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

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.

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.

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

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.

6 The  d scattering problem

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

8 Dynamics

9 g 2 g 1

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

11 Different data analysis  N Scattering length extracted from  N   N  N  N  N  N Krusche i0.394 Arima and Yazaki i0.37 Batinic et al i0.274 Bhalerau and Liu 0.27+i0.22 Wilkin i0.30 Bennhold and Tanabe 0.25+i0.16

12 Batinic et al. model

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

Phys. Rev. C 60, A. M. Green and S. Wycech A, B, C, D models confirm larger value for Re a  N  2 /dof 1999 A 0.87+i B C D i

15 Eta N Scattering length eta-d MST eta-d Faddeev 0.25+i i i i i i i i i i i i i i i2.05 Non-dynamical  N model as input

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

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

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

19

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

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.

22 The pp   pp reaction

23 impulse  and  exchange  and  exchange 1S01S0 3P03P0  exchange

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

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+  + 

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.

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

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

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.

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

33 Off-shell structure given by the Dirac structure.

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