1

Collaborators

Johan Durand, CEA - Saclay

Jun He, CEA - Saclay

Zhenping Li, Univ. of Maryland

Qiang Zhao, IHEP - Beijing

PLAN:

Motivations

Chiral constituent quark approach

Results for p → ηp ; ELab ≈ 0.7 to 3.0 GeV W ≈ 1.5 to 2.6 GeV MN*

Role of N*s: “known” and “New”

Summary & concluding remarks

NSTAR2007, Bonn, Sept. 5, ’07

Chiral constituent quark model study of the process p → ηp

Bijan Saghai

CEA – Saclay

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New generation of data for p ηp

Lab / Collaboration

Observable

(GeV)

# of data

pointsReference

MAMI / TAPS dσ / dΩ 0.716 – 0.790 100 B. Krusche et al., PRL 74, 3736 (1995)

ELSA/PHOENICS T 0.717 – 1.105 50 A. Bock et al., PRL 81, 534 (1998)

JLab / CLAS dσ / dΩ 0.775 – 1.925 190 M. Dugger et al., PRL 89, 222002 (2002)

ELSA / CB dσ / dΩ 0.775 – 2.900 631 V. Credé et al., PRL 94, 012004 (2005)

LNS dσ / dΩ 0.718 – 1.142 180T. Nakabayashi et al.,PR C74, 035202 (2006)

GRAALdσ / dΩ

Σ

0.714 – 1.477

0.724 – 1.472

487

150O. Bartalini et al., EPJ A (2007)[PRL 81, 1797 (1998); PL B528, 215 (2002)]

ELSA / CB-TAPS Σ 0.843 – 1.345 34 D. Elsner et al., nucl-ex/0702032

ELab

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What do we learn from those data? • Need a formalism robust enough to

Allow embodying all known N*s (i.e. PDG, one to four star resonances)

Introduce new resonances reported by several authors

S11, P11, P13, D13, D15 & H1,11

Build a model with “reasonable” number of adjustable parameters

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.

3rd S11

M [Γ](MeV)

APPROACH REF.

1945 Constituent quark model (CQM) Capstick & Roberts, PRD 49 (1994)

1712 [184] KY quasi-bound state Li & Workman, PRC 53 (1996)

1792 [360]Coupled channel analysis

N → N, ηN & ηN → ηN Batinic et al., nucl-th/9703023

1780 [280]Constituent quark model (CQM)

p → ηpSaghai & Li, EPJ A11 (2001) ;nucl-th/0305004 (N* 2002)

1861 Hypercentral CQM Giannini et al.,nucl-th/0111073

1846Coupled channel analysis

N → N & γN → NG.-Y. Chen et al., NP A723 (2003)

1945 Reggeized isobar model γp → η′p W.T. Chiang et al., PRC 68 (2003)

1825 [160] Isobar model γp → ηp V.A. Trasuchev, EPJ A22 (2004)

1806 [300] Coupled-channel & CQM γp → K+Λ B. Juliá-Díaz et al., PRC 73 (2006)

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3rd P13

M [Γ](MeV)

APPROACH REF.

1870, 1910, 1950, 2030

Constituent quark model Capstick & Roberts, PRD 49 (1994)

1816, 1894, 1939

Hypercentral CQM Giannini et al., nucl-th/0111073

2068 [165]BES Collaboration Data

J/ψ → π+n , π-pAblikim et al., PRL 97 (2006);Fang et al., Int. J. Mod. Phys. A21 (2006)

1893 [204] Coupled-channel & CQM p → K+Λ B. Juliá-Díaz et al, PRC 73 (2006)

3rd D13

1960 Constituent quark model Capstick & Roberts, PRD 49 (1994)

1895 Isobar model γp → K+Λ Mart & Bennhold, PRC 61 (1999)

1875 [80]Isobar model

γp → N, ηN, K+Λ, K+Σ°, K°Σ+

Anisovich et al. EPJ A25 (2005); Sarantsev et al., EPJ A25 (2005)

1954 [249]Coupled-channel & CQM

p → K+ΛB. Juliá-Díaz et al., PRC 73 (2006)

p n

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Additional P11, D15 & H1,11 resonances?

Anisovich et al., EPJ A 25 (2005) 427 ; Isobar model, γp πN, ηN:

P11(1840), D15(1875) ↔ D15(2200) in PDG?

Sarantsev et al., EPJ A 25 (2005) 441 ; Isobar model, γp Κ+Λ, Κ+Σ°, Κ°Σ+:

P11(1840)

Corthals et al., PRC 73 (2006) 045207 ; Regge + Resonance Approach, γp Κ+Λ:

P11(1900)

Arndt et al., PRC 74 (2006) 045205, EPWA, πN πN, ηN:

H1,11(2247)

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Present approach

p → ηp

Chiral Constituent Quark Model

Starting point: low energy QCD Lagrangian derived by

Manohar & Georgi, Nucl. Phys. B234 (1984),

which ensures that the meson-baryon interaction is invariant under the chiral transformation

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Chiral Constituent Quark Model

Chiral Constituent Quark Model

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SU(6)O(3) symmetry predicts: C2N* = 0 or 1

e.g. C2N* = 1 for S11(1535) & D13(1520)

C2N* = 0 for S11(1650) & D13(1700)

SU(6)O(3) symmetry is broken due to the configuration mixings caused by

one-gluon exchange (Isgur, Karl & Koniuk, PRL 1978)

Configuration mixings between two SU(6)O(3) states with the total quark

spin 1/2 or 3/2:

S11: N(2PM)1/2- N(4PM)1/2-

D13: N(2PM)3/2- N(4PM)3/2-

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Configuration mixing

│S11(1535) = │N(2PM)1/2- cosθS - │N(4PM)1/2- sinθS │S11(1650) = │N(2PM)1/2- sinθS + │N(4PM)1/2- cosθS

Transition amplitudes:

AN* N│Hm(│N* N*│He│N

AS11 N│Hm(cosθS │N(2PM)1/2- - sinθS │N(4PM)1/2-) (cos θS N(2PM)1/2- │- sinθS N(4PM)1/2- │) He│N

N(4PM)1/2- │He│N = 0, due to Moorhouse selection rule (PRL 1966)

AS11 (cos2θS – R sinθS cosθS ) N│Hm│N(2PM)1/2- N(2PM)1/2-│ He│N

RS = [ N│Hm │N(4PM)1/2- ] / [ N│Hm │N(2PM)1/2- ]

SU(6)O(3) RS = -1 & RD = 1/√10, for p → ηp

CS11(1535) = cosθS (cosθS – sinθS) CD13(1520) = cosθD (cosθD – sinθD /√10 )

CS11(1650) = - sinθS (cosθS + sinθS) CD13(1700) = sinθD (cosθD /√10 + sinθD)

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Ingredients

s-channel: all known I=1/2 N*s & 6 “new” ones

u-channel: nucleon Born term + N*s

t-channel: & ω exchanges

Previous study (Eγlab ≤ 2 GeV)

B. Saghai & Z. Li, EPJ A11 (2001);

Limited to n ≤ 2 shell & no t-channel n = 1: 2 S11, 2 D13, 1 D15

n = 2: 2 P11, 2 P13, 2 F15, 1 F17

Present work: besides t-channel embodies also:

n = 3: S11, D13, D15, G17, G19

n = 4: P11, H19

Degenerate n=5: I1,11

n=6: K1,13

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All I=1/2 PDG N* + 6 new ones

. PDG Star

N* PDG Star

N* PDG Star

N*

4 S11(1535) 4 D13(1520) 4 G17(2190)

4 S11(1650) 3 D13(1700) 4 G19(2250)

1 S11(2090) 2 D13(2080)

S11(1730) D13(1850)

4 P11(1440) 4 D15(1675) 4 H19(2220)

3 P11(1710) 2 D15(2200) H1,11(2200)

1 P11(2100) D15(1950)

P11(1810) 3 I1,11(2600)

4 P13(1720) 4 F15(1680) 2 K1,13(2700)

2 P13(1900) 2 F15(2000)

P13(2170) 2 F17(1990)

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Full model

21 known N*s 6 new N*s

Fitted on 1822 data points

χ2 = 1.81

Mixing angles: θS ≈ - 35° ; θD ≈ 15°

(in good agreement with findings by Isgur, Karl, Chizma, Capstick…)

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Differential cross-section

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Polarization observables

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Removing one resonance

. PDG Star

N* PDG Star

N* PDG Star

N*

4 S11(1535) 4 D13(1520) 4 G17(2190)

4 S11(1650) 3 D13(1700) 4 G19(2250)

1 S11(2090) 2 D13(2080)

S11(1730) D13(1850)

4 P11(1440) 4 D15(1675) 4 H19(2220)

3 P11(1710) 2 D15(2200) H1,11(2200)

1 P11(2100) D15(1950)

P11(1810) 3 I1,11(2600)

4 P13(1720) 4 F15(1680) 2 K1,13(2700)

2 P13(1900) 2 F15(2000)

P13(2170) 2 F17(1990)

χ2 variation δχ2 < 5% 5% ≤ δχ2 ≤ 15%

Nb of N*s 15 3

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“Reduced” model

Remove ALL 18 N*s (δχ2 ≤ 15%)

Then, re-fit the data with remaining 9 N*s

χ2 =1,81 → 2,12

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Schematic presentation of the role played by the most relevant resonances in the process p → ηp

Switched-off

N*

d.o.f

(Full Model: =2.1)

S11(1535) 39.2

D13(1520) 9.0

S11(2090) 2.3

S11(1724) 2.3

S11(1650) 2.2

F15(1680) 2.2

P13(1520) 2.1

P13(1900) 2.1

D13(1700) 2.1

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Polarization observables

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Differential cross-section

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Summary & Concluding remarks (I)

Direct channel formalism for p →ηp, within a chiral constituent quark approach. All data for d/dΩ, Σ & T are well reproduced.

All 21 Known N*s and 6 new ones included in the model.

Rather few and severely constrained adjustable parameters.

Reaction mechanism dominated by 6N*.

HOWEVER,

Direct channel investigations: mandatory, but

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Summary & Concluding remarks (II)

To go further, two directions:

Experimental: polarization asymmetries, especially with polarized target

Theoretical: coupled-channel approach (cf. talk by Harry Lee):

Already investigated by our collaboration (Argonne, Barcelona, Pittsburgh, Saclay)

p → [N ; N ; KY ] → K+ Λ

W.-T. Chiang, B. Saghai, F. Tabakin, T.-S.H. Lee, PRC 69, 065208 (2004).

B. Juliá-Díaz, B. Saghai, T.-S.H. Lee, F. Tabakin, PRC 73, 055204 (2006).

In progress

J. Durand, J. He, B. Juliá-Díaz, T.-S.H. Lee, T. Sato, B. Saghai, N. Suzuki

p → [N ; ; N ; N ; ηN] → ηp