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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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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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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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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