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1 Eta production Resonances, meson couplings Humberto Garcilazo, IPN Mexico Dan-Olof Riska, Helsinki … exotic hadronic matter?

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2 1) Motivation. Generalities.Generalities. 2) The N system and the (non)existence of an eta-NN quasi-bound state. The d scattering problem.problem. The riddle of the enhancement of the pn eta d at threshold.at threshold. 3) The pp pp reaction at threshold.at threshold Probing NN NN* couplings.

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3 The eta is I=0. It is isospin selective and a clean probe for N*(I=1/2) resonances, contrarily to the pion. Threshold is dominated by s wave production (centrifugal barrier). S11(1353) resonance has a large eta branching ratio. Eta production data is a learning ground for studying the S11. etaN scattering length is very strong (min 0.3fm). May imply an exotic of hadronic matter: eta-mesic nuclei and eta-mesic hypernuclei.

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4 ( , ) Reactions Quasi-free 1 nucleon production Scaling with A 2/3 M.Robig-Landau,Phys.Rev. Lett.B 176, 257 (1986)

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5 Large cross-sections for eta absorption give eta mesons a small chance of escaping from nuclei. Mean free path at normal density is 2 fm. Study of eta-nuclei may provide clues on possible chiral symmetry restoration in a nuclear medium at normal densities (0.17 fm -3 ) In the SU(6) model, eta differs from 0 in an additional ss quark-antiquark structure. Information on the dynamical role of this pair in I) meson-baryon interactions for calculations of nuclear matter with strangeness. (Bruckner-Hartree-Fock) II) isospin symmetry breaking in few-body reactions (relate to the mixing angle). (Brookhaven, Nefkens et al. )Nefkens et al.

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6 The d scattering problem

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7 = + + = S11 d n n d d Reliable way of dealing with re-scattering: Faddeev summation

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8 Dynamics

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9 g 2 g 1

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10 N Dynamics Separable t directly fixed to scattering length t calculated dynamically from coupled LS equations and potentials A+p 2

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11 Different data analysis N Scattering length extracted from N N N N N N 1992 1985 1995 Krusche 0.579+ i0.394 Arima and Yazaki 0.980+ i0.37 Batinic et al. 0.876+ i0.274 Bhalerau and Liu 0.27+i0.22 Wilkin 0.30+ i0.30 Bennhold and Tanabe 0.25+i0.16

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12 Batinic et al. model

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13 Example of description quality obtained for the d NN reaction with model from Batinic et al.

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14 1999 Phys. Rev. C 60, 035208 A. M. Green and S. Wycech A, B, C, D models confirm larger value for Re a N 2 /dof 1999 A 0.87+i0.27 0.89 1999 B 1.23 1999 C 2.66 1999 D 1.54 1997 0.75+i0.27 0.83

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15 Eta N Scattering length eta-d MST eta-d Faddeev 0.25+i0.16 0.66+i0.71 0.64+i0.71 0.30+i0.30 0.39+i1.28 0.38+i.125 0.579+i0.399 -0.13+i2.64 -0.08+i2.31 0.876+i0.274 -0.76+i4.24 -1.54+i2.55 0.98+i0.37 -2.75+i2.77 -1.16+i2.05 Non-dynamical N model as input

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16 Deuteron-eta Real(a 0 ) changes sign as etaN a 0 increases This is not the whole story … there is NN short-range repulsion Energy

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17 Largest 2 Dynamical N models as input Larger than the value for which non-dynamical models give sign change Realistic NN short-range correlations wipe out the sign change

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18 A genuine three-particle scattering effect No resonant effect from a quasi-bound state.

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20 Ratio between A and driving term Minimum: 2.5 Maximum: 5.1

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21 Conclusions on np d : The enhancement for the reaction np d is explained within our calculations as a genuine three- body re-scattering effect. We predict a an enhancement factor from 2.5 to 5.1 depending on the off-shell properties of the etaN model. No evidence of a quasi-bound state for the etaNN system. Dynamical N models and realistic short-range interactions prevent it.

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22 The pp pp reaction

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23 impulse and exchange and exchange 1S01S0 3P03P0 exchange

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24 g NN coupling not sufficiently constrained by NN models g NN 2 /4 =0.25g NN 2 /4 =3-7 In this calculation : g NN 2 /4 =0.4 from photoproduction (L. Tiator, C. Bennhold)

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26 Impulse + re-scattering

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27 Another unknown coupling: NN* coupling cannot be determined from the decay width of N* N : N* lies below the threshold for that decay. A 3 quark-model was used for the baryons Impulse + re-scattering+ +

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28 Short-range contributions associated to the short-range NN force The NN interaction contains an isospin independent scalar exchange component Vs = v s (1-p 2 /M 2 )... The p 2 /M 2 term can be combined with the kinetic term: M*= M(1+ v s /M) two body correction from scalar and vector exchanges.

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29 Impulse + re-scattering+ short-range+ +

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30 Theoretical uncertainty The mechanism involves high momentum transfer Different NN interactions may have different effects

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31 Conclusions relative to the pp pp reaction: Large effect of the cross-section on the off-shell N scattering amplitude. Agreement with Batinic, Svarc and H. Lee. Large effect from non-resonant amplitudes from isoscalar scalar and vector exchanges. Only with a NN coupling constant smaller than the one used in earlier NN OBE models, namely the one extracted from the analysis of eta photoproduction data, allows a description of the data. ISI and FSI NN interactions are important. Dependence on the off-shell N scattering amplitude enables discrimination between extant models.

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32 A scientific theory cannot be verified ; only falsified. Karl Popper

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33 Off-shell structure given by the Dirac structure.

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34 N Dynamics Separable t directly fixed to scattering length t calculated dynamically from coupled LS equations and potentials A+p 2

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