Jülich-Georgia meson-baryon model - Paralle… · Cutkosky79 1510 5 114 10 35 2-12 5 (1232) P33...
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Jülich-Georgia meson-baryon model M. D ¨ oring, C. Hanhart, F. Huang 1 , S. Krewald, K. Nakayama 1 , U.-G. Meißner, D. R ¨ onchen Forschungszentrum J ¨ ulich, University Bonn, Germany 1 University of Athens, Georgia, USA MENU 2010 , Williamsburg, May 31-June 4, 2010 – p.1/30
Transcript of Jülich-Georgia meson-baryon model - Paralle… · Cutkosky79 1510 5 114 10 35 2-12 5 (1232) P33...
Jülich-Georgia meson-baryon modelM. Doring, C. Hanhart, F. Huang1,
S. Krewald, K. Nakayama1, U.-G. Meißner, D. Ronchen
Forschungszentrum Julich, University Bonn, Germany1University of Athens, Georgia, USA
MENU 2010 , Williamsburg, May 31-June 4, 2010 – p.1/30
ContentsThe Jülich coupled reaction channels approach
Photoproduction of mesons
π+p → K+Σ+
Meeting the lattice
Conclusions
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Partial wave amplitudes: πN → πN1200 1400 1600 1800
-0.4
-0.2
0
0.2
0.4
1200 1400 1600 1800 1200 1400 1600 1800 1200 1400 1600 1800
-0.4
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0
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0
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1
0
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1
-0.4
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0
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-0.4
-0.2
0
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1200 1400 1600 1800W [MeV]
0
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1
1200 1400 1600 1800W [MeV]
1200 1400 1600 1800W [MeV]
1200 1400 1600 1800W [MeV]
0
0.2
0.4
0.6
0.8
1
Re S11
Im S11
Re P11
Im P11
Re S31
Im S31
Re P31
Im P31
Re P13
Im P13
Re D13
Im D13
Re P33
Im P33
Re D33
Im D33
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dσ/dΩ and Σγ for γp → π+n
Gauge invariant approach Fei Huang et al., in progress
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dσ/dΩ and Σγ for γn → π−p
Fei Huang et al., in progress
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dσ/dΩ and Σγ for γp → π0p
Fei Huang et al., in progress
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π+p → K+Σ
+
20
40
60
80
100
Candlin et al., NPB 226, 1 (1983)Final 3
-1 -0.5 0 0.5 10
20
40
60
80
100
-0.5 0 0.5 1 -0.5 0 0.5 1 -0.5 0 0.5 1
dσ/dΩ
[ µb
/ co
sθ ]
cosθ
Z=1822 MeV 1845 MeV 1870 MeV 1891 MeV
1926 MeV 1939 MeV 1970 MeV 1985 MeV
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π+p → K+Σ
+, polarization
-1.5
-1
-0.5
0
0.5
1
1.5
Candlin et al., NPB 226, 1 (1983)Final 3
-1 -0.5 0 0.5 1-1.5
-1
-0.5
0
0.5
1
1.5
-0.5 0 0.5 1 -0.5 0 0.5 1-1 -0.5 0 0.5 1
pola
rizat
ion
cosθ
Z=1822 MeV 1845 MeV 1870 MeV 1891 MeV
1926 MeV 1939 MeV 1970 MeV 1985 MeV
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Nπ, S3,1andP3,1
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-0.3
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-0.1
0
Gasparyan 2002This fit
0.2
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0.6
0.8
1200 1400 1600 1800 2000
s1/2
[MeV]
-0.5
-0.4
-0.3
-0.2
-0.1
1200 1400 1600 1800 2000
s1/2
[MeV]
0
0.2
0.4
Re τ Im τ
S31
P31
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Nπ, F3,7andG1,7
-0.1
0
0.1
0.2
SAID solutionThis fit
including π+p --> K
+ Σ+
0.1
0.2
0.3
0.4
0.5
1200 1400 1600 1800 2000z [MeV]
-0.1
0
0.1
1200 1400 1600 1800 2000z [MeV]
0
0.1
0.2
Re τ Im τ
F37
G17
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Complex plane: S11
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Poles and residues: DeltaRe z0 -2 Im z0 |R| θ [deg][MeV] [MeV] [MeV] [0]
∆(1232) P33 1218 90 47 -37ARN 1211 99 52 -47HOE 1209 100 50 -48CUT 1210±1 100±2 53±2 -47±1∆∗(1620) S31 1593 72 12 -108ARN 1595 135 15 -92HOE 1608 116 19 -95CUT 1600±15 120±20 15±2 -110±20∆∗(1910) P31 1840 221 12 -153ARN 1771 479 45 +172HOE 1874 283 38CUT 1880±30 200±40 20±4 -90±30
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Meeting the lattice: Pole path
1220 1240 1260Re z [MeV]
10
20
30
40
50
60
Im z
[M
eV]
mπ
2.1 mπ
∆*(1232)
1500 1510 1520 1530 1540 1550Re z [MeV]
46
48
50
52
54
56
58
Im z
[M
eV]
mπ
N*(1520)
2.3 mπ
1600 1650 1700Re z [MeV]
36
37
38
39
40
Im z
[M
eV]
∆*(1620)
mπ2.3 mπ
1500 1550 1600 1650 1700 1750Re z [MeV]
60
80
100Im
z [
MeV
] N*(1535) N*(1650)
mπ
2.3 mπ
mπ
2.3 mπ
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Pion mass dependence
150 200 250 300mπ [MeV]
1300
1400
1500
1600
1700
Re z
0 [
MeV
]
N*(1535)
N*(1650)
∆∗ (1620)
N*(1520)
∆* (1232)
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ConclusionsPhotoproductionCombined treatment of πN → πNand π+p → K+Σ+.XSeparation of amplitude into contributions from bare resonancesand background is model dependent.Resonances characterized by poles and residues of the S-matrixM. Döring et al., NPA829,170(2009).Study mπ dependence of poles.
X
XOutlook:photoproduction of Kaon Hyperonelectroproduction
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S11: background and poles
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Re
S 11
1200 1400 1600 1800z [MeV]
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1
Im S
11
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0
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Re
S 11
1200 1400 1600 1800z [MeV]
0.2
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1
Im S
11
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S11: background and poles
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0
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Re
S 11
1200 1400 1600 1800z [MeV]
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1
Im S
11
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-0.2
0
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Re
S 11
1200 1400 1600 1800z [MeV]
0.2
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1
Im S
11
??
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S11: cusp
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0
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Re
S 11
1200 1400 1600 1800z [MeV]
0.2
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1
Im S
11
1st ηN sheet
2nd ηN sheet
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P11: analytical structure
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Poles and residues IRe Z0 -2 Im Z0 |R| θ [deg][MeV] [MeV] [MeV] [0]
N∗(1520) D13 1505 95 32 -18Arndt06 1515 113 38 -5Hohler93 1510 120 32 -8Cutkosky79 1510±5 114±10 35±2 -12±5∆(1232) P33 1218 90 47 -37Arndt06 1211 99 52 -47Hohler93 1209 100 50 -48Cutkosky79 1210±1 100±2 53±2 -47±1∆∗(1700) D33 1637 236 16 -38Arndt06 1632 253 18 -40Hohler93 1651 159 10Cutkosky79 1675±25 220±40 13±3 -20±25MENU 2010 , Williamsburg, May 31-June 4, 2010 – p.20/30
Poles and residues IIRe Z0 -2 Im Z0 |R| θ [deg][MeV] [MeV] [MeV] [0]
N∗(1535) S11 1519 129 31 -3Arndt06 1502 95 16 -16Hohler93 1487Cutkosky79 1510±50 260±80 120±40 +15±45N∗(1650) S11 1669 136 54 -44Arndt06 1648 80 14 -69Hohler93 1670 163 39 -37Cutkosky79 1640±20 150±30 60±10 -75±25N∗(1440) P11 1387 147 48 -64Arndt06 1359 162 38 -98Hohler93 1385 164 40Cutkosky79 1375±30 180±40 52±5 -100±35MENU 2010 , Williamsburg, May 31-June 4, 2010 – p.21/30
Poles and residues IIIRe Z0 -2 Im Z0 |R| θ [deg][MeV] [MeV] [MeV] [0]
∆∗(1620) S31 1593 72 12 -108Arndt06 1595 135 15 -92Hohler93 1608 116 19 -95Cutkosky79 1600±15 120±20 15±2 -110±20∆∗(1910) P31 1840 221 45 -153Arndt06 1771 479 38 +172Hohler93 1874 283 19Cutkosky79 1880±30 200±40 20±4 -90±30N∗(1720) P13 1663 212 14 -82Arndt06 1666 355 25 -94Hohler93 1686 187 15Cutkosky79 1680±30 120±40 8±12 -160±30MENU 2010 , Williamsburg, May 31-June 4, 2010 – p.22/30
Background
TNP aP0 Ratio
N∗(1440) P11 15.3 − 7.60i −10.9 + 7.92i 0.26
∆∗(1620) S31 9.01 − 6.37i −1.21 + 0.24i 0.9
∆∗(1910) P31 4.58 − 2.76i −0.78 + 0.24 0.9
N∗(1720) P13 1.76 − 0.10i 0.45 − 0.56i 1.3
N∗(1520) D13 −4.62 − 0.56i 3.03 + 1.23i 0.4
∆(1232) P33 −16.7 − 3.57i 17.1 + 10.6i 0.4
∆∗(1700) D33 0.80 − 0.52i 0.40 + 0.11i 1.3
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Poles and background P33
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Re P
33
1100 1200 1300 1400 1500Z [MeV]
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Im P
33
Vicinity of Pole:
T (Z) ∼ a−1
Z−Z0+ TNP (Z)
T (Z) ∼ a−1
Z−Z0+ a0
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Poles and background D33
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0
Re D
33
1200 1400 1600 1800
s1/2
[MeV]
0
0.1
0.2
Im D
33
Vicinity of Pole:
T (Z) ∼ a−1
Z−Z0+ TNP (Z)
T (Z) ∼ a−1
Z−Z0+ a0
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Amplitudes for charge exchange
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Analyticity and UnitarityPole and Non-Pole T-Matrix
T = TP + TNP
T = a−1
Z−Z0+ a0 + O(Z − Z0)
a−1 =Γd Γ
(†)d
1− ∂
∂ZΣ
a0 = TNP + aP0
aP0 = a−1
Γd Γ(†)d
∗
∗(
∂∂Z (Γd Γ
(†)d ) + a−1
2∂2
∂Z2 Σ)
Γ(†)d
=
γ(†)b
+
Gγ(†)b TNP
Σ ≡ =
Gγ(†)b Γd
Sd =
Sb
+
Sb Σ Sd
TP
=
Γd Sd Γ(†)d
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Tool: X-ray plot (Gauss)Re[T(z)]=0
Im[T(z)]=0
1x−iy = x+iy
x2+y2
T [2](Z) = a−1(1535)Z−Z0(1535)
+ a−1(1650)Z−Z0(1650)
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Second Riemann sheet: P33
TNP
TP + TNP
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γN → πN Gauge invariance
Haberzettl, PRC56 (1997), Haberzettl, Nakayama, Krewald,PRC74 (2006)
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