analysis of new polarization data from frost · analysis of new polarization data from frost...

Analysis of new polarization data from FROST

Michael Doring

Julich-Athens-GWU: D. Ronchen, H. Haberzettl, J. Haidenbauer, C. Hanhart, F. Huang, S.Krewald, U.-G. Meißner, K. Nakayama

GW/INS Data Analysis Centre: W. Briscoe, I. Strakovsky, R. Workman

Future Directions in Spectroscopy Analysis Workshop, Nov. 18-20, 2014

MotivationPhoton-induced reactions Resonance analysis

Resonances

JP = 1/2+, I = 3/2

1200 1400 1600 1800 2000

E [MeV]

-0.5

-0.4

-0.3

-0.2

-0.1 Re S31

1200 1400 1600 1800 2000

E [MeV]

0.2

0.4

0.6

Im S31

πN-->πN

1200 1400 1600 1800 2000

E [MeV]

-30

-20

-10

0 Re E0+

(3/2)

1200 1400 1600 1800 2000

E [MeV]

0

2

4

6

8 Im E0+

(3/2)γN-->πN

Points: SAID 2006 and CM12

Breit-Wigner parameterization:

MResba = − gbga

E2−M2BW +iEΓBW

- MBW , ΓBW channel dependent- background? overlapping resonances? thresholds?

Resonances: poles in the T -matrix

Pole position E0 is the same in all channelsthresholds: branch points

Re(E0) = “mass”-2Im(E0) = “width”residues→ branching

ratios

2/ 36


The scattering matrix

S = 1+ iT

Unitarity: SS† = 1 ⇔ −i(T − T †) = T T †

3-body unitarity:discontinuities from t-channel exchanges→ Meson exchange from requirements of

the S-matrix [Aaron, Almado, Young, Phys. Rev. 174, 2022 (1968)]

Other cuts

to approximate left-hand cut → Baryon u-channel exchangeσ, ρ exchanges from crossing plus analytic continuation.

p3, λ3 p4, λ4

q, λ

p2, λ2p1, λ1

~q = ~p1 − ~p3

p4, λ4 p3, λ3

q, λ

p1, λ1 p2, λ2

~q = ~q1 − ~p4

p3, λ3 p4, λ4

p2, λ2p1, λ1

q, λ

~q = ~p1 + ~p2 = 0

π π

π π

π

π

N

N

σ, ρ

s (πN→ πN)

t (NN→ ππ)

3/ 36


A dynamical coupled-channel approach: the hadronic 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

q2 dq〈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

4/ 36


A dynamical coupled-channel approach: the hadronic 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

q2 dq〈L′S′p′|V IJµγ |L′′S′′q〉

1E − Eγ(q) + iε

〈L′′S′′q|T IJγν |LSp〉

Analyticity is respected (correct structure of branch points and cuts)→ reliable extraction of resonance parameters

Unitarity

J ≤ 9/2

πN ππN

1077 1215π∆

ηN

1486

σN

KΛ

1611

KΣ

1688

NρECM[MeV]

∼ 2.3 GeV

4/ 36


πN → ηN,KΛ selected resultsEur.Phys.J. A49 (2013) 44, Nucl.Phys. A851 (2011) 58-98

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

2148 MeV

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]

2107 MeV

Full results

5/ 36


πN → KΣ selected results

π−p→ K 0Σ0

-1 -0.5 0 0.5 1

cosΘ

0

20

40

60

80

dσ

/dΩ

[µ

b/s

r]

E = 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

-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

-1

-0.5

0

0.5

1

P

2031 MeV

-1 -0.5 0 0.5 1

cosΘ

-2

0

2

4

6

β [ra

d]

2021 MeV

Full results

6/ 36


Photon-induced vs. Pion-induced reactions

7/ 36


Improvement in Modern Experimental Facilities: πN → πNEPECUR & GWU/SAID, Alekseev et al., arXiv:1410.6418

Black: WI08 prediction; Red: WI14 fit; green: KA84.

9/ 36


πN → πN partial wave amplitudes Coupled-channels at work

-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)

10/ 36


πN → πN partial wave amplitudes Coupled-channels at work

-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

motivated by KΛ

N(1710)1/2+

-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

Genuine N(1710)1/2+:

1500 1600 1700 1800 1900

E [MeV]

-0.1

0

0.1

1500 1600 1700 1800 1900

E [MeV]

0.4

0.5

0.6

Im P11

Re P11

Black line: input to fit(energy-dependent solution)Inclusion of P11(1710) necessary toimprove KΛ

Coupled-channels essential( Fit to πN observables )

10/ 36


Resonance content: I=1/2

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

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

Numbers x: branch points Notation: N(“name”) J parity

11/ 36


Resonance content: I=3/2

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]

-450

-400

-350

-300

-250

-200

-150

-100

-50

0

Im E

[M

eV

]

Fit AFit B

πN ππN

π∆

KΣ

ρN

∆(1910) 1/2+

∆(1920) 3/2+

∆(1700) 3/2-

∆(2200) 7/2-

∆(2400) 9/2-

∆(1232) 3/2+ ∆(1905) 5/2

+

∆(1950) 7/2+

∆(1620) 1/2−

physical axis

∆(1930) 5/2−

∆(1600) 3/2+

Numbers x: branch points Notation: ∆(“name”) J parity

12/ 36

MotivationPhoton-induced reactions

Data analysis and fit results

Photoproduction of pseudoscalar mesons [D. Ronchen, M.D., et. al., Eur. Phys. J. A (2014) 50: 101]

Photocouplings of resonanceshigh precision data from ELSA, MAMI, JLab...→ resolve questionable/find new states

Photoproduction amplitude of pseudoscalar mesons:

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

⇒ 16 polarization observables:asymmetries composed of beam, target and/or recoil polarization measurements

⇒ 8 carefully selected observables: complete experiment→ Caveat: in reality more observables needed (data uncertainties)

Focus of the present analysis:

extraction of electromagnetic resonance parameters⇒ flexible, “model-independent” parameterization of photo excitation

Advantage: easy to implement, analyze large amounts of dataDisadvantage: no information on microscopic reaction dynamics

⇒ intermediate steptowards a combined DCCanalysis of pion- andphoton-induced reactions

13/ 36



Data base of γp → π0p, π+n

Fit 1 Fit 2Line style

# of data 21,627 23,518Excluded data π0p: E > 2.33 GeV and

θ < 40 for E > 2.05 GeVπ+n: E > 2.26 GeV and

θ < 9 for E > 1.60 GeVds/dΩ, P, T included includedΣ included included

(CLAS 2013 predicted)∆σ31, G, H predicted includedE, F, Cx′L , Cz′L predicted predicted

Complete experiment

one possibility:

σ, Σ, T , P , E , G, Cx , Cz

⇒ Influence of new doublepolarization observableson resonance parameters

Minimization using parallelized code on JUROPA (FZ Julich)

14/ 36



Single polarization observables selected results

dσ/dΩ Polarization: Beam Target Recoil0 0 0

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]

2

4 [2][3][4]

1462

0 30 60 90 120150

Θ [deg]

0.1

1

[5]

2248

[1] Schmidt 2001 (MAMI) [2] Beck 2006 (MAMI)[3] Dugger 2007 (JLab) [4] Bartholomy 2005 (ELSA)[5] Crede 2011 (ELSA)

γp→ π+n

0 30 60 90 120150

Θ [deg]

5

10

15

dσ

/dΩ

[µ

b/s

r] [6]

1162

0 30 60 90 120150

Θ [deg]

2

4

6

8

[7]

1648

0 30 60 90 120150

Θ [deg]

0.1

1

[8][7]

2140

[6] Ahrens 2004 (MAMI) [7] Dugger 2009 (JLab) [8] Buschhorn 1966

Beam asymmetry Σ Polarization:Beam Target Recoil⊥ 0 0‖ 0 0

γp→ π0p

0 30 60 90 120150

Θ [deg]

-1

-0.5

0

0.5

1

Σ

[1]

1075

0 30 60 90 120150

Θ [deg]

[2][3][4]

1785

0 30 60 90 120150

Θ [deg]

[5]2027

γp→ π+n

0 30 60 90 120150

θ [deg]

-1

-0.5

0

0.5

1

Σ

[6]

1140

0 30 60 90 120150

Θ [deg]

[7][8]

1660

0 30 60 90120150

Θ [deg]

[5] 2092

[1] Hornidge 2013 (MAMI)[2] Elsner 2009 (ELSA)[3] Sparks 2010 (ELSA)[4] Bartalini 2005 (GRAAL)[5] Dugger 2013 (JLab)[6] Blanpied 2001 (LEGS)[7] Bartalini 2002 (GRAAL)[8] Ajaka 2000 (GRAAL)

15/ 36



Double polarization observables selected results

∆σ31 ∆σ31 = −2 dσdΩ E

predictionfit

Beam Target Recoil+1 −z 0−1 −z 0

γp→ π0p

0 30 60 90120150

-45

-30

-15

-∆σ

31

[µb

/sr] [1]

0 30 60 90120150

Θ [deg]

-2

0

2

[2]

0 30 60 90120150

-2

0

2

1240 1430 1519

[1] Ahrens et al. 2004 (MAMI) [2] Ahrens et al. 2002 (MAMI)

γp→ π+n

0 30 60 90 120150

0

5

10

15

20

-∆σ

31 [

µb

/sr]

[1]

0 30 60 90 120150

Θ [deg]

-5

0

5

[3]

0 30 60 90 120150

-10

-5

0

51121

1364

1533

[3] Ahrens et al. 2006 (MAMI)

Predictions of EBeam Target Recoil+1 −z 0−1 −z 0

[4] Gottschall et al. 2013 (ELSA) γp→ π0p

0 30 60 90 120 150

-1

-0.5

0

0.5

1

E

[4]

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]

16/ 36



Double polarization observables selected results

GBeam Target Recoil⊥′ −z 0‖′ −z 0

γp→ π0p

0 30 60 90 120 150

-1

-0.5

0

0.5

1

G

[1]

0 30 60 90 120 150 0 30 60 90 120 150 0 30 60 90 120 150 180

171616031543 1660

Θ [deg]

γp→ π+n

0 30 60 90 120150

Θ [deg]

-1

-0.5

0

0.5

1

G

[2]

0 30 60 90 120150180

Θ [deg]

[3]

1232

1885predictionfit

[1] Thiel et al. 2012 (ELSA)[2] Ahrens et al. 2005 (MAMI)[3] Bussey et al. 1980

Cx′Beam Target Recoil+1 0 −x′−1 0 −x′γp→ π0p

1500 2000

-0.5

0

0.5

1

[1]

[2]

1500 2000

θ=(75±5)0

θ=(105±5)0

Cx’

L

θ=750

θ=1050

1500 2000 1500 2000

[3]

θ=(140±10)0

θ=(115±5)0

1430

1350

1200

[1] Sikora et al. 2013 (MAMI) E [MeV] [3] Luo et al. 2012 (JLab)

[2] Wijesooriya et al. 2002 (JLab)

Predictions offit 1, angle averagedfit 2, angle averaged

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

fit 2, not angle averaged

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

fit 2, not angle averaged

17/ 36



Multipoles: E0+ (π0p) at threshold

Mγ

π0p =γ

p

π0

p

π0

p

π+

n

π0

p

γ

pp

γπ0

p+ +

T T

+ ...

-1

-0.5

0

Data analysis (A2 & CB-TAPS 2012)

Data analysis (TAPS/MAMI, 2001)

ChPT (09, 11) [Im. part]

Chiral MAID (2013)

ChPT (2005)

Fit 1Fit 2

150 160 170 180E

γ[MeV]

0

0.5

1

1.5

π+

n

Im E0+

Re E0+

E0

+(π

0p

) [1

0-3

/Mπ

+]

Different π & Nmasses→ cusp effect

18/ 36



Photocouplings at the pole selected results

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 A3/2

pole ϑ3/2

[10−3 GeV−1/2 ] [deg] [10−3 GeV−1/2 ] [deg]

fit→ 1 2 1 2 1 2 1 2

N(1710) 1/2+ 15 28+9−2 13 77+20

−9

∆(1232) 3/2+ -116 −114+10−3 -27 −27+4

−2 -231 −229+3−4 -15 −15+0.3

−0.4

Fit 1: only single polarization observables includedFit 2: also double polarization observables included

19/ 36



First FROST results: E in ~γ~p → π+nS. Strauch et al., in preparation

Blue dashed: Prediction BnGa Eur. Phys. J. A 48, 15 (2012)

Green dashed-dotted: Prediction MAID07 Eur. Phys. J. A 34, 69 (2007)

Red solid: Refit DAC at GWU (SAID)Black short-dashed; Refit Julich

20/ 36



Refits (Julich & GWU/SAID)

21/ 36



Impact on resonance parameters

A [10−3 GeV−1/2]; ϑ [deg].Pole values (P) or Breit-Wigner Parameters (BW).“;” separates before and after new FROST E-measurement.

A1/2pole ϑ1/2 A3/2

pole ϑ3/2

N(1535) 1/2−SAID BW 120± 10; 128± 4Julich P 49; 50 −46;−45BnGa P 116± 10 7± 6

ANL-Osaka P 161 9WTS P 77± 5 4PDG BW 90± 30

N(1650) 1/2−SAID BW 60± 30; 55± 30Julich P 26; 23 −58;−29BnGa P 33± 7 −9± 15

ANL-Osaka P 40 −44WTS P 35± 3 −16PDG BW 53± 16

22/ 36



Impact on resonance parameters

A1/2pole ϑ1/2 A3/2

pole ϑ3/2

N(1440) 1/2+

SAID BW -60± 5; −56± 1Julich P −52;−54 −51;−43BnGa P −44± 7 −38± 5

ANL-Osaka P 49 −10WTS P −66± 5 −38PDG BW −60± 4

N(1675) 5/2−SAID BW 10± 3; 13± 1 16± 4; 16± 1Julich P 28; 22 40; 38 63; 36 −19;−41BnGa P 24± 3 −16± 5 26± 8 −19± 6

ANL-Osaka P 5 −22 33 −23PDG BW 19± 8 15± 9

23/ 36



T and F in γp → ηp (MAMI) preliminary

25/ 36



FROST E in γp → ηp preliminaryPreliminary data thanks to M. Dugger and I. Senderovich

26/ 36



FROST E in γp → ηp: Excitation function preliminaryPreliminary data thanks to M. Dugger and I. Senderovich

-1

-0.5

0

0.5

1

1600 1800 2000

1600 1800 2000-1

-0.5

0

0.5

1

1600 1800 2000

Experiment

Fit

Fit; (W,cosθ) averaged

Rebinning included

Rebinning & averaged

cosθ=-0.9 / 154° cosθ=-0.6 / 127°cosθ=-0.2 / 102°

cosθ=0.2 / 78° cosθ=0.6 / 53°

E

W [MeV]

NO additional structure at W = 1.68 GeV → interferences & KΣ threshold.27/ 36



MAMI Cx ′ in γp → ηp preliminaryPreliminary data thanks to D. Watts and M. Sikora

1600 1700 1800W [MeV]

-1

-0.5

0

0.5

1

Cx’ L

(γp

->

ηp

)

1600 1700 1800W [MeV]

θ=(70+-20)o θ=(115+-25)

o

(Data not included in fit)

28/ 36



First results in γp → KΛ very preliminary

29/ 36



Putting different analyses on common ground... and have eventually convergence of results among different groups (?)

BnGa, Julich, MAID, Zagreb. . . fit to SAID elastic πN partial waves or useit as FSI.Single-energy solutions of SAID: narrow structures & consistency, butlittle statistical meaning.No control of the statistical impact of elastic πN data on multi-reactionfits, performed by other groups.Q: is it possible to provide a simple to use interface, such that other groupscan fit to SAID elastic πN PWs and get the same χ2 as if they had fittedto the elastic πN data?

30/ 36



Work in progress: Monte-Carlo error propagation

Bands: Monte-Carlo error propagation using bootstrap (energy-dependent fit).Statistically meaningfulbut: correlations between different partial waves/multipoles are also there!How to provide? Solution: Instead of PWs, we plan to provide correlationmatrices for the SES.

31/ 36



Work in progress: Correlated χ2 fits

0.90 0.95 1.00 1.05 1.10 1.15

0.85

0.90

0.95

1.00

1.05

1.10

1.15

PW 1

PW

2

Fit “observable” O(E) with

O(E) = (PW 1)E + (PW 2) E2

100Data generated around

O(E) = E +E2

100

Stochastic estimate of correlation matrix.Correlated χ2: χ2(x) = (x − x)T C−1(x − x), x = (S11,S31, . . . )

but does this provide the same χ2 as a fit to the original data?

32/ 36



Work in progress: Correlated χ2 fits

... almost; the function

χ2 = (x − x)T C−1(x − x) + χ2best + corrections

does.Difference between correlated χ2 and actual χ2 of the data themselves(toy model):

33/ 36



Summary and Outlook

Extraction of the N∗ and ∆ resonance spectrum

DCC analysis of πN → πN , ηN , KΛ and KΣ

Julich model: lagrangian based, unitarity & analyticity respected→ analysis of over 6000 data points (PWA, dσ/dΩ, P , β)

→ extraction of resonance parameters (poles & residues)

Pion photoproduction in a semi-phenomenological approach

hadronic final state interaction: Julich DCC analysis→ analysis of more than 23 000 data points for single and double polarization observables

→ extraction of photocouplings at the pole

Next: η (world data fitted) and Kaon photoproduction (in progress)

Next: High-energy constraints through FESR.

34/ 36

Pion-induced reactions

Analysis of pion-induced reactionsEur.Phys.J. A49 (2013) 44, Nucl.Phys. A851 (2011) 58-98

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 base1/ 38

Pion-induced reactions Data analysis and fit results

Data base and fit

Data base:elastic πN PWA SAID 2006 [Arndt et al., PRC 74 (2006)]

πN → ηN , KY observables (dσ/dΩ, P , β)

∼ 6000 data points

Fit parameters:T P : 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)

T NP : 68 free parameters

196 freeparameters

⇒ Simultaneous fit of T P and T NP using MINUIT on the JUROPA supercomputer (FZJ)

Sensitivity of results to starting conditions?

=⇒ Perform 2 fits, start from different scenarios in parameter set

Fit A: start from parameter set of a preceding Julich model [Gasparyan et al. PRC68 , (2003) ]

Fit B: start from a new scenario

2/ 38


Photoproduction in a semi-phenomenological approach

Multipole amplitude

M IJµγ = V IJ

µγ +∑κ

T IJµκGκV IJ

κγ

(partial wave basis)

γ

N

π

N

Vπγ

γ

N

π

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;i(q)

mNPNPµ (E) +

∑i

γaµ;i(q)PP

i (E)

E − mbi

γaµ;i , γ

aµ;i : hadronic vertices→ correct threshold behaviour

i: resonance number per multipole; µ: channels πN , ηN , π∆

Method inspired by SAID

but differentPolynomials

3/ 38


Multipoles: Comparison with GWU/SAID CM12

0

5

10

15

Re(A

) [1

0-3

fm

]

-2

0

2

4

0

1

2

-2

0

2

-4

0

4

-2

0

2

1.25 1.5 1.75 2 2.25

0

4

8

Im(A

) [1

0-3

fm

]

1.25 1.5 1.75 2 2.25

-2

0

2

4

6

1.25 1.5 1.75 2 2.25

0

0.4

0.8

1.2

1.25 1.5 1.75 2 2.25-0.5

0

0.5

1

1.25 1.5 1.75 2 2.25

0

4

8

1.25 1.5 1.75 2 2.25

0

2

4

0

0.25

0.5

0.75

Re(A

) [1

0-3

fm

]

-0.4

-0.2

0

0.2

-1

0

1

2

-1

0

1

0.05

0.1

0.15

0.2

0.25

-0.2

-0.1

0

1.25 1.5 1.75 2 2.25-0.1

0

0.1

0.2

0.3

Im(A

) [1

0-3

fm

]

1.25 1.5 1.75 2 2.25

0

0.2

0.4

1.25 1.5 1.75 2 2.25

0

1

2

3

1.25 1.5 1.75 2 2.25

0

0.5

1

1.5

2

1.25 1.5 1.75 2 2.25

0

0.02

0.04

0.06

0.08

1.25 1.5 1.75 2 2.25

-0.02

0

0.02

0.04

0.06

0

0.1

0.2

0.3

0.4

Re(A

) [1

0-3

fm

]

0

0.1

0.2

0

0.04

0.08

-0.08

-0.04

0

0.05

0.1

0.15

0.2

0

0.05

0.1

1.25 1.5 1.75 2 2.25-0.04

-0.02

0

0.02

0.04

0.06

Im(A

) [1

0-3

fm

]

1.25 1.5 1.75 2 2.25

0

0.1

0.2

0.3

1.25 1.5 1.75 2 2.25-0.02

-0.01

0

0.01

0.02

1.25 1.5 1.75 2 2.25

0

0.04

0.08

1.25 1.5 1.75 2 2.25

0

0.02

0.04

0.06

0.08

1.25 1.5 1.75 2 2.25

0

0.05

0.1

0.15

E0+

(1/2,p) M1-

(1/2,p) E1+

(1/2,p) M1+

(1/2,p) E2-

(1/2,p) M2-

(1/2,p)

E2+

(1/2,p) M2+

(1/2,p) E3-

(1/2,p) M3-

(1/2,p) E3+

(1/2,p)

E4-

(1/2,p)

M3+

(1/2,p)

M4-

(1/2,p) E4+

(1/2,p) M4+

(1/2,p) E5-

(1/2,p) M5-

(1/2,p)

E [GeV]

4/ 38


Multipoles: Comparison with GWU/SAID CM12

-30

-20

-10

0

Re(A

) [1

0-3

fm

]

-10

-5

0

-3

-2

-1

0

-30

-15

0

15

30

45

-10

-5

0

-1

-0.5

0

0.5

1.25 1.5 1.75 2 2.25

0

2

4

6

8

Im(A

) [1

0-3

fm

]

1.25 1.5 1.75 2 2.25-1

0

1

2

3

1.25 1.5 1.75 2 2.25

-2

0

2

1.25 1.5 1.75 2 2.25

0

20

40

60

1.25 1.5 1.75 2 2.25

-6

-4

-2

0

2

1.25 1.5 1.75 2 2.25

-0.5

0

0.5

1

1.5

2

-1.5

-1

-0.5

0

Re(A

) [1

0-3

fm

]

-0.8

-0.4

0

0.4

-2-1.5

-1-0.5

00.5

1

-0.2

0

0.2

-0.4

-0.3

-0.2

-0.1

0

-1

0

1

2

1.25 1.5 1.75 2 2.25

-0.1

0

0.1

0.2

0.3

Im(A

) [1

0-3

fm

]

1.25 1.5 1.75 2 2.25

-0.2

-0.1

0

0.1

1.25 1.5 1.75 2 2.25

-0.4

0

0.4

0.8

1.25 1.5 1.75 2 2.25

0

0.2

0.4

0.6

1.25 1.5 1.75 2 2.25

-0.1

-0.05

0

0.05

0.1

1.25 1.5 1.75 2 2.25

0

1

2

3

-0.6

-0.4

-0.2

0

Re(A

) [1

0-3

fm

]

-0.1

-0.05

0

0.05

0.1

-0.15

-0.1

-0.05

0

-0.1

-0.05

0

0.05

0.1

0.15

-0.25

-0.2

-0.15

-0.1

-0.05

0

-0.1

-0.05

0

0.05

0.1

0.15

1.25 1.5 1.75 2 2.25

-0.2

-0.1

0

0.1

0.2

Im(A

) [1

0-3

fm

]

1.25 1.5 1.75 2 2.25-0.05

0

0.05

0.1

1.25 1.5 1.75 2 2.25

-0.04

-0.02

0

0.02

1.25 1.5 1.75 2 2.25

-0.1

-0.05

0

0.05

0.1

1.25 1.5 1.75 2 2.25

-0.1

-0.05

0

0.05

1.25 1.5 1.75 2 2.25

-0.04

-0.02

0

0.02

0.04

E0+

(3/2) M1-

(3/2) E1+

(3/2) M1+

(3/2) E2-

(3/2) M2-

(3/2)

E2+

(3/2) M2+

(3/2) E3-

(3/2) M3-

(3/2) E3+

(3/2)

E4-

(3/2)

M3+

(3/2)

M4-

(3/2) E4+

(3/2) M4+

(3/2) E5-

(3/2) M5-

(3/2)

E [GeV]

4/ 38


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

5/ 38


Isospin breaking in the πN channel

Hadronic reactions: data well above threshold → isospin averaged masses

Pion-photoproduction: data near threshold → include isospin breaking→ use exact π0 (π+) and p (n) mass

Ecm < 1140 MeV:

Mγ

π0p =

Mγ

π+n =

γ

p

π0

p

π0

p

π+

n

π0

p

γ

pp

γπ0

p+ +

T T

γ

p

π0

p

π+

n

π+

n

π+

n

γ

pp

γπ+

n

+ +T T

+ ...

+ ...

6/ 38


πN → πN: Partial wave amplitudes I=1/2

-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

-0.2

-0.1

0

0.1

0.2

0.3

0.4

-0.4

-0.2

0

0.2

0.4

0

0.2

0.4

0.6

0.8

Re P13

Re D13

Im P13

Im D13

1200 1400 1600 1800 2000

z [MeV]

-0.1

0

0.1

0.2

1200 1400 1600 1800 2000

z [MeV]

0.1

0.2

0.3

0.4Re D

15Im D

15

-0.4

-0.2

0

0.2

0.4

0

0.2

0.4

0.6

0.8Re F

15 Im F15

-0.05

0

0.05

0.05

0.1

0

0.1

0

0.1

0.2

Im F17

Im G17

Re F17

Re G17

-0.05

0

0.05

0.05

0.1

1200 1600 2000

z [MeV]

0

0.1

1200 1600 2000

z [MeV]

0

0.1

0.2

Im G19

Im H19

Re G19

Re H19

back 7/ 38


πN → πN: Partial wave amplitudes I=3/2

-0.5

-0.4

-0.3

-0.2

-0.1

0.2

0.4

0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Re S31

Re P31

Im S31

Im P31

-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

1200 1400 1600 1800 2000

z [MeV]

-0.15

-0.1

-0.05

0

1200 1400 1600 1800 2000

z [MeV]

0

0.05

0.1

0.15

Re D35

Im D35

-0.15

-0.1

-0.05

0

0.05

0

0.05

0.1

0.15

Re F35

Im F35

-0.1

0

0.1

0.2

0.3

0.1

0.2

0.3

0.4

-0.1

-0.05

0

0

0.05

0.1

0.15

Im F37

Re F37

Re G37 Im G

37

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.02

0.04

0.06

0.08

0.1

0.12

0.14

1200 1600 2000

z [MeV]

-0.04

-0.02

0

0.02

0.04

1200 1600 2000

z [MeV]

0

0.01

0.02

0.03

0.04

Im G39

Re H39

Re G39

Im H39

back 8/ 38


Full results ηN: dσ/dΩ

0

0.05

0.1

0.15

0.2

0

0.05

0.1

0.15

0.2

0.25

z=1489 MeV 1492 MeV 1496 MeV 1498 MeV

1499 MeV 1503 MeV 1507 MeV 1509 MeV

dσ

/dΩ

[ m

b/s

r ]

0

0.1

0.2

0.3

0.4

0

0.1

0.2

0.3

0.4dσ

/dΩ

[ m

b/s

r ]

z = 1512 MeV 1517 MeV 1522 MeV 1526 MeV

1531 MeV 1534 MeV 1545 MeV 1576 MeV

0

0.1

0.2

0.3

0.4

-1 -0.5 0 0.5 10

0.1

0.2

0.3

0.4

-1 -0.5 0 0.5 1-1 -0.5 0 0.5 1-1 -0.5 0 0.5 1

dσ

/dΩ

[ m

b/s

r ]

z = 1587 MeV 1608 MeV 1636 MeV 1648 MeV

1664 MeV 1674 MeV 1691 MeV 1729 MeV

cosΘ

0

0.1

0.2

0.3

0.4

0

0.1

0.2

0.3dσ

/dΩ

[ m

b/s

r ]

z = 1740 MeV 1793 MeV 1805 MeV 1833 MeV

1872 MeV 1897 MeV 1904 MeV 1949 MeV

back

9/ 38


Full results ηN: dσ/dΩ & Polarization

0

0.05

0.1

0.15

-1 -0.5 0 0.5 1

-1 -0.5 0 0.5 10

0.05

0.1

0.15

-1 -0.5 0 0.5 1-1 -0.5 0 0.5 1

dσ

/dΩ

[ m

b/s

r ]

cosΘ

z = 1989 MeV 2024 MeV 2070 MeV 2114 MeV

2149 MeV 2235 MeV 2412 MeV

-0.025

0

0.025

0.05

0.075

-0.025

0

0.025

0.05

0.075

z = 1740 MeV 1793 MeV 1833 MeV 1872 MeV

1904 MeV 1949 MeV 1989 MeV 2024 MeV

P x

dσ

/dΩ

[ m

b/s

r ]

-1 -0.5 0 0.5-0.05

-0.025

0

0.025

0.05

0.075

-1 -0.5 0 0.5 -1 -0.5 0 0.5 -1 -0.5 0 0.5 1

cosΘ

z = 2070 MeV 2114 MeV 2148 MeV 2235 MeV

back

10/ 38


π−p → ηN: Total cross section

1490 1500 1510 1520 1530

0

0.5

1

1.5

2

2.5

3

1500 1600 1700 1800 1900 2000 2100 2200 2300

z [MeV]

0

0.5

1

1.5

2

2.5

3

3.5

σ [

mb

]

KΛ KΣ thresholds

Partial wave content

11/ 38


ηN: Partial wave content

1500 1600 1700 1800 1900 2000 2100 2200 2300

z [MeV]

1e-05

0.0001

0.001

0.01

0.1

1

σ [m

b]

S11P

11

P13

D13

D15

F15

F17

G17

G19

H19

back

12/ 38


Full results KΛ: dσ/dΩ

0

20

40

60

80

100

120

20

40

60

80

100

120

dσ

/dΩ

[ µ

b/s

r ]

1633 MeV 1648 MeV 1661 MeV

1671 MeV 1676 MeV 1678 MeV 1682 MeV

z = 1626 MeV

0

20

40

60

80

100

120

20

40

60

80

100

120

dσ

/dΩ

[

µb/s

r ]

z = 1684 MeV 1686 MeV 1687 MeV 1689 MeV

1693.5 MeV 1698 MeV 1701 MeV 1707 MeV

0

20

40

60

80

100

120

-1 -0.5 0 0.5 1

20

40

60

80

100

120

-1 -0.5 0 0.5 1-1 -0.5 0 0.5 1-1 -0.5 0 0.5 1

dσ

/dΩ

[ µ

b/s

r ]

z = 1724 MeV 1742 MeV 1758 MeV 1792 MeV

1797 MeV 1819 MeV 1825 MeV 1846 MeV

cosΘ

z = 1879 MeV 1909 MeV 1930 MeV 1934 MeV

1938 MeV 1966 MeV 1973 MeV 1978 MeV

back13/ 38


Full results KΛ: dσ/dΩ

z = 1999 MeV 2026 MeV 2059 MeV 2097 MeV

2104 MeV 2137 MeV 2159 MeV 2182 MeV

-1 -0.5 0 0.5 1-1 -0.5 0 0.5 1

-1 -0.5 0 0.5 1-1 -0.5 0 0.5 1

cosΘ

z = 2208 MeV 2244 MeV 2259 MeV 2305 MeV

2316 MeV 2405 MeV

back

14/ 38


Full results KΛ: Polarization

-1

-0.5

0

0.5

1

-0.5

0

0.5

1

1.5

Pz = 1633 MeV 1661 MeV 1683 MeV 1694 MeV

1724 MeV 1741 MeV 1758 MeV 1792 MeV

-1

-0.5

0

0.5

1

1.5

2

-1

-0.5

0

0.5

1

1.5

Pz = 1797 MeV

1819 MeV 1825 MeV 1845.5 MeV

1851 MeV 1879 MeV 1909 MeV 1939 MeV

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-1 -0.5 0 0.5 1-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-1 -0.5 0 0.5 1-1 -0.5 0 0.5 1-1 -0.5 0 0.5 1

P

z = 1966 MeV 1999 MeV 2028 MeV 2060 MeV

2105 MeV 2159 MeV 2183 MeV 2208 MeV

cosΘ

-1-0.5 0 0.5 1

-40

-20

0

20

40

60

-1-0.5 0 0.5 1-1-0.5 0 0.5 1

P x

dσ

/dΩ

[µ

b/s

r]

cosΘ

z=1627 MeV 1648 MeV1672 MeV

back

15/ 38


Full results KΛ: Spinrotation parameter β

-2

0

2

4

6

-1 -0.5 0 0.5 1

-1 -0.5 0 0.5 1

-2

0

2

4

6

-1 -0.5 0 0.5 1-1 -0.5 0 0.5 1

z = 1852 MeV 1941 MeV 2031 MeV 2063 MeV

2107 MeV 2160 MeV 2262 MeVβ [

rad

]

cosΘ

β = arctan(

2Im(h∗fi gfi)

|gfi|2 − |hfi|2

)

back

16/ 38


π−p → K 0Λ: Total cross section Eur.Phys.J. A49 (2013) 44

1700 1800 1900 2000 2100 2200 2300

z [MeV]

0

0.2

0.4

0.6

0.8

1

σ [

mb

]

1625 1650 1675 1700 1725

0

0.2

0.4

0.6

0.8

1

KΣ threshold

KΣ

back

17/ 38


KΛ: Partial wave content

1700 1800 1900 2000 2100 2200 2300

z [MeV]

0.0001

0.001

0.01

0.1

1σ

[m

b]

P11

S11

P13

D13 D

15

F15

F17

G17

G19

H19

back

18/ 38


Full results K 0Σ0: dσ/dΩ

0

20

40

60

80

20

40

60

80

dσ

/dΩ

[

µb

/sr

]

z = 1694 MeV 1724 MeV 1741 MeV 1758 MeV

1792 MeV 1797 MeV 1819 MeV 1825 MeV

0

20

40

60

80

-1 -0.5 0 0.5 1

20

40

60

80

-1 -0.5 0 0.5 1-1 -0.5 0 0.5 1-1 -0.5 0 0.5 1

dσ

/dΩ

[

µb

/sr

]

z = 1845.5 MeV 1879 MeV 1909 MeV 1930 MeV

1934 MeV 1938 MeV 1966 MeV 1978 MeV

cosΘ

z = 1999 MeV 2026 MeV 2059 MeV 2097 MeV

2104 MeV 2137 MeV 2182 MeV 2208 MeV

-1 -0.5 0 0.5 1-1 -0.5 0 0.5 1-1 -0.5 0 0.5 1

-1 -0.5 0 0.5 1

cosΘ

z = 2244 MeV 2259 MeV 2305 MeV 2316 MeV

2405 MeV

back19/ 38


Full results K 0Σ0: Polarization

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-1.5

-1

-0.5

0

0.5

1

1.5

P

z = 1694 MeV1724.5 MeV 1758 MeV

1792.5 MeV

1825.5 MeV 1847.5 MeV 1879 MeV 1909 MeV

-1

-0.5

0

0.5

1

-1

-0.5

0

0.5

1

-1 -0.5 0 0.5 1

-1 -0.5 0 0.5 1

-1

-0.5

0

0.5

1

-1 -0.5 0 0.5 1-1 -0.5 0 0.5 1

P

cosΘ

z=1938 MeV

1966 MeV 1999 MeV 2027 MeV

2059 MeV 2104 MeV 2159 MeV 2183 MeV

2208 MeV 2259 MeV 2316 MeV

back

20/ 38


K 0Σ0: Partial wave content I=1/2

1700 1800 1900 2000 2100 2200 2300

z [MeV]

1e-05

0.0001

0.001

0.01

0.1

σ [

mb]

S11

P11

P13

D13

D15

F15

F17 G

17

G19

H19

back

21/ 38


K 0Σ0: Partial wave content I=3/2

1700 1800 1900 2000 2100 2200 2300

z [MeV]

1e-05

0.0001

0.001

0.01

0.1

σ [

mb]

P33

S31

P31

D33

D35

F35

F37

G37

G39

back

22/ 38


Full results K+Σ−: dσ/dΩ

20

40

60

20

40

60

80

dσ

/dΩ

[

µb/s

r ]

z = 1739 MeV 1763 MeV 1792 MeV 1818 MeV

1843 MeV 1930 MeV 1973 MeV 1978 MeV

10

20

30

-1 -0.5 0 0.5 1

-1 -0.5 0 0.5 1

10

20

30

40

-1 -0.5 0 0.5 1-1 -0.5 0 0.5 1

dσ

/dΩ

[

µb/s

r ]

cosΘ

z = 2025 MeV 2097 MeV 2137 MeV 2180 MeV

2244 MeV 2305 MeV 2405 MeV

no Polarization data !

back

23/ 38


π−p → K+Σ−: Total cross section Eur.Phys.J. A49 (2013) 44

1700 1800 1900 2000 2100 2200 2300

z [MeV]

0

0.05

0.1

0.15

0.2

0.25

σ [

mb

]

back

24/ 38


Full results K+Σ+: dσ/dΩ

10

20

30

40

50

10

20

30

40

50dσ

/dΩ

[

µb

/sr

]

z = 1729 MeV 1732 MeV 1757 MeV 1764 MeV

1783 MeV 1789 MeV 1790 MeV 1813 MeV

20

40

60

80

100

-1 -0.5 0 0.5 1

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/s

r ]

z = 1822 MeV 1845 MeV 1870 MeV 1891 MeV

1926 MeV 1939 MeV 1970 MeV 1985 MeV

cosΘ

20

40

60

80

100

120

20

40

60

80

100

120

dσ

/dΩ

[

µb/s

r ]

z = 2019 MeV2031 MeV

2059 MeV 2074 MeV

2106 MeV 2118 MeV 2147 MeV 2158 MeV

20

40

60

80

-1 -0.5 0 0.5 1

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/s

r ]

cosΘ

z = 2188 MeV 2202 MeV 2224 MeV 2243 MeV

2261 MeV 2282 MeV 2304 MeV 2318 MeV

back

25/ 38


Full results K+Σ+: Polarization

-1

-0.5

0

0.5

1

1.5

-1

-0.5

0

0.5

1

1.5P

z = 1729 MeV 1732 MeV 1757 MeV 1764 MeV

1783 MeV 1789 MeV 1790 MeV 1813 MeV

-1

-0.5

0

0.5

1

-1 -0.5 0 0.5 1

-1

-0.5

0

0.5

1

1.5

-0.5 0 0.5 1 -0.5 0 0.5 1 -0.5 0 0.5 1

P

z = 1822 MeV 1845 MeV 1870 MeV 1891 MeV

1926 MeV 1939 MeV 1970 MeV 1985 MeV

cosθ

-1

-0.5

0

0.5

1

-1

-0.5

0

0.5

1

1.5

z = 2019 MeV 2031 MeV 2059 MeV 2074 MeV

2106 MeV 2118 MeV 2147 MeV 2158 MeVP

-1

-0.5

0

0.5

1

-0.5 0 0.5 1

-1

-0.5

0

0.5

1

1.5

-0.5 0 0.5 1 -0.5 0 0.5 1 -0.5 0 0.5 1

cosΘ

z = 2188 MeV 2202 MeV 2224 MeV 2243 MeV

2261 MeV 2282 MeV 2304 MeV 2318 MeVP

back

26/ 38


π+p → K+Σ+: Total cross section Eur.Phys.J. A49 (2013) 44

1700 1800 1900 2000 2100 2200 2300 2400

z [MeV]

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

σ [m

b]

back

27/ 38


Resonance content: I = 1/2

Re z0 -2Im z0 |rπN | θπN→πN ΓπN/Γtot

[MeV] [MeV] [MeV] [deg] [%]fit→ A B A B A B A B A B

N(1535) 1/2− 1498 1497 74 66 17 13 -37 -43 40 44N(1650) 1/2− 1677 1675 146 131 45 27 -43 -38 61 41N(1440) 1/2+

(a) 1353 1348 212 238 59 62 -103 -111 56 52N(1710) 1/2+ 1637 1653 97 112 4 8 -30 34 8.2 14N(1750) 1/2+

(∗,a) 1742 (nf) 318 - 8 - 161 - 5.1 -N(1720) 3/2+ 1717 1734 208 306 7 18 -76 -23 6.6 11.6N(1520) 3/2− 1519 1525 110 104 42 36 -16 10 79 69N(1675) 5/2− 1650 1640 126 178 24 34 -19 -32 39 38N(1680) 5/2+ 1666 1667 108 120 36 41 -24 -24 67 68N(1990) 7/2+ 1788 1936 282 244 4 4 -84 -87 3.2 3.6N(2190) 7/2− 2092 2054 363 486 42 44 -31 -57 23 18N(2250) 9/2− 2141 2036 465 442 17 13 -67 -62 7.5 5.7N(2220) 9/2+ 2196 2156 662 565 87 46 -67 -72 26 16

back

28/ 38


Resonance content: I = 1/2 Branching ratios

Γ1/2πN Γ

1/2ηN

ΓtotθπN→ηN

Γ1/2πN Γ

1/2KΛ

ΓtotθπN→KΛ

Γ1/2πN Γ

1/2KΣ

ΓtotθπN→KΣ

[%] [deg] [%] [deg] [%] [deg]A B A B A B A B A B A B

N(1535) 1/2− 51 48 120 115 7.7 8.3 68 77 15 34 -74 -83N(1650) 1/2− 15 12 57 46 25 18 -46 -43 26 15 -63 -59N(1440) 1/2+

(a) 2 5 -40 -26 2 11 156 152 1 2 67 189N(1710) 1/2+ 24 23 130 164 9.4 17 -83 -41 3.9 0.1 -136 -112N(1750) 1/2+

(∗,a) 0.5 - -140 - 0.8 - -170 - 2.2 - 4 -N(1720) 3/2+ 1.2 3.1 98 117 3.1 2.9 -89 -63 1.7 2.2 64 90N(1520) 3/2− 3.5 3.0 87 113 5.8 6.3 158 177 0.8 3.6 163 164N(1675) 5/2− 6.0 3.6 -40 -66 0.3 1.7 -93 -122 3.3 3.7 -168 179N(1680) 5/2+ 0.4 1.5 -47 -54 0.2 0.3 -99 72 0.1 0.1 141 141N(1990) 7/2+ 0.4 0.5 -99 90 1.7 1.5 -123 -99 0.8 1.2 28 70N(2190) 7/2− 0.1 0.4 -28 99 1.9 0.3 -51 -75 1.3 0.5 -63 -105N(2250) 9/2− 0.6 0.1 -92 -96 1.1 0.7 -103 -106 0.3 0.7 -114 62N(2220) 9/2+ 0.1 0.3 63 74 0.9 0.8 53 59 0.8 0.1 -138 52

back

29/ 38


Resonance content: I = 3/2

Re z0 -2Im z0 |rπN | θπN→πN

[MeV] [MeV] [MeV] [deg]fit→ A B A B A B A B

∆(1620) 1/2− 1599 1596 71 80 17 18 -107 -107∆(1910) 1/2+ 1788 1848 575 376 56 20 -140 -143∆(1232) 3/2+ 1220 1218 86 96 44 50 -35 -38∆(1600) 3/2+

(a) 1553 1623 352 284 20 27 -158 -124[∆(1920) 3/2+ 1724 1808 863 887 36 19 163 -70 ]∆(1700) 3/2− 1675 1705 303 185 24 14 -9 -4∆(1930) 5/2− 1775 1805 646 580 18 14 -159 3∆(1905) 5/2+ 1770 1776 259 143 17 9 -59 -40∆(1950) 7/2+ 1884 1890 234 232 58 58 -25 -19∆(2200) 7/2− 2147 2111 477 353 17 20 -52 7∆(2400) 9/2− 1969 1938 577 559 25 19 -80 -112

back

30/ 38


Resonance content: I = 3/2 Branching ratios

ΓπN/ΓtotΓ

1/2πN Γ

1/2KΣ

ΓtotθπN→KΣ

[%] [%] [deg]fit→ A B A B A B

∆(1620) 1/2− 48 45 22 24 -107 -107∆(1910) 1/2+ 20 10 4.7 1.9 -144 -115∆(1232) 3/2+ 100 100∆(1600) 3/2+

(a) 11 19 11 13 -7 41

[∆(1920) 3/2+ 8.3 4.3 16 14 -20 50∆(1700) 3/2− 16 16 1.5 1.6 -150 -121∆(1930) 5/2− 5.6 4.8 3.1 1.7 -3 135∆(1905) 5/2+ 13 12 0.5 0.1 -142 -99∆(1950) 7/2+ 50 50 4.0 3.8 -78 -71∆(2200) 7/2− 7.2 11 0.6 0.1 -98 -33∆(2400) 9/2− 8.7 5.7 1.3 0.8 40 6

back

31/ 38


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

32/ 38


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

33/ 38


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

33/ 38


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

33/ 38


t and u, contd.; s-channel exchanges

Λ

K

Ξ*

K

Λ Σ K

Ξ

K Λ Λ

K

Ξ*

K

Σ K

Ξ*

K

ΣΣ K

Ξ

K Σ Σ

π, η, K π

N, Λ, Σ Δ N

ρ

N*, Δ*

34/ 38


Potentials for resonances with J > 3/2

Correct dependence on the orbital angular momentum (centrifugal barrier)

vγ 5

2− =

kM v

γ 32+

vγ 5

2+ =

kM v

γ 32−

vγ 7

2− =

k2

M2 vγ 3

2−

vγ 7

2+ =

k2

M2 vγ 3

2+

γ = πN , ρN , ηN , π∆, σN , KΛ and KΣ

M : mass of the baryon in the particular channel

35/ 38


Phenomenological potential:

γ

N

m

B

γ

N

m

B

N ∗,∆∗

PNPµ

PPi

γaµ

+Vµγ =(E, q) =γaµ;i(q)

mNPNPµ (E) +

∑i

γaµ;i(q)PP

i (E)

E − mbi

PPi , PNP

µ : energy-dependentpolynomials

γaµ;i , γ

aµ;i : hadronic vertices → correct threshold behaviour

i: resonance number per multipoleµ: channels πN , ηN , π∆ Polynomials

36/ 38


Helicity multipoles AhL±:

J = L + 1/2:

A1/2L+ = −1

2 [(L + 2)EL+ + L ML+]

A3/2L+ =

12√

L(L + 2) [EL+ −ML+]

J = L− 1/2:

A1/2L− = −1

2 [(L− 1) EL− − (L + 1)ML−]

A3/2L− = −1

2√

(L− 1)(L + 1) [EL− + ML−]

37/ 38


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 size effectsPredict lattice spectra

38/ 38

analysis of new polarization data from frost · analysis of new polarization data from frost...

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