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).
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.
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…
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. …
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.
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 …
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.
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.
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.
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 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…
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…
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…
We study the photoproduction of scalar mesons close to the threshold of f_0(980) and a_0(980) using a unitary chiral model. Peaks for both resonances show up in the invariant mass distributions of pairs of pseudoscalar mesons. A discussion is made on the photoproduction of these resonances in nuclei, which can shed light on their nature, a subject of continuous debate.
[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…
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.
Amplitude- and truncated partial-wave analyses are combined into a single procedure and a novel, almost theory-independent single-channel method for extracting multipoles directly from measured data is developed. In practice, we have created a two-step procedure which is fitted to the same data base: in the first step we perform an energy independent amplitude analysis where continuity is achieved by constraining the amplitude phase, and the result of this first step is then taken as a constraint for the second step where a constrained, energy independent, truncated partial-wave analysis is do…
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.
The possibilities of a model-independent partial wave analysis for pion, eta or kaon photoproduction are discussed in the context of complete experiments. It is shown that the helicity amplitudes obtained from at least 8 polarization observables including beam, target and recoil polarization can not be used to analyze nucleon resonances. However, a truncated partial wave analysis, which requires only 5 observables will be possible with minimal model assumptions.
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…
A gauge-invariant formalism is presented for the practical treatment of photo- and electroproduction of pseudoscalar mesons off nucleons that allows an explicit incorporation of hadronic final-state interactions. The semi-phenomenological approach is based on a field theory developed by one of the authors. It generalizes an earlier approach by allowing for systematic improvement of approximations in a controlled manner. The practical feasibility is illustrated by applying the lowest-order result to the photoproduction of both neutral and charged pions.
General expressions for the unpolarized differential cross section and for various polarization observables in the coherent pseudoscalar meson photo- and electroproduction on the deuteron target have been obtained in one-photon-exchange approximation. The spin structure of the matrix element is explicitly derived in terms of structure functions. The correspondence with the helicity amplitudes is given. The polarization effects have been investigated for the case of a longitudinally polarized electron beam and vector or tensor polarized deuteron target. The polarization (vector or tensor) of th…
Recent CLAS photoproduction results using a tagged bremsstrahlung photon beam for the ground-state pseudoscalar meson photoproduction channels ($K^+ Λ$, $K^+ Σ^0$, $ηp$, $π^+ n$ and $π^0 p$) show a normalization discrepancy with older results from SLAC, DESY and CEA that used an untagged bremsstrahlung beam. The CLAS results are roughly a factor of two smaller than the older data. The CLAS $K^+Λ$ and $K^+Σ^0$ results are in excellent agreement with the latest LEPS results that also employed a tagged beam. For the vector meson ($ωp$ and $ϕp$) channels, CLAS agrees with SLAC results that employe…
The kaon photoproduction is analyzed up to $E_γ^{\rm Lab}$=2.0 GeV by using an isobaric model based on effective Lagrangians and by taking a cross symmetry into account. Both {\it pseudovector} and {\it pseudoscalar} couplings for kaon-baryon-baryon (baryon spin=1/2) interactions are considered with form factors. A vector meson($K^*(890)$), an axial vector meson($K_1(1270)$), nucleon resonances($J\le5/2$), and hyperon resonances($J\le3/2$) are treated as participating particles. By determining unknown coupling constants through a systematic fitting of the differential cross section, the total …
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 …
We compare the methods of amplitude reconstruction, for a complete experiment and a truncated partial wave analysis, applied to the photoproduction of pseudo-scalar 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).
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…
We provide an analysis of vector meson photoproduction in the channel of the vector meson decaying into a pseudoscalar meson plus a photon, i.e. $V\to Pγ$. It is shown that non-trivial kinematic correlations arise from the measurement of the $Pγ$ angular distributions in the overall c.m. system in comparison with those in the vector-meson-rest frame. In terms of the vector meson density matrix elements, the implication of such kinematic correlations in the measurement of polarization observables is discussed. For the $ω$ meson production, due to its relatively large branching ratios for $ω\toπ…
A study of nonstrange meson-baryon systems has been made with the idea of understanding the properties of the low-lying $1/2^-$ $N^*$ and $Δ$ resonances. The coupled channels are built by considering the pseudoscalar and vector mesons together with the octet baryons. The formalism is based on obtaining the interactions from the lowest order chiral Lagrangian when dealing with pseudoscalar mesons and relying on the hidden local symmetry in case of the vector mesons. The transition between the two systems is obtained by replacing the photon by a vector meson in the Kroll-Ruderman theorem for the…
We compare the methods of amplitude reconstruction, for a complete experiment and a truncated partial-wave analysis, applied to the electroproduction of pseudoscalar mesons. We give examples which show, 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 connection is made to existing data.
The $γp \to ϕηp$ reaction is studied in the kinematic region where the $ηp$ final state originates dominantly from the decay of the N*(1535) resonance. The threshold laboratory photon energy for this reaction (at the peak of the S11 resonance) is $E_γ^{Lab} = $3 GeV. We will discuss it somewhat above threshold, at $E_γ^{Lab}\simeq 4-5$ GeV, in order to reach lower (absolute) values of the squared 4-momentum transfer from the initial photon to the final $ϕ$-meson. In these conditions, we expect the t-channel $π^0$- and $η$-meson exchanges to drive the dynamics underlying the $γp \to ϕηp$ proces…
We introduce an extension to the ladder truncated Bethe-Salpeter equation for mesons and the rainbow truncated quark Dyson-Schwinger equations which includes quark-loop corrections to the gluon propagator. This truncation scheme obeys the axialvector Ward-Takahashi identity relating the quark self-energy and the Bethe-Salpeter kernel. Two different approximations to the Yang-Mills sector are used as input: the first is a sophisticated truncation of the full Yang-Mills Dyson-Schwinger equations, the second is a phenomenologically motivated form. We find that the spectra and decay constants of p…
We investigate the reaction mechanism of the $ϕ$-meson photoproduction off the proton target, i.e., $γp\toϕp$, up to $\sqrt{s}=2.8$ GeV. For this purpose, we employ an effective Lagrangian approach in the tree-level Born approximation, and we employ various experimental and theoretical inputs. As a theoretical setup, the vectorlike Pomeron ($C=+1$) is taken into account as a parameterized two-gluon exchange contribution. We also consider $f_1(1285)$ axial-vector-meson, ($π,η$) pseudoscalar-meson, and ($a_0,f_0$) scalar-meson exchanges in the $t$ channel, in addition to the experimentally confi…
In this paper, we calculate the masses and mixing angles of L=1 negative parity N* resonances in an extended GBE (Goldstone-boson-exchange model) with harmonic-oscillator wave functions. By using those mixing angles, we get their photoproduction amplitudes, and compare them with experimental data and the results of OPE (one-pion-exchange model), OPsE (only pseudoscalar meson exchange model), and OGE (one-gluon-exchange model). We find that the extended GBE gives right internal wave functions. It is essential to extend GBE to include not only pseudoscalar meson exchanges but also vector meson e…
The pseudoscalar and pseudovector $ηN$ coupling constants are calculated from an effective vertex associated with the $a_0(980)πN$ triangle diagram. The predicted values are in agreement with the ones concluded from fitting $η$ photoproduction amplitudes. In this context we stress the importance of the properties of the scalar meson octet for $η$ meson physics.
Photoproduction of neutral pseudoscalar mesons $π^0,η(547)$ and $η'(958)$ in the Coulomb field of an atomic nucleus is studied using a model which describes the Primakoff and nuclear parts of the production amplitude. At high energies the nuclear background is dominated by the exchange of $C$-parity odd Regge trajectories. In the coherent production the isospin filtering makes the $ω(782)$ a dominant trajectory. The calculations are in agreement with $π^0$ data from JLAB provided the photon shadowing and final state interactions of mesons are taken into account. The kinematic conditions which …
We show that the contact couplings of neutral pseudoscalar and axial mesons to the nucleon are proportional to $Δs$, the fraction of nucleon spin carried by the strange quark sea, and thus are strongly suppressed relative to the couplings of charged mesons to the nucleon. On the other side, recent high accuracy data on $η$ photoproduction at threshold reveal the need for non--negligibile $ηNN$ vertices, while fitting $\bar N N$ phase shifts by means of effective meson exchange potentials requires a substantial presence of $f_1$ mesons there. We here advocate the idea to attribute the couplings…
The LEPS/SPring-8 experiment made a comprehensive measurement of the spin-density matrix elements for $γp \to ϕp$, $γd \to ϕp n$ and $γd \to ϕd$ at forward production angles. A linearly polarized photon beam at $E_γ$=1.6-2.4 GeV was used for the production of $ϕ$ mesons. The natural-parity Pomeron exchange processes remains dominant nearthreshold. The unnatural-parity processes of pseudoscalar exchange is visible in the production from nucleons but is greatly reduced in the coherent production from deuterons. There is no strong $E_γ$-dependence, but some dependence on momentum-transfer. A smal…
Based on Compton scattering and meson photoproduction data the polarizabilities of the nucleon are precisely studied and well understood due to recent experimental and theoretical work based on nonsubtracted dispersion relations. The {\it recommended} experimental values are $α_p=12.0\pm 0.6$, $(12.0)$, $β_p=1.9\mp 0.6$, $(1.9)$, $α_n=12.5\pm 1.7$, $(12.7\pm 0.9)$, $β_n=2.7\mp 1.8$, $(2.5\mp 0.9)$ in units of $10^{-4}$fm$^3$ and $γ^{(p)}_π=-36.4\pm 1.5$, $(-36.6)$, $γ^{(n)}_π=+58.6\pm 4.0$, $(58.3)$, $(γ^{(p)}_0=-0.58\pm 0.20)$, $γ^{(n)}_0=0.38\pm 0.22)$ in units of $10^{-4}$fm$^4$ [1]. The nu…
