the julich partial-wave analysis¨...deborah ronchen, pwa 8 / athos 3¨ the j¨ulich partial-wave...
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The Julich Partial-Wave Analysis
a dynamical coupled-channel analysis of pion- and photon-induced reactions
Deborah Ronchen
HISKP, Bonn University
In collaboration with:
M. Doring, H. Haberzettl, J. Haidenbauer, C. Hanhart, F. Huang, S. Krewald, U.-G. Meißner,
and K. Nakayama
PWA 8 / ATHOS 3April 14, 2015
Motivation and IntroductionData analysis and fit results
Outlook
The excited hadron spectrumThe Julich model
The excited hadron spectrum:Connection between experiment and QCD in the non-perturbative regime
Excited hadron spectrum: testing ground for theories of the strong force at low and medium energy
Experimental study of hadronic reactions
source: ELSA; data: ELSA, JLab, MAMI
⇐⇒
Theoretical predictions of excited hadronse.g. from lattice calculations:(with some limitations)
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
mπ = 396 MeV [Edwards et al., Phys.Rev. D84 (2011)]
⇒ Partial wave decomposition:decompose data with respect to a conservedquantum number:total angular momentum and parity JP
missing resonance problem
→ analyze πN → X and γN → Xsimmultaneously
→ coupled-channel approach
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 2/ 21
Motivation and IntroductionData analysis and fit results
Outlook
The excited hadron spectrumThe Julich model
A dynamical coupled-channel approach: the Julich model
Dynamical coupled-channels (DCC): simultaneous analysis of different reactions
The scattering equation in partial-wave basis
〈L′S′p′|T IJµν |LSp〉 = 〈L′S′p′|V IJ
µν |LSp〉+
∑γ,L′′S′′
∞∫0
dq q2 〈L′S′p′|V IJµγ |L′′S′′q〉
1E − Eγ(q) + iε
〈L′′S′′q|T IJγν |LSp〉
potentials V constructed fromeffective L
s-channel diagrams: T P
genuine resonance states
t- and u-channel: T NP
dynamical generation of polespartial waves strongly correlated
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 3/ 21
Motivation and IntroductionData analysis and fit results
Outlook
The excited hadron spectrumThe Julich model
The Julich DCC approach
(2-body) unitarity and analyticity respected
Resonances: poles in the T -matrix
Re(E0) = “mass”, -2Im(E0) = “width”
pole position E0 is the same in allchannelsresidues→ branching ratios
opening of inelastic channels
⇒ branch point and new Riemann sheetAnalytic structure (P11)
from PW decomposition, e.g. Vu =1∫
−1
dx P`(x)u −m2
N + iε ,3-body ππN channel:
parameterized effectively as π∆, σN ,ρNπN/ππ subsystems fit the respectivephase shifts
branch points move into complex plane
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 4/ 21
Motivation and IntroductionData analysis and fit results
Outlook
The excited hadron spectrumThe Julich model
Analysis of pion-induced reactions
calculate observables from T -matrix
fit free parameters of T to data or partial waveamplitudes
σ = 12
4πp2
∑JLS,L′S′ |τ
JL′S′LS |2
with τfi = −π√ρf ρiT fi
ρ: phase factor
s-channel: resonances (T P )
N∗
N π
KΛ
mbare + fπNN∗
t- and u-channel exchange: “background“ (T NP )
K Λ,Σ
π N
K∗
Λ,Σ K
Σ,Σ∗
π N
Λ
Σ K
π N
cut offs Λ in form factors(
Λ2−m2ex
Λ2+~q2
)n
(couplings fixed from SU(3))
⇒ search for poles in the complex energy plane of T
All exchange diagrams data baseDeborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 5/ 21
Motivation and IntroductionData analysis and fit results
Outlook
The excited hadron spectrumThe Julich model
PhotoproductionDifferent approaches
Field theoretical approaches : DMT, ANL-Osaka, Julich-Athens-Washington, ...
Example: Gauge invariant formulation by Haberzettl, Huang and NakayamaPhys. Rev. C56 (1997), Phys. Rrev. C74 (2006), Phys. Rev. C85 (2012)
↓complicated, involved construction/calculation
Focus of the present analysis:
extraction of resonance parameters⇒ flexible, phenomenological parameterization of photo excitation
Advantage: easy to implement, analyze large amounts of dataDisadvantage: no information on microscopic reaction dynamics
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 6/ 21
Motivation and IntroductionData analysis and fit results
Outlook
The excited hadron spectrumThe Julich model
Photoproduction in a semi-phenomenological approach
Multipole amplitude
M IJµγ = V IJ
µγ +∑κ
T IJµκGκV IJ
κγ
(partial wave basis)
γ
N
π, η
N
Vπγ
γ
N
π, η
N
m
B
VκγG
T
m = π, η , B = N , ∆
Tµκ: Julich hadronic T -matrix → Watson’s theorem fulfilled by construction→ analyticity of T: extraction of resonance parameters
Phenomenological potential:
γ
N
m
B
γ
N
m
B
N ∗,∆∗
PNPµ
PPi
γaµ
+Vµγ =(E, q) =γaµ(q)
mNPNPµ (E) +
∑i
γaµ;i(q)PP
i (E)
E − mbi
γaµ , γa
µ;i : hadronic vertices→ correct threshold behaviour, cancellation of singularity at E = mbi
→ γaµ;i affects pion- and photon-induced production of final state mB
i: resonance number per multipole; µ: channels πN , ηN , π∆ Polynomials
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 7/ 21
Motivation and IntroductionData analysis and fit results
Outlook
Fit resultsResonance parameters
Data analysis and fit results
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 8/ 21
Motivation and IntroductionData analysis and fit results
Outlook
Fit resultsResonance parameters
Combined analysis of pion- and photon-induced reactionsSimultaneous fit
Fit parameter:
πN → πNπ−p→ ηn, K 0Λ, K 0Σ0, K+Σ−
π+p→ K+Σ+
s-channel: resonances (T P )
N∗
N π
KΛ
mbare + fπNN∗⇒ 128 free parameters
11 N∗ resonances × (1 mbare+ couplings to πN , ρN , ηN , π∆, KΛ, KΣ))+ 10 ∆ resonances × (1 mbare+ couplings to πN , ρN , π∆, KΣ)
γp→ π0p, π+n, ηp
⇒ up to 456 free parameterscouplings of the polynomials
γ
N
m
B
γ
N
m
B
N ∗,∆∗
PNPµ
PPi
γaµ
+
calculations on the JUROPA supercomputer: parallelization in energy (∼ 300 - 400 processes)
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 9/ 21
Motivation and IntroductionData analysis and fit results
Outlook
Fit resultsResonance parameters
Data base simultaneous fit to π- and γ-induced reactions
Fit A Fit B
πN → πN PWA GW-SAID WI08 [Arndt et al., PRC 86 (2012)]
π−p→ ηn dσ/dΩ, P
π−p→ K 0Λ dσ/dΩ, P , β
π−p→ K 0Σ0 dσ/dΩ, P
π−p→ K+Σ− dσ/dΩ
π+p→ K+Σ+ dσ/dΩ, P , β
∼ 6000 data points
γp→ π0p dσ/dΩ, Σ, P , T , ∆σ31, G, H
γp→ π+n dσ/dΩ, Σ, P , T , ∆σ31, G, H
γp→ ηp dσ/dΩ, P , Σ dσ/dΩ, P , Σ, T , F
29,392 data points 29,680 data points
More single/doublepolarization:E , Cx′L , Cz′L ,T ,P,H (ELSA 2014)(γp→ π0p)⇒ predictions
→ T , F : Akondi et al.(A2 at MAMI)PRL 113 10, 102001 (2014)
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 10/ 21
Motivation and IntroductionData analysis and fit results
Outlook
Fit resultsResonance parameters
Eta production: π−p → ηn and γp → ηp
Inelastic channels → possibility resolve ”missing resonance” problem
Data quality in π−p→ ηn:
-1 -0.5 0 0.5 1
cosΘ
0
0.05
0.1
0.15
0.2
0.25
dσ
/dΩ
[m
b/s
r]
1507 MeV
-1 -0.5 0 0.5 1
cosΘ
-1
0
1
2
3
P
1793 MeV # data points π−p→ ηn: 732γp→ ηp: 6164
data situation much better in γp→ ηp
⇒ Fix N∗Nη coupling from photoproduction (to a large extent)
γ
N
η
N
N ∗
π
N
η
N
N ∗
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 11/ 21
Motivation and IntroductionData analysis and fit results
Outlook
Fit resultsResonance parameters
Fit results γp → ηp selected results, arXiv:1504.01643 [nucl-th]T , F not included T , F included
Differential cross section
0 30 60 90120150
Θ [deg]
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
dσ
/dΩ
[µ
b/s
r]
[1]
1488
0 30 60 90 120150
Θ [deg]
0
0.2
0.4
0.6
0.8
1
[2]
1755
0 30 60 90 120150
Θ [deg]
0
0.1
0.2
0.3
0.4
[3]
[4]
2142
[1] McNicoll 2010 (MAMI), [2] Williams 2009 (JLab), [3] Crede 2009 (ELSA), [4] Crede 2005 (ELSA)
Beam asymmetry
0 30 60 90 120150
Θ [deg]
-1
-0.5
0
0.5
1
Σ
[4]
1496
0 50 100 150
Θ [deg]
-1
-0.5
0
0.5
1
1754
0 50 100 150
Θ [deg]
-1
-0.5
0
0.5
1
[5]1843
[4] Bartalini 2007 (GRAAL), [5] Elsner 2007 (ELSA)
Recoil polarization- only 7 data points in total -
-1
-0.5
0
0.5
1
P
[6] 1561
0 50 100 150
Θ [deg]
-1
-0.5
0
0.5
1
P
1680
[6] Heusch (Caltech),PRL25, 1381 (1970)
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 12/ 21
Motivation and IntroductionData analysis and fit results
Outlook
Fit resultsResonance parameters
F and T in γp → ηp arXiv:1504.01643 [nucl-th]
Data: Akondi et al. (A2 at MAMI) PRL 113 10, 102001 (2014)
0
0.5
1497 15161534 1558F
1588 1617
0 30 60 90 120 150-1
-0.5
0
0.5
1
0 30 60 90 120 150
1646 1674
0 30 60 90 120 150 0 30 60 90 120 150 0 30 60 90 120 150 0 30 60 90 120 150
17021743 1796
1847
predictionfit
Polarization:
Beam Target Recoil+1 +x 0−1 +x 0
0
0.5
1497 15161534 1558T
15881617
0 30 60 90 120 150-1
-0.5
0
0.5
1
0 30 60 90 120 150
1646 1674
0 30 60 90 120 150 0 30 60 90 120 150 0 30 60 90 120 150 0 30 60 90 120 150
1702 1743 17961847
Polarization:
Beam Target Recoil0 +y 00 −y 0
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 13/ 21
Motivation and IntroductionData analysis and fit results
Outlook
Fit resultsResonance parameters
Pion-induced eta production: π−p → ηn arXiv:1504.01643 [nucl-th]
0.1
0.2
0.3
0.4
dσ
/dΩ
[m
b/s
r]
1509 MeV 1576 MeV 1664 MeV
-1 -0.5 0 0.5 1cosθ
0
0.1
0.2
dσ
/dΩ
[m
b/s
r]
1729 MeV
-1 -0.5 0 0.5 1
cosθ
1805 MeV
-1 -0.5 0 0.5 1
cosθ
2235 MeV
0
0.05
0.1
P x
dσ
/dΩ
[m
b/s
r]
1740 MeV 1872 MeV 1989 MeV
-1 -0.5 0 0.5 1cosθ
0
0.05
0.1
P x
dσ
/dΩ
[m
b/s
r]
2024 MeV
-1 -0.5 0 0.5 1
cosθ
2070 MeV
-1 -0.5 0 0.5 1
cosθ
2235 MeV
fit A: T , F not included fit B: T , F included fit Ahad: Julich2012, only pion-induced data
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 14/ 21
Motivation and IntroductionData analysis and fit results
Outlook
Fit resultsResonance parameters
Resonance content: I=1/2 arXiv:1504.01643 [nucl-th]
Pole search on the 2nd sheet ofthe scattering matrix Tµν
Resonance parameter:
”mass” = Re(E0)
”width”= −2Im(E0)
Residues → branchingratios
E0: pole position1000 1200 1400 1600 1800 2000 2200
Re E [MeV]
-300
-250
-200
-150
-100
-50
0
Im E
[M
eV
]
Fit AFit B
1620 1640 1660
-100
-50
Fit AFit B
πN ππN
π∆
KΣ
ρN
N(1720) 3/2+
N(1650) 1/2-
N(1675) 5/2-N(1520) 3/2
-
N(2190) 7/2-
N(1440) 1/2+
N(1680) 5/2+
N(2250) 9/2-
N(1990) 7/2+
N(1710) 1/2+
N(1535) 1/2-
physical axisηN KΛ
N(1750) 1/2+
N(2220) 9/2+
σN
N(1710) 1/2+
N(1675) 5/2-
N(1680) 5/2+
N(1650) 1/2-
x: branch points Notation: N(“name”) J parity
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 15/ 21
Motivation and IntroductionData analysis and fit results
Outlook
Fit resultsResonance parameters
Resonance parameters selected results, arXiv:1504.01643 [nucl-th]
Re E0 -2Im E0 |rπN | θπN→πNΓ
1/2πN Γ
1/2ηN
ΓtotθπN→ηN
[MeV] [MeV] [MeV] [deg] [%] [deg]
fit
N(1535) 1/2− A 1497 105 23 −48 51 110
B 1499 104 22 −46 51 112
Ahad 1498 74 17 −37 51 120
N(1710) 1/2+ A 1611 140 2.7 −40 6.1 175
B 1651 121 3.2 55 16 −180
Ahad 1637 97 4 −30 24 130
fit A: T , F not included fit B: T , F included fit Ahad: Julich2012, only pion-induced data
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 16/ 21
Motivation and IntroductionData analysis and fit results
Outlook
Fit resultsResonance parameters
Photocouplings at the pole selected results, arXiv:1504.01643 [nucl-th]
Ahpole = Ah
poleeiϑh
h = 1/2, 3/2Ah
pole = IF√
qpkp
2π (2J+1)E0mN rπN
Res AhL±
IF : isospin factorqp (kp ): meson (photon) momentum at the poleJ = L ± 1/2 total angular momentumE0: pole positionrπN : elastic πN residue
A1/2pole ϑ1/2
[10−3 GeV−12 ] [deg]
fit
N(1535) 1/2− A 107 4.6
B 106 5.2
2 50+4−4 −14+12
−10
N(1710) 1/2+ A 7.1 −177
B 20 −83
2 28+9−2 103+20
−6
fit A: T , F not included
it B: T , F included
fit 2: Julich2013, onlypion photoproduction
(same pole positions as fit Ahad)
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 17/ 21
Motivation and IntroductionData analysis and fit results
Outlook
Fit resultsResonance parameters
Summary
Extraction of the N∗ and ∆ resonance spectrum
from a simultaneous analysis of pion- and photon-induced reactions
DCC analysis of πN → πN , ηN , KΛ and KΣ
The Julich model: lagrangian based, unitarity & analyticity respected→ analysis of over 6000 data points (PWA, dσ/dΩ, P , β)
π and η photoproduction in a semi-phenomenological approach
hadronic final state interaction: Julich DCC analysis→ analysis of more than 30 000 data points for single and double polarization observables
→ extraction of resonance parameters (poles & residues)
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 18/ 21
Motivation and IntroductionData analysis and fit results
Outlook
Outlook
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 19/ 21
Motivation and IntroductionData analysis and fit results
Outlook
Kaon photoproduction: preliminary results for γp → K+Λ
simultaneous fit of γp→ π0p , π+n , ηp, K+Λ
and πN → πN , ηN , KΛ , KΣ
Differential cross section
0 30 60 90 120150
Θ [deg]
0
0.1
0.2
dσ
/dΩ
[µ
b/s
r] [1]
1645 MeV
0 30 60 90 120 150
Θ [deg]
0
0.1
0.2
0.3
0.4
0.5
1845
0 30 60 90 120150
Θ [deg]
0
0.1
0.2
0.3
0.4
0.5
[2]
2206
[1] McCracken et al. 2010 (JLab), [2] Glander et al. 2004 (ELSA)
Recoil polarization
0 30 60 90 120150
Θ [deg]
-1
-0.5
0
0.5
1
P
[3]
1649
0 30 60 90 120150
Θ [deg]
-1
-0.5
0
0.5
1
[1]
1925
0 30 60 90 120150
Θ [deg]
-1
-0.5
0
0.5
1 2315
[3] Lleres et al. 2007 (GRAAL)
Future projects:
More double polarizationobservables in mesonphotoproduction to bepublished in the near futureγN → KΣ
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 20/ 21
Motivation and IntroductionData analysis and fit results
Outlook
Thank you for your attention!
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 21/ 21
Photon-induced reactions
Pion-induced reactions πN → πN, ηN, KΛ, KΣ arXiv:1504.01643 [nucl-th]
Selected results: Fit A and Fit B
-0.4
-0.2
0
0.2
0.4
1200 1400 1600 1800 2000
E [MeV]
0.2
0.4
0.6
0.8
1
πΝ −> πΝ
Im S11
Re S11
-1 -0.5 0 0.5 1
cosΘ
0
20
40
60
80d
σ/d
Ω [
µb/s
r]1763 MeV
K+Σ
−
-1 -0.5 0 0.5 1
cosΘ
0
0.05
Pxd
σ/d
Ω [
µb
/sr]
2148 MeV
ηN
-1 -0.5 0 0.5 1
cosΘ
-2
0
2
4
6
β [ra
d]
1852 MeV
KΛ
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 1/ 16
Photon-induced reactions
Multipoles for γp → ηp
-16
-8
0
8
Re
(A)
[10
-3 f
m]
-2
0
-0.8
-0.4
0
-2
-1
0
1
-0.6
-0.3
0
0.3
0.6
0
0.2
0.4
0.6
1600 1800 2000 2200
-16
-8
0
Im(A
) [1
0-3
fm
]
1600 1800 2000 2200
-2
-1
0
1
1600 1800 2000 2200
-0.6
-0.4
-0.2
0
1600 1800 2000 2200
-0.2
0
0.2
1600 1800 2000 2200
-0.6
-0.3
0
1600 1800 2000 2200
-0.6
-0.4
-0.2
0
0.2
-0.2
0
0.2
Re
(A)
[10
-3 f
m]
-0.2
0
0.2
-0.2
0
0.2
-0.1
0
0.1
0.2
-0.03
0
0.03
-0.1
0
1600 1800 2000 2200
-0.4
-0.2
0
Im(A
) [1
0-3
fm
]
1600 1800 2000 2200
-0.2
-0.1
0
0.1
0.2
0.3
1600 1800 2000 2200
-0.2
-0.1
0
0.1
1600 1800 2000 2200
-0.2
-0.1
0
0.1
0.2
1600 1800 2000 2200
-0.08
-0.04
0
1600 1800 2000 2200
-0.05
0
0.05
-0.15
-0.1
-0.05
0
0.05
Re
(A)
[10
-3 f
m]
0
0.1
0.2
-0.04
-0.02
0
0.02
0.04
-0.04
0
0.04
0.08
0
0.02
0.04
0
0.02
1600 1800 2000 2200
-0.03
-0.02
-0.01
0
0.01
Im(A
) [1
0-3
fm
]
1600 1800 2000 2200
-0.1
0
1600 1800 2000 2200
-0.01
0
0.01
0.02
1600 1800 2000 2200
-0.02
0
0.02
0.04
1600 1800 2000 2200
-0.01
-0.005
0
0.005
1600 1800 2000 2200
-0.02
-0.01
0
E0+
M1-
E1+ M
1+E
2-M
2-
E2+
M2+ E
3-M
3- E3+
E4-
M3+
M4-
E4+ M
4+E
5-M
5-
E [MeV]
Figure : (Black) dash-dotted line: BG 2014-02 solution. Dashed (blue) line: fit A; solid(red) line: fit B.
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 2/ 16
Photon-induced reactions
Pion photoproduction: selected fit results arXiv:1504.01643 [nucl-th]
γp→ π0p
0 30 60 90 120150
Θ [deg]
0
0.01
dσ
/dΩ
[µ
b/s
r] [1]
1074 MeV
0 30 60 90 120150
Θ [deg]
-1
-0.5
0
0.5
1
Σ
[2][3][4]
1785
0 30 60 90120150
Θ [deg]
-1
-0.5
0
0.5
1
G
[5]1660
0 30 60 90 120 150 180
Θ [deg]
-4
-2
0
2
-∆σ
31
[6] 1469
[1] Schmidt 2001 (MAMI)[2] Elsner 2009 (ELSA)[3] Sparks 2010 (ELSA)[4] Bartalini 2005 (GRAAL)[5] Thiel 2012 (ELSA)[6] Ahrens 2002 (MAMI)
γp→ π+n
0 50 100 150 200
Θ [deg]
5
10
15
20
dσ
/dΩ
[µ
b/s
r] [7]
1162
0 50 100 150
Θ [deg]
-1
-0.5
0
0.5
1
Σ
[8][9]
1660
0 50 100 150
Θ [deg]
-1
-0.5
0
0.5
1
G
[10]
1232
0 50 100 150
Θ [deg]
-5
0
5
10
-∆σ
31
[11]
1364
[7] Ahrens 2004 (MAMI)[8] Bartalini 2002 (GRAAL)[9] Ajaka 2000 (GRAAL)[10] Ahrens 2005 (MAMI)[11] Ahrens 2006 (MAMI)
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 3/ 16
Photon-induced reactions
Double polarization in γp → π0p selected results, arXiv:1504.01643 [nucl-th]Data NOT included in fit
[1] Gottschall et al. 2013 (ELSA) PRL. 112 1, 012003
Polarization
Beam Target Recoil+1 −z 0−1 −z 0
0 30 60 90 120 150
-1
-0.5
0
0.5
1
E
[1]
0 30 60 90 120 150 0 30 60 90 120 150
E=1456 -1543 MeV
1638 - 1716 1848 - 1898
0 30 60 90 120 150 0 30 60 90 120 150 0 30 60 90 120 150
1898 - 1947 1947 - 1995 2109 - 2280
Θ [deg][2] Hartmann et al. 2014 (ELSA) PRL 113, 062001
-1
-0.5
0
0.5
1
[2]
0 30 60 90 120 150-1
-0.5
0
0.5
1
0 30 60 90 120 150 0 30 60 90 120 150 0 30 60 90 120 150
H
1471 MeV 1491 1513 1533
1553 15741594 1613
1491
Θ [deg]
Polarization
Beam Target Recoil⊥′ x 0‖′ x 0
new ELSA T,P data
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 4/ 16
Photon-induced reactions
T , P in γp → π0pData NOT included in the Fit
Data: J. Hartmann et al. 2014 (ELSA)
-1
-0.5
0
0.5
1
-1
-0.5
0
0.5
1
-1
-0.5
0
0.5
1
0 30 60 90 120 150-1
-0.5
0
0.5
1
0 30 60 90 120 150 0 30 60 90 120 150 0 30 60 90 120 150
T
P
1471 MeV 1491 1513 1533
15531574
15941613
1471 MeV
1491
1491 1513 1533
1613159415741553
arXiv:1504.01643[nucl-th] back
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 5/ 16
Photon-induced reactions
Partial wave contribution in F and T in γp → ηp arXiv:1504.01643 [nucl-th]
0 30 60 90 120 150-1
-0.5
0
0.5
1
0 30 60 90 120 150
θ [deg]
Fit B, full solution
S11
, P13
, D13
0 30 60 90 120 150
15341646
1847
F
0 30 60 90 120 150-1
-0.5
0
0.5
1
0 30 60 90 120 150
θ [deg]
Fit B, full solution
S11
, P13
, D13
0 30 60 90 120 150
15341646 1847
T
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 6/ 16
Photon-induced reactions
Partial wave contribution in F and T in γp → ηp arXiv:1504.01643 [nucl-th]
0 30 60 90 120 150-1
-0.5
0
0.5
1
0 30 60 90 120 150
θ [deg]
Fit B, full solution
S11
, P13
, D13
all s-, p-, d-, f-waves
0 30 60 90 120 150
15341646
1847
F
0 30 60 90 120 150-1
-0.5
0
0.5
1
0 30 60 90 120 150
θ [deg]
Fit B, full solution
S11
, P13
, D13
all s-, p-, d-, f-waves
0 30 60 90 120 150
15341646 1847
T
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 6/ 16
Photon-induced reactions
Details of the formalism
Polynomials:
PPi (E) =
n∑j=1
gPi,j
(E − E0
mN
)je−gP
i,n+1(E−E0)
PNPµ (E) =
n∑j=0
gNPµ,j
(E − E0
mN
)je−gNP
µ,n+1(E−E0)
- E0 = 1077 MeV
- gPi,j , gNP
µ,j : fit parameter
- e−g(E−E0): appropriatehigh energy behavior
- n = 3
back
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 7/ 16
Photon-induced reactions
Data basesimultaneous fit to πN → πN, ηN, KΛ, KΣ
World data base on ηN , KΛ, KΣ
PWA σtotdσdΩ
P β
πN → πN GWU/SAID 2006
up to J=9/2
π−p → ηn 62 data points 38 energy points 12 energy points
z=1489 to 2235 MeV 1740 to 2235 MeV
π−p → K 0Λ 66 data points 46 energy points 27 energy points 7 energy points
1626 to 1405 MeV 1633 to 2208 MeV 1852 to 2262 MeV
π−p → K 0Σ0 16 data points 29 energy points 19 energy points
1694 to 2405 MeV 1694 to 2316 MeV
π−p → K+Σ− 14 data points 15 energy points
1739 to 2405 MeV
π+p → K+Σ+ 18 data points 32 energy points 32 energy points 2 energy pionts
1729 to 2318 MeV 1729 to 2318 MeV 2021 and 2107 MeV
∼ 6000 data pointsback
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 8/ 16
Photon-induced reactions
back
NN
N N
NN
N
N
N
N
N
N
N N
N N
N N
N N
N N
N
π
π π π
π π
π π
π π π π π π
π
N
N
Δ
Δ
σ ρ
ρ
ρ ρ ρ ρ
N
N
π
ρ
π
N
ω a1
a0
η η
N N N N N Nπ π π π π π
Δ Δ Δ
ΔN ρ
π π π
N
σN σ
π
N
K*
K Λ
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 9/ 16
Photon-induced reactions
back
N N N N N N
N N
π π π π π π
π π
KΛ ΛK KΛ
Σ κ Σ* K*
ΣK
Σ
Σ K Σ K
Λ
κ
Σ ΣK K
Σ*
N
N
N N
N N
N N
N
N N
ρ
ρρ
ρ
ρ
ρ ρ
ρ
ρ
ρ ρ
π π
Δ
π
Δ Δ
N
N
N N
N
η
η
η
η
f0
N N
Δ
Δ
π
π π
π Δ
Δ
ρρ
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 9/ 16
Photon-induced reactions
back
Δ
Δ
Δ
π
π Δπ
π
NNσ σ
σ σ
σ
σ
N
N N
N Λ
Λ
Λ
Λ
f0
K
K
K
K
ω
K
K
Λ
Λ
N
φ
ΛK
K Σ
ρ f0
K
K
Σ
Σ
ω φ ρ
K K K
KKK Σ
Σ Σ
Σ Σ
Σ
Nη
K*
ΛK
N
Λ K
η
Λ K*
K Σ
Nη N
K
η
Σ
Σ
N
K
Σ*
η
Σ Λ K
Ξ
K Λ
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 9/ 16
Photon-induced reactions
Error analysis
χ2 + 1 criterion: determination of the non-linear parameter errorerror of parameter pi determined by range of pi such that χ2
min rises by lessthan 1
⇒ error on pole positions and residues.
1600 1800 2000z [MeV]
-0.1
0
1600 1800 2000z [MeV]
0
0.1
Re F35 Im F35
1740 1760 1780
Re z0
[MeV]
-140
-120
-100
Im z
0 [
MeV
]
NPBA 851, 58 (2011)
BUT: numerically not possible with ≥ 500 free parameters
Work in progress: Developing of techniques to apply Monte-Carlo error propagation usingbootstrap method (M. Doring et al.)
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 10/ 16
Photon-induced reactions
Matching to latticePrediction & analysis of lattice data [M. Doring et al., EPJ A47, 163 (2011)]
Scattering equation:
T (q′′, q′) = V (q′′, q′) +
∞∫0
dq q2 V (q′′, q)1
z − E1(q)− E2(q) + iεT (q, q′)
Discretization of momenta in the scattering equation:∫ ~d 3q(2π)3 f (|~q |2) →
1L3
∑~ni
f (|~qi|2), ~qi =2πL~ni, ~ni ∈ Z3
T (q′′, q′) = V (q′′, q′) +2π2
L3
∞∑i=0
ϑ(i)V (q′′, qi)1
z − E1(qi)− E2(qi)T (qi, q′),
ϑ(P)(i) seriesStudy finite-volume effectsPredict lattice spectra
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 11/ 16
Photon-induced reactions
πN → πN partial wave amplitudes selected results, arXiv:1504.01643 [nucl-th]
Fit A and Fit B
-0.4
-0.2
0
0.2
0.4
0.2
0.4
0.6
0.8
1
1200 1400 1600 1800 2000
E [MeV]
-0.4
-0.2
0
0.2
0.4
1200 1400 1600 1800 2000
E [MeV]
0.2
0.4
0.6
0.8Im P
11
Im S11
Re S11
Re P11
-0.4
-0.2
0
0.2
0.4
0.2
0.4
0.6
0.8
1
1200 1400 1600 1800 2000
E [MeV]
-0.2
-0.1
0
1200 1400 1600 1800 2000
E [MeV]
0.05
0.1
0.15
0.2
0.25
Re P33
Re D33
Im P33
Im D33
Notation: L2I 2J
Input to fit: energy-dependent partial wave analysis, GWU/SAID 2006up to J = 9/2 ( ∼ H39)
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 12/ 16
Photon-induced reactions
πN → ηN,KΛ selected results, arXiv:1504.01643 [nucl-th]
π−p→ ηN
-1 -0.5 0 0.5 1
cosΘ
0
0.05
0.1
0.15
0.2
0.251496 MeV
dσ
/dΩ
[ m
b/s
r ]
-1 -0.5 0 0.5 1
cosΘ
1507 MeV
-1 -0.5 0 0.5 1
cosΘ
1897 MeV
-1 -0.5 0 0.5 1
cosΘ
-0.05
0
0.05
0.1
P x
dσ
/dΩ
[m
b/s
r]
1793 MeV
-1 -0.5 0 0.5 1
cosΘ
2070 MeV
-1 -0.5 0 0.5 1
cosΘ
0
0.05
Pxd
σ/d
Ω [
µb/s
r]
2148 MeV
ηN
π−p→ K 0Λ
-1 -0.5 0 0.5 1
cosΘ
0
40
80
120
dσ
/dΩ
[µ
b/s
r]
z = 1626 MeV
-1 -0.5 0 0.5 1
cosΘ
1707 MeV
-1 -0.5 0 0.5 1
cosΘ
2316 MeV
-1 -0.5 0 0.5 1
cosΘ
-1
-0.5
0
0.5
1
1.5
2
P
1661 MeV
-1 -0.5 0 0.5 1
cosΘ
2159 MeV
-1 -0.5 0 0.5 1
cosΘ
-2
0
2
4
6
β [ra
d]
1852 MeV
KΛ
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 13/ 16
Photon-induced reactions
πN → KΣ selected results, arXiv:1504.01643 [nucl-th]
π−p→ K 0Σ0
-1 -0.5 0 0.5 1
cosΘ
0
20
40
60
80
dσ
/dΩ
[µ
b/s
r]
z = 1694 MeV
-1 -0.5 0 0.5 1
cosΘ
2026 MeV
-1 -0.5 0 0.5 1
cosΘ
-2
-1
0
1
2
P
1724.5 MeV
-1 -0.5 0 0.5 1
cosΘ
2208 MeV
π−p→ K+Σ−
-1 -0.5 0 0.5 1
cosΘ
0
20
40
60
80
dσ
/dΩ
[µ
b/s
r]
1763 MeV
K+Σ
−
-1 -0.5 0 0.5 1
cosΘ
2305 MeV
No polarization data!
π+p→ K+Σ+
-1 -0.5 0 0.5 1
cosΘ
20
40
60
80
100
dσ
/dΩ
[µ
b/s
r]
z = 1729 MeV
-1 -0.5 0 0.5 1
cosΘ
2261 MeV
-1 -0.5 0 0.5 1
cosΘ
2031 MeV
-1 -0.5 0 0.5 1
cosΘ
-2
0
2
4
6
β [ra
d]
z = 2021 MeV
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 14/ 16
Photon-induced reactions
Partial wave contribution to F in γp → ηp arXiv:1504.01643 [nucl-th]
Switch off different PWs in Fit B
0
0.5
-1
-0.5
0
0.5
1
0 30 60 90 120 150-1
-0.5
0
0.5
1
E0+
switched off
0 30 60 90 120 150 0 30 60 90 120 150 0 30 60 90 120 150
1497 15161534 1558
15881617
1646 1674
1702 1743 17961847
F
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 15/ 16
Photon-induced reactions
Partial wave contribution to F in γp → ηp arXiv:1504.01643 [nucl-th]
Switch off different PWs in Fit B
0
0.5
-1
-0.5
0
0.5
1
0 30 60 90 120 150-1
-0.5
0
0.5
1
M1-
switched off
0 30 60 90 120 150 0 30 60 90 120 150 0 30 60 90 120 150
1497 15161534 1558
15881617
1646 1674
1702 1743 17961847
F
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 15/ 16
Photon-induced reactions
Partial wave contribution to F in γp → ηp arXiv:1504.01643 [nucl-th]
Switch off different PWs in Fit B
0
0.5
-1
-0.5
0
0.5
1
0 30 60 90 120 150-1
-0.5
0
0.5
1
E1+
, M1+
switched off
0 30 60 90 120 150 0 30 60 90 120 150 0 30 60 90 120 150
1497 15161534 1558
15881617
1646 1674
1702 1743 17961847
F
Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 15/ 16
Photon-induced reactions
Photoproduction of pseudoscalar meson
Photocouplings of resonanceshigh precision data from ELSA, MAMI, JLab...→ resolve questionable/find new states
Photoproduction amplitude of pseudoscalar mesons:Chew, Goldberger, Low, and Nambu, Phys. Rev. 106, 1345 (1957)
M = F1~σ · ~ε+ iF2~ε · (k × q) + F3~σ · k q · ~ε+ F4~σ · qq · ~ε
~q: meson momentum~k (~ε): photon momentum
(polarization)
Fi : complex functions of the scattering angle, constructed from multipole amplitudes M IJµγ
⇒ 16 polarization observables:asymmetries composed of beam, target and/or recoil polarization measurements
⇒ Complete Experiment: unambiguous determination of the amplitude
8 carefully selected observables, including Chiang and Tabakin, PRC 55, 2054 (1997)
single and double polarization observbalesmeasurement of beam, target and recoil polarization
easier to realize in K than in π or η photoproduction
→ Caveat: in reality more observables needed (data uncertainties)Deborah Ronchen, PWA 8 / ATHOS 3 The Julich Partial-Wave Analysis 16/ 16