That number of measurements is one less than previously believed. We approach this problem in two distinct ways: (1) solving for the amplitude magnitudes and phases directly; and (2) using a bilinear helicity product formulation to map an algebra of measurements over to the well-known algebra of the $4\times 4$ Gamma matrices. It is…
Spin-observables in pseudoscalar meson photoproduction is discussed. This work is complementary to the earlier works on this topic. Here, the reaction amplitude is expressed in Pauli-spin basis which allows to calculate all the observables straightforwardly. We make use of the fact that the underlying reflection symmetry about the reaction plane can be most conveniently and easily exploited in this basis to help finding the non-vanishing and independent observables in this reaction. The important issue of complete experiments is reviewed. By expressing the reaction amplitude in Pauli-spin basi…
It is shown that within a truncated partial wave analysis for photoproduction of two pseudoscalar mesons, it is possible to halve the number of independent partial amplitudes by taking into account parity conservation. In addition, within the framework of the proposed formalism, one can rather easily resolve the double discrete ambiguity arising from the symmetry under complex conjugation of the helicity amplitudes. This leads to essential simplifications of the complete experiment problem, at least as far as mathematical aspects are concerned.
[Background] A complete set is a minimum set of observables which allows one to determine the underlying reaction amplitudes unambiguously. Pseudoscalar-meson photoproduction from the nucleon is characterized by four such amplitudes and complete sets involve single- and double-polarization observables. [Purpose] Identify complete sets of observables, and study how measurements with finite error bars impact their potential to determine the reaction amplitudes unambiguously. [Method] The authors provide arguments to employ the transversity representation in order to determine the amplitudes in p…
We study the coherent photoproduction of pseudoscalar mesons---particularly of neutral pions---placing special emphasis on the various sources that put into question earlier nonrelativistic-impulse-approximation calculations. These include: final-state interactions, relativistic effects, off-shell ambiguities, and violations to the impulse approximation. We establish that, while distortions play an essential role in the modification of the coherent cross section, the uncertainty in our results due to the various choices of optical-potential models is relatively small (of at most 30%). By far t…
This dissertation treats the problem of complete experiments for pseudoscalar meson photoproduction, in the context of a truncated partial-wave analysis (TPWA). The work contains algebraic and numerical considerations. The influence of measurement uncertainties is examined using bootstrap methods. The thesis was originally published online by the University of Bonn in the 1st quarter of 2019 (links are given in the comments).
To learn about a physical system of interest, experimental results must be able to discriminate among models. We introduce a geometrical measure to quantify the distance between models for pseudoscalar-meson photoproduction in amplitude space. Experimental observables, with finite accuracy, map to probability distributions in amplitude space, and the characteristic width scale of such distributions needs to be smaller than the distance between models if the observable data are going to be useful. We therefore also introduce a method for evaluating probability distributions in amplitude space t…
Amplitude and partial wave analyses for pion, eta or kaon photoproduction are discussed in the context of `complete experiments'. It is shown that the model-independent helicity amplitudes obtained from at least 8 polarization observables including beam, target and recoil polarization can not be used to determine underlying resonance parameters. However, a truncated partial wave analysis, which theoretically requires only 5 observables will be possible with minimal model input.
Positivity constraints have proved to be important for spin observables of exclusive reactions involving polarized initial and final particles. Attention is focused in this note on the photoproduction of pseudoscalar mesons from spin 1/2 baryons, more specifically gamma+ N -> K+ Lambda, gamma+ N -> K Sigma, for which new experimental data are becoming available.
The complete experiment problem in the truncated partial wave analysis of pseudoscalar meson photoproduction with suppressed t-channel exchanges is investigated. The focus is set to ambiguities of the group S observables with the unpolarized differential cross section, $σ_0$, and the three single-spin observables, $Σ$, $T$ and $P$. For this purpose, the approach and formalism already worked out by Omelaenko in 1981 is revisited in this work. A numerical study using multipoles of the PWA solution MAID2007 shows how only one additional double polarization observable can resolve all ambiguities. …
A multipole analysis of vector meson photoproduction is formulated as a generalization of the pseudoscalar meson case. Expansion of spin observables in the multipole basis and behavior of these observables near threshold and resonances are examined.
In two meson photoproduction off a nucleon, for the case in which two of the three final state hadrons are products of the decay of an intermediate resonance, general expressions for its decay distribution and for polarization observables are derived in a model independent way. These are functions of either the spin density matrix elements (SDME's) or statistical tensors of the resonance, and the angles of its decay products. The expressions are general enough that it also describes cases where more than one resonance of arbitrary quantum numbers contributes, including interference effects. Th…
By exploiting the underlying symmetries of the relative phases of the pseudoscalar meson photoproduction amplitude, we determine all the possible sets of four double-spin observables that resolve the phase ambiguity of the amplitude in transversity basis up to an overall phase. The present results corroborate the original findings by Chiang and Tabakin [Phys. Rev. C 55, 2054 (1997)]. However, it is found that the completeness condition of four double-spin observables to resolve the phase ambiguity holds only when the relative phases do not meet the condition of equal magnitudes. In situations …
We have evaluated pseudoscalar and scalar neutral pion photoproduction in $\vecγp\toπ^0p$ and $\vecγp\to a_0^0p$ above the resonance region and within Regge phenomenology. Our fit, including GlueX $Σ$ pseudoscalar photoproduction data, shows that previous SLAC $Σ$ measurements for $\vecγp \to π^0p$ above $E_γ= 4~\mathrm{GeV}$ are at variance with SLAC data with more recent measurements made by GlueX in vicinity of $E_γ= 9~\mathrm{GeV}$. The Regge model predicts that the beam polarization asymmetry $Σ$ of the scalar meson is opposite to that of pseudoscalar meson photoproduction, however, the c…
A fully gauge-invariant (pseudoscalar) meson photoproduction amplitude off a nucleon including the final-state interaction is derived. The approach based on a comprehensive field-theoretical formalism developed earlier by one of the authors replaces certain dynamical features of the full interaction current by phenomenological auxiliary contact currents. A procedure is outlined that allows for a systematic improvement of this approximation. The feasibility of the approach is illustrated by applying it to both the neutral and charged pion photoproductions.
This paper combines the graph-theoretical ideas behind Moravcsik's theorem with a completely analytic derivation of discrete phase-ambiguities, recently published by Nakayama. The result is a new graphical procedure for the derivation of certain types of complete sets of observables for an amplitude-extraction problem with $N$ helicity-amplitudes. The procedure is applied to pseudoscalar meson photoproduction ($N = 4$ amplitudes) and electroproduction ($N = 6$ amplitudes), yielding complete sets with minimal length of $2N$ observables. For the case of electroproduction, this is the first time …
Partial wave amplitudes of meson photoproduction reactions are an important source of information in baryon spectroscopy. We investigate a new approach in single-energy partial wave analyses of these reactions. Instead of using a constraint to theoretical models in order to achieve solutions which are continuous in energy, we enforce the analyticity of the amplitudes at fixed values of the Mandelstam variable $t$. We present an iterative procedure with successive fixed-$t$ amplitude analyses which constrain the single-energy partial wave analyses and apply this method to the $γp \to ηp$ reacti…
Unconstrained partial-wave amplitudes obtained at discrete energies from fits to complete sets of experimental data may not vary smoothly with energy, and are in principle non-unique. We demonstrate how this behavior can be ascribed to the continuum ambiguity. Starting from the spinless scattering case, we demonstrate how an unknown overall phase depending on energy and angle mixes the structures seen in the associated partial-wave amplitudes making the partial wave decomposition non-unique, and illustrate it on a simple toy model. We then apply these principles to pseudo-scalar meson photopro…
Strangeness photoproduction in the elementary reactions $γN\rightarrow KY$ offers the possibility to study nucleon resonances in the mass region above 1.7 GeV, where the number of states and their properties are still under debate. These reactions could allow the first 'complete' experiment in pseudoscalar meson photoproduction due to the easier access to recoil polarization observables in experiments. In addition to measurements on proton targets, a full isospin decomposition of the $I=1/2$ electromagnetic amplitudes requires also data obtained from quasifree neutron targets. This contributio…
In this paper, we show that the low energy theorem (LET) of the threshold pion-photoproduction can be fully recovered in the quark model. An essential result of this investigation is that the quark-pion operators are obtained from the effective chiral Lagrangian, and the low energy theorem does not require the constraints on the internal structures of the nucleon. The pseudoscalar quark-pion coupling generates an additional term at order $μ=m_π/M$ only in the isospin amplitude $A^{(-)}$. The role of the transitions between the nucleon and the resonance $P_{33}(1232)$ and P-wave baryons are als…
Based on the hadronic model with the gauge prescription suggested by Ohta and Haberzettl, we investigate the possibility of determining the parity state of the $Θ^+$ baryon using photon induced processes, $γn\to K^- Θ^+$ and $γp\to \bar{K}^0 Θ^+$. The total and differential cross sections are simulated in two versions of pseudovector(PV) and pseudoscalar(PS) coupling schemes and the results are reported both on the positive and negative parity states of the $Θ^+$ baryon. It is found that in both coupling schemes the total cross sections from the neutron target are in general larger than those …
