1

Eta productionResonances, meson couplings

Humberto Garcilazo, IPN Mexico Dan-Olof Riska, Helsinki

… exotic hadronic matter?

2

1) Motivation. Generalities.

2) The N system and the (non)existence of an eta-NN quasi-bound state. The d scattering problem.

The riddle of the enhancement of the pn eta d at threshold.

3) The pp pp reaction 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)

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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. )

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The d scattering problem

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=

+

+

=

S11

dn

n

d d

Reliable way of dealing with re-scattering: Faddeev summation

8

Dynamics

9

g2

g1

10

N Dynamics

Separable t directly fixed to

scattering length

t calculated dynamically from coupled LS equations and potentials

A+p2

11

Different data analysis

N Scattering length extracted from

N N N N NN

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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0 50 100 150 200 250 300-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Real T Imag T

TN

-N

p (MeV/c)

Batinic et al. model

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-1.0 -0.5 0.0 0.5 1.0-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

684 MeV/c 65o / 65o Brookhaven data full model impulse

d/d

(cos

) (

mb/

sr)

cos

Example of description quality obtained for the d NN reaction

with model from Batinic et al.

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1999 Phys. Rev. C 60, 035208

A. M. Green and S. Wycech

A, B, C, D models confirm larger value for Re aN

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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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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Deuteron-eta Real(a0) changes sign as etaN a0 increases

This is not the whole story … there is NN short-range repulsion

Energy

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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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A genuine three-particle scattering effect

0 5 10 15 201

10

100

1000

6

16

1

IMPULSE THREE-BODY

ELA

S

(mb)

TCM (MeV)

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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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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The pp pp reaction

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impulse and exchange and exchange1S0

3P0

exchange

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gNN coupling not sufficiently constrained by NN models

gNN2/4 =0.25 gNN

2/4 =3-7

In this calculation : gNN2/4 =0.4 from photoproduction

(L. Tiator, C. Bennhold)

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26

1260 1280 1300 1320

1E-3

0.01

0.1

1

1E-3

0.01

0.1

1

N-N on-shell amplitude

N-N off-shell amplitude

N-N + Impulse

[b

]

TLAB

Impulse + re-scattering

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1260 1280 1300 1320

0.01

0.1

1

0.01

0.1

1

off-shell N-N + Imp

off-shell N-N + Imp + off-shell N-N + Imp + +

[b

]

TLAB

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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Short-range contributions associated to the short-range NN force

• The NN interaction contains an isospin independent scalar exchange component Vs = vs (1-p2/M 2) ...

• The p2/M 2 term can be combined with the kinetic term: M*= M(1+ vs

/M) two body correction from scalar and vector exchanges.

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1260 1280 1300 1320

0.01

0.1

1

0.01

0.1

1

N-N + Imp

N-N + Imp + short-range

N-N + Imp + short-range + N-N + Imp + short-range + +

[b

]

TLAB

Impulse + re-scattering+ short-range+ +

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1260 1280 1300 13200

1

2

3

4

5

0

1

2

3

4

5

Green et al; A

Green et al; A

Batinic et al

Batinic et al

BONN B PARIS

[b

]

TLAB

Theoretical uncertainty

The mechanism involves high momentum transfer

Different NN interactions may have different effects

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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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A scientific theory cannot be verified ; only falsified.

Karl Popper

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Off-shell structure given by the Dirac structure.

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N Dynamics

Separable t directly fixed to

scattering length

t calculated dynamically from coupled LS equations and potentials

A+p2