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تسجيل مستخدم جديدComplete Experiments for Pion Photoproduction
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Lothar Tiator
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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.
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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 b
asis 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 where this condition occurs, it is shown that one needs extra chosen observables, resulting in the minimum number of observables required to resolve the phase ambiguity to reach up to eight, depending on the particular set of four double-spin observables considered. Furthermore, a way of gauging when the condition of equal magnitudes occurs is provided.
The electromagnetic pion production reactions are investigated within the dynamical coupled-channels model developed in {bf Physics Reports, 439, 193 (2007)}. The meson-baryon channels included in this study are $gamma N$, $pi N$, $eta N$, and the $p
iDelta$, $rho N$ and $sigma N$ resonant components of the $pipi N$ channel. With the hadronic parameters of the model determined in a recent study of $pi N$ scattering, we show that the pion photoproduction data up to the second resonance region can be described to a very large extent by only adjusting the bare $gamma N to N^*$ helicity amplitudes, while the non-resonant electromagnetic couplings are taken from previous works. It is found that the coupled-channels effects can contribute about 10 - 20 % of the production cross sections in the $Delta$ (1232) resonance region, and can drastically change the magnitude and shape of the cross sections in the second resonance region. The importance of the off-shell effects in a dynamical approach is also demonstrated. The meson cloud effects as well as the coupled-channels contributions to the $gamma N to N^*$ form factors are found to be mainly in the low $Q^2$ region. For the magnetic M1 $gamma N to Delta$ (1232) form factor, the results are close to that of the Sato-Lee Model. Necessary improvements to the model and future developments are discussed.
The reactions $gamma ptopi^0 p$ and $gamma ptopi^+ n$ are analyzed in a semi-phenomenological approach up to $Esim2.3$ GeV. Fits to differential cross section and single and double polarization observables are performed. A good overall reproduction o
f the available photoproduction data is achieved. The Julich2012 dynamical coupled-channel model -which describes elastic $pi N$ scattering and the world data base of the reactions $pi Ntoeta N$, $KLambda$, and $KSigma$ at the same time - is employed as the hadronic interaction in the final state. The framework guarantees analyticity and, thus, allows for a reliable extraction of resonance parameters in terms of poles and residues. In particular, the photocouplings at the pole can be extracted and are presented.
[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 pseudoscalar-meson photoproduction. It is studied whether the amplitudes in the transversity basis for the $gamma p to K^+Lambda$ reaction can be estimated without ambiguity. To this end, data from the GRAAL collaboration and mock data from a realistic model are analyzed. [Results] It is illustrated that the moduli of normalized transversity amplitudes can be determined from precise single-polarization data. Starting from mock data with achievable experimental resolution, it is quite likely to obtain imaginary solutions for the relative phases of the amplitudes. Also the real solutions face a discrete phase ambiguity which makes it impossible to obtain a statistically significant solution for the relative phases at realistic experimental conditions. [Conclusions] Single polarization observables are effective in determining the moduli of the amplitudes in a transversity basis. Determining the relative phases of the amplitudes from double-polarization observables is far less evident. The availability of a complete set of observables does not allow one to unambiguously determine the reaction amplitudes with statistical significance.
The relativistic amplitudes of pion photoproduction are evaluated by dispersion relations at t=const. The imaginary parts of the amplitudes are taken from the MAID model covering the absorption spectrum up to center-of-mass energies W = 2.2 GeV. For
sub-threshold kinematics the amplitudes are expanded in powers of the two independent variables u and t related to energy and momentum transfer. Subtracting the loop corrections from this power series allows one to determine the counter terms of covariant baryon chiral perturbation theory. The proposed continuation of the amplitudes into the unphysical region provides a unique framework to derive the low-energy constants to any given order as well as an estimate of the higher order terms by global properties of the absorption spectrum.
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