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Register a new userDispersion Theory and the Low Energy Constants for Neutral Pion Photoproduction
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B. Pasquini Universita din Pavia
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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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We study $eta$ photoproduction off the deuteron ($gamma dtoeta pn$) at a special kinematics: $sim 0.94$ GeV of the photon beam energy and $sim 0^circ$ of the scattering angle of the proton. This kinematics is ideal to extract the low-energy $eta$-nucleon scattering parameters such as $a_{eta N}$ (scattering length) and $r_{eta N}$ (effective range) because the $eta$-nucleon elastic scattering is significantly enhanced. We show that if a ratio $R$, the $gamma dtoeta pn$ cross section divided by the $gamma ptoeta p$ cross section convoluted with the proton momentum distribution in the deuteron, is measured with 5% error, ${rm Re}[a_{eta N}]$ (${rm Re}[r_{eta N}]$) can be determined at the precision of $simpm$0.1 fm ($simpm$0.5 fm), significantly narrowing down the currently estimated range of the parameters. The measurement is ongoing at the Research Center for Electron Photon Science (ELPH), Tohoku University.
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 of 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.
The few available data for the reactions $gamma p rightarrow K^{0} Sigma^{+}$ and $gamma n rightarrow K^{+} Sigma^{-}$ are compared to models developed for the processes $gamma p rightarrow K^{+} Sigma^{0}$ and $gamma p rightarrow K^{+} Lambda$. It is found that some of these phenomenological models overpredict the measurements by up to a factor of 100. Fitting the data for all of these reactions leads to drastically reduced Born coupling constants.
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.
Within a dynamical coupled-channels model which has already been fixed from analyzing the data of the pi N -> pi N and gamma N -> pi N reactions, we present the predicted double pion photoproduction cross sections up to the second resonance region, W< 1.7 GeV. The roles played by the different mechanisms within our model in determining both the single and double pion photoproduction reactions are analyzed, focusing on the effects due to the direct gamma N -> pi pi N mechanism, the interplay between the resonant and non-resonant amplitudes, and the coupled-channels effects. The model parameters which can be determined most effectively in the combined studies of both the single and double pion photoproduction data are identified for future studies.
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