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Determination of the eta-proton scattering length in free space

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 Added by Eryk Czerwinski
 Publication date 2014
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and research's language is English




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Taking advantage of both the high mass resolution of the COSY-11 detector and the high energy resolution of the low-emittance proton-beam of the Cooler Synchrotron COSY we determine the excitation function for the pp --> pp eta reaction close-to-threshold. Combining these data with previous results we extract the scattering length for the eta-proton potential in free space to be Re(a_{p eta}) = 0+-0.43 fm and Im(a_{p eta}) = 0.37(+0.40)(-0.16) fm.



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The $pp to pp eta^{prime}$ (958) reaction has been measured at COSY using the internal beam and the COSY-11 facility. The total cross sections at the four different excess energies mbox{$ Q = ~1.5 ~MeV, ~1.7 ~MeV, ~2.9 ~MeV,$ and $ ~4.1 MeV$} have been evaluated to be mbox{$ sigma = 2.5 pm 0.5~nb$, $~~~ 2.9 pm 1.1~nb$, $~~~ 12.7 pm 3.2~nb$, ~ and $~~~ 25.2 pm 3.6 ~nb $}, respectively. In this region of excess energy the $eta^{prime}$ (958) cross sections are much lower compared to those of the $pi ^0$ and $eta$ production.
A comparison of the close-to-threshold total cross sections for the eta-prime meson production in both the pp --> pp eta-prime and pn --> pn eta-prime reactions should provide insight into the flavour-singlet (perhaps also into gluonium) content of the eta-prime meson and the relevance of quark-gluon or hadronic degrees of freedom in the creation process. The excitation function for the reaction pp --> pp eta-prime has been already established. At present, experimental investigations of the quasi-free pn --> pn X reactions are carried out at the COSY-11 facility using a beam of stochastically cooled protons and the deuteron cluster target. A method of measurement and preliminary results from the test experiments of the pn --> pn eta reaction are presented in this report.
The present paper reports high-accuracy cross-section data for the 2H(n,nnp) reaction in the neutron-proton (np) and neutron-neutron (nn) final-state-interaction (FSI) regions at an incident mean neutron energy of 13.0 MeV. These data were analyzed with rigorous three-nucleon calculations to determine the 1S0 np and nn scattering lengths, a_np and a_nn. Our results are a_nn = -18.7 +/- 0.6 fm and a_np = -23.5 +/- 0.8 fm. Since our value for a_np obtained from neutron-deuteron (nd) breakup agrees with that from free np scattering, we conclude that our investigation of the nn FSI done simultaneously and under identical conditions gives the correct value for a_nn. Our value for a_nn is in agreement with that obtained in pion-deuteron capture measurements but disagrees with values obtained from earlier nd breakup studies.
We describe a novel technique for comparing total cross sections for the reactions pp --> pp pi(0), pp --> pp eta, and pp --> pp eta close to threshold. The initial and final state proton-proton interactions are factored out of the total cross section, and the dependence of this reduced cross section on the volume of phase space is discussed. Different models of the proton-proton interaction are compared. We argue that the scattering length of the S-wave eta-proton interaction is of the order of 0.1 fm.
Photoproduction of the $omega$ meson on the proton has been experimentally studied near the threshold. The total cross sections are determined at incident energies ranging from 1.09 to 1.15 GeV. The 1/2 and 3/2 spin-averaged scattering length $a_{omega p}$ and effective range $r_{omega p}$ between the $omega$ meson and proton are estimated from the shape of the total cross section as a function of the incident photon energy: $a_{omega p} = left(-0.97^{+0.16_{rm stat}}_{-0.16_{rm stat}}{}^{+0.03_{rm syst}}_{-0.00_{rm syst}}right)+i left(0.07^{+0.15_{rm stat}}_{-0.14_{rm stat}}{}^{+0.17_{rm syst}}_{-0.09_{rm syst}}right)$ fm and $r_{omega p}=left(+2.78^{+0.68_{rm stat}}_{-0.54_{rm stat}}{}^{+0.11_{rm syst}}_{-0.13_{rm syst}}right)+ileft(-0.01^{+0.46_{rm stat}}_{-0.50_{rm stat}}{}^{+0.07_{rm syst}}_{-0.00_{rm syst}}right)$ fm, resulting in a repulsive force. The real and imaginary parts for $a_{omega p}$ and $r_{omega p}$ are determined separately for the first time. A small $P$-wave contribution does not affect the obtained values.
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