Giessen coupled-channel results for pion and photon ... NSTAR III-A Parallels/Shklyar... · Giessen...

Giessen coupled-channel results for pion andphoton induced reactions

V. Shklyar U. Mosel H. Lenske

Institut fur Theoretische PhysikUniversitat Giessen

Vitaly Shklyar Giessen coupled-channel results for pion and photon induced reactions

Partial wave version of optical theorem

constraints on partial wave cross sections

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1

sqrt(s) (GeV)

0.01

0.1

1

10

σ (

mb)

π−p->nπ−π+

π−p->ηn

π−p->ωn

π+p->K

+Σ+π−

p->K0Λ

πΝ−>πΝ

ImT JPπN→πN =

k2

4π(σJP

πN→πN + σJPπN→2πN + σJP

πN→ηN

+σJPπN→ωN + σJP

πN→KΛ + σJPπN→KΣ + ...)

all reaction data are linked

→ need for coupled-channel unitary analysis


Giessen model. PRC71, 055206 (2005)

Bethe-Salpeter in K -matrix: dynamical model: based on eff. LmBB

T-matrtixInteraction term V

︸︷︷︸

Resonance

︸︷︷︸

Background

multidmentional T-matrix

T =

Tγγ Tγπ Tγη Tγω · · ·

Tπγ Tππ Tπη Tπω · · ·

Tηγ Tηπ Tηη Tηω · · ·

· · · · · · · · · · · · · · ·

How many channels?

γN → γN

γN → πN

γN → ηN

γN → ωN

γN → KΛ

γN → KΣ

πN → πN

πN → 2πN

πN → ηN

πN → ωN

πN → KΛ

πN → KΣ


K-matrix approximation:

To solve Bethe-Salpeter equation take the imaginary part of thepropagator:

∫

dq1

q2 −m2 ± iε= P

∫

dq1

q2 −m2∓ iπ

∫

dqδ(q2 −m2)

where all intermediate particles are on-shell.

main features

neglect real part of self energy

Minkowsky space

resonance parameters: coupling constants at interactionLagrangians


(γ, π)N → KΛ. Giessen model PRC72:015210

0

0.1

0.2cos θ = −0.95 cos θ = −0.85 cos θ = −0.75

cos θ = −0.55 cos θ = −0.35 cos θ = −0.15

cos θ = 0.15 cos θ = 0.35 cos θ = 0.55

cos θ = 0.75 cos θ = 0.85 cos θ = 0.95

SAPHIRCLASCS

0

0.1

dσ/d

Ω (

µb/s

r)

0

0.1

0.2

0.3

1.6 1.7 1.8 1.90

0.1

0.2

0.3

0.4

1.6 1.7 1.8 1.9

√S (GeV)

1.6 1.7 1.8 1.9 2

0

30

60

90

1201.633 GeV 1.661 GeV 1.683 GeV

1.878 GeV 1.908 GeV

1.758 GeV

1.966 GeV

1.825 GeV

1.792 GeV

1.938 GeV

1.724 GeV

1.999 GeV

ANLRAL78CS

0

30

60

90

120

dσ/d

Ω (

µb/s

r)

0

30

60

90

RAL80

-1 -0.5 0 0.50

30

60

90

-1 -0.5 0 0.5

cos(θ c.m.

)-1 -0.5 0 0.5 1

γp → K+Λ

π−p → K 0Λ

Two independent solutions:C(CLAS) and S(SAPHIR)

The difference between the C andS-calculations is mostly due tonon-resonance contributions.(next transp.)

Disagreement between the CLASand SAPHIR data does not affectthe the π−p → K 0Λ reaction.


KΛ-production. Reaction mechanism

Giessen PRC72, 015210 (2005).γp → K+Λ

1.6 1.7 1.8 1.90

0.5

1

1.5

2

2.5

3

3.5

σ (µ

b)

C-calculations S-calculations

S11 S

11

P13

P13

tot.

tot.

1.6 1.7 1.8 1.9 2

√S (GeV)

π−p → K 0Λ

1.6 1.7 1.8 1.9 2

√S (GeV)

0

0.5

1

σ (m

b)

C-calc.

S11

P13

P11

1.6 1.7 1.8 1.9 2

√S (GeV)

0

0.5

1

σ (m

b)

S-calc.

S11

P13

Resonance contributions: S11(1650)P13(1720) and P13(1900)

L2I ,2S RKΛ(C ) RKΛ(S)

S11(1650) 3.2(+) 4.6(+)

P13(1720) 4.6(+) 4.0(+)P13(1900) 2.4(+) 2.3(+)

Table: N∗ decay ratios to KΛ


Giessen model. Results for the (π, γ)N → ωN reactions

Combined analysis =⇒ more constraint on resonance properties.Giessen model, PRC 71:055206,2005

πN → ωN γN → ωN

0

0.02

0.04

0.06

0.081.725 GeV 1.728 GeV 1.732 GeV

1.736 GeV 1.742 GeV 1.748 GeV

1.756 GeV 1.764 GeV

1.800 GeV

1.900 GeV 2.000 GeV

Karami et al. [54]Keyne et al. [57]

Binnie et al.[56]

Giessen’04

0

0.1

0.2

dσ/d

Ω (

mb/

sr)

0

0.1

0.2

0.3

-1 -0.5 0 0.5 1

Danburg et al. [55]

-1 -0.5 0 0.50

0.1

0.2

0.3

-1 -0.5 0 0.5 1

cos θ c.m.

0

0.5

1

1.5

Giessen’04SAPHIR

0

0.5

1

dσ/Ω

[µb/

sr]

0

1

2

-1 -0.5 0 0.50

1

2

3

-1 -0.5 0 0.5cos θ

c.m.

-1 -0.5 0 0.5 1

1.736 GeV 1.750 GeV 1.763 GeV

1.783 GeV 1.809 GeV 1.835 GeV

1.860 GeV 1.885 GeV 1.910 GeV

1.934 GeV 1.959 GeV 1.982 GeV


Giessen model. Results for (π, γ)N → ωN

Giessen model, PRC 71:055206,2005πN → ωN

1.7 1.8 1.9 2

√S (GeV)

0

1

2

3

4

σ (m

b)

π−p -> ωn S11

P11P13D13D15F15

γN → ωN

1.7 1.8 1.9 2

√S (GeV)

0

5

10

σ (µ

b)

γ p -> ωp

S11P11P13D13D15+F15

P13: interference betweenresonance and background

strong N∗(52) coupling to ωN

D13(1520) minor contributions

strong Born and π0-exchangecontributions

D13 is due to π0-exchange


Results for the π−p → ηp production

0

0.1

0.2

0.3

0.4

dσ/d

Ω (

mb)

DebenhamDeinetRichardsCB (2005)

0

0.1

0.2

0.3

0.4

-1 -0.5 0 0.5 1cosθ

0

0.1

0.2

0.3

0.4

-1 -0.5 0 0.5 1

1.507 GeV 1.523 GeV

1.586 GeV 1.674 GeV

1.730 GeV 1.900 GeV

π−p -> η p

π−p → η n: Solution from the Giessen coupled-channel analysisV.Shklyar et al, PRC.71. 055206 (2005).


Results for the γp → ηp

dσdΩ as a function of cos(θ) dσ

dΩ as a function of W

0

0.5

1

1.5

CB-ELSACLASGRAAL

0

0.4

0.8

dσ/d

Ω[µ

b]

-1 -0.5 0 0.5 1cos θ

0

0.2

0.4

-1 -0.5 0 0.5 1

1.528 1.588

γ p -> η p

1.646 1.675

1.730 1.835

0

0.5

1

1.5

CBELSA

0

0.5

1

1.5

dσ/d

Ω[µ

b]1.5 1.6 1.7 1.8 1.9 2

W(GeV)

0

0.5

1

1.5

1.5 1.6 1.7 1.8 1.9 2

cosθ=-0.65 cosθ=-0.35

cosθ= 0.35cosθ= 0.15

cosθ= 0.55 cosθ= 0.85

The structure at 1.67 GeV in γp → ηp is due to S11(1650)Shklyar et al PLB650, 172(2007)

no need for any exotic state!


Giessen model

S11(1535) dominatesboth γp → ηp and π−p → ηn reactions

1.6 1.8 2

√S (GeV)

0

10

20

σ (µ

b)

γ p -> η ptotS

11

P11

P13

D13

D15

+ F15

CB-ELSA

1.6 1.8 2

√S (GeV)

0

1

2

3

σ (m

b)

π−p -> η n

totP11S11

strong S11(1535) excitation

kink structure at 1.72 GeV isdue to the ωN threshold

seems no room for othercontributions

destructive effect fromS11(1650)

above 1.6 GeV - P11(1710) -consistent with πN inelasticity


γn∗ → ηn

V. Kuznetsov, et al. PLB 647 (2007) 23 for GRAAL collaborationγn∗ → ηn γp∗ → ηp

0

0.25

0.5

0.75

1

dσ/d

Ω, µ

b/st

r

0.5

1

0

0.25

0.5

0.75

dσ/d

Ω, µ

b/st

r

0.5

1

0

0.25

0.5

0.75

1.5 1.6 1.7 1.8W,GeV

dσ/d

Ω, µ

b/st

r

0.5

1

1.5 1.6 1.7 1.8 1.9W,GeV

quasi-free neutron: resonance-likestructure at 1.67 GeV

confirmed by B.Krusche, I. Jaegle atMAMI, CB-ELSA

Possible explanations

Polyakov, Strakovsky, Arndt,Workman; Polyakov Kuznetzov:pentaquark parthner

Shklyar, Mosel, Lenske: well knownS11(1650), P11(1710)

M. Doering: cusp in KΣ


Results for the γn → ηn

Giessen Model PLB650, 172(2007): total γn → ηn cross section

1.6 1.8 2

√S (GeV)

0

10

σ (µ

b)

γ n -> η ntotS

11

P11

P13

D13

D15

+F15

An

1/2(1650) = −9× 10−3GeV− 12

An

1/2(1710) = 24× 10−3GeV− 12


π−p → ηn

Giessen Model: Shklyar, Mosel, Lenske PLB650, 172(2007)vs. data Richards etl al PR 1, 10 (1970)

0

0.05

0.1

0.15

0.2

d σ

/d Ω

(m

b)

Giessen modelRichards

1.5 1.6 1.7 1.8 1.9

W(GeV)

1.5 1.6 1.7 1.8 1.9

cosθ= - 0.5 cosθ= - 0.1

cosθ= 0.1 cosθ= 0.5

S11

(1535) P11

(1710) ?S11

(1535) P11

(1710) ?

S11

(1650)S11

(1650)

Richards data show an excess structure at 1.7 GeV

hard to make conclusion: the data is of poor quality

Giessen calculations: destructive S11(1535) and S11(1650)interference; P11(1710) excitation.


Next step: improve description of the 2πN channel

so far: N∗ decay into ’generic’ 2π channel

take 2πN inelastic flux into account

N∗ → 2πN couplings constrained by σJIπN→2πN

2π

σ

ρ

N*

N*

N*

N

N

N

...


New multichannel problem

N

π πρ

NN

π

=

π

NN

+

ππ

N

+ ...

N

T JI

ππ = K JI

ππ + iK JI

ππTJI

ππ

+i

∫ (√s−mN)

2

4m2π

dµ′ρ2K JI

πρ(µ′ρ2)Aρ(µ

′ρ2)T JI

ρπ(µ′ρ2)

summation instead of integration

T JI

ππ = K JI

ππ + iK JI

ππTJI

ππ

+i

∑

mρi

2mρi ∆mρi KJI

πρi(mρi

2)Aρi (mρi2)T JI

ρiπ(mρi

2)


N(1520) D13 state

Manley et al: PRD(1984)

MR = 1520MeVΓtot=120MeV

strong N(1520)→ 2πNBr(ρN) ≈20%

Giessen Model (CC): πN → ρN

1 1.2 1.4 1.6 1.8 2W(GeV)

0

1

2

3

4

5

6

σ(π

Ν−>

ρΝ) [m

b] N(1520) BR(ρΝ)= 23%D

13

Manley analysis: distribution:Giessen: non-symmetricManley : symmetric

Gi Model: no contributions below 1.4GeV

Manley: no ρ-spectral function: shouldbe revised


πN → 2πN

Summary of the πN → 2πN reactions

strong contributions to the πN inelasticity

important for understanding for ρ-meson dynamicsand resonance couplings

could solve many puzzles in non-strange baryonspectroscopy: origin and properties of theP11(1440), P11(1710), D13(1520) etc.

Theory

analysis of Manley et. al. should be revised!

Experiment

need for new measurements πN → 2πN in region1.2...2.GeV → challenge for HADES collaboration

pion beams at HADES contact [email protected]


university-lo

Why D15(1675) with ΓηN = 17% is a bad

Optical theorem for πN → πN scattering

(J+ 12)ImT

52

+ 12

πN→πN = k2

4π (σ52

+ 12

πN→πN +σ52

+ 12

πN→2πN +σ52

+ 12

πN→ηN)

σ52

+ 12

inel . = σ52

+ 12

πN→2πN +σ52

+ 12

πN→ηN ≈ 12mb

1.2 1.4 1.6 1.8

√S [GeV]

0

4

8

12

σinel

(mb)

total inel. cross section πΝ −>XN

σπΝinel

(GW’02)

σπΝinel

(Giessen)

Assuming dominant D15(1675)

TπN→2πN ∼Γ

N(1675)πN Γ

N(1675)2πN

s−m21675−iΓtot/2

TπN→ηN ∼Γ

N(1675)πN Γ

N(1675)ηN

s−m21675−iΓtot/2

σπN→ηN/σπN→2πN =(Γ1675

ηN /Γ16752πN )2

η-MAID L. Tiator (hep-ex/0601002):ΓηN ≈ 17%, Γ2πN ≈ 40%

σ52πN→ηN |1675MeV = 12(17

40)2 ≈ 2.2mb1.6 1.8 2

√S (GeV)

0

1

2

3

σ (m

b)

π−p -> η n

D15

(1675)

P11S11

Vitaly Shklyar , Eta meson production in the resonance energy region p. 1


Giessen model

1.2 1.4 1.6 1.8 2

√S (GeV)

10

20

30

σ (m

b)

π−p elastic

Previous analysis:Penner and Mosel RRC66,055211 (2002)

no spin-52 resonances !


Giessen model

1.2 1.4 1.6 1.8 2

√S (GeV)

10

20

30

σ (m

b)

π−p elastic

new

New results:V. Shklyar et al .PRC71,055206 (2005)

with spin-52 resonances !But! It is so important for theωN production ?

Optical theorem:

ImTπN→πN ∼ σπN→ωN + ...


Results for pion-induced reactions

S11

P11

P13

D13

D15 F

15

-0.4

0

0.4

0.8 P11

(1440)

S11

(1650)

P11

(1710)

S11

(1535)

P13

(1720)

D13

(1520)

P13

(1900) D13

(2050)

D15

(1675)F

15(1680)

F15

(2000)

Re(T) SAID

Im(T) SAID

Re(T)

Im(T)

-0.4

0

0.4

1.2 1.4 1.6 1.8 21.2 1.4 1.6 1.8 2

√S [GeV]

-0.4

0

0.4

πN elastic amplitudes:

reach spectrum

not only πN decay

I = 12 resonances important:

S11(1535), S11(1650)P11(1440), P11(1710)P13(1720), P13(1900)D13(1520), D13(2050)D15(1675)F15(1680), F15(2000)

Vitaly Shklyar , Nucleon resonances in πN and γN scattering. p. 22


πN inelasticity and inelastic channels

S11

P11

P13

D13

D15

F15

πΝ −>2πΝ

0

2

4

6

0

4

8

σ(m

b)

Manley et al.

SAIDσ2πΝ

σπΝinel.

1.2 1.4 1.6 1.8 21.2 1.4 1.6 1.8

√S [GeV]

0

4

8

12

S11

(1535)

S11

(1650)P

11(1440)

P11

(1710)

P13

(1720)P

13(1920)

D13

(1720)D

13(1900)

D15

(1675) F15

(1680)

F15

(2000)

Optical theorem :[

4π

k2cm

ImT JIπN − σ

JIπN→πN

]

= σJIπN→2πN + σ

JIπN→ηN

+σJIπN→ωN+σ

JIπN→KΛ

+σJIπN→KΣ

— πN inelasticity— 2πN partial wave cross

sections

Vitaly Shklyar , Nucleon resonances in πN and γN scattering. p. 23


Giessen model. Pion photoproductionproton multipoles

0

10

20Re(A)Im(A)

0

1

2

E0+

p

E1+

p

E2-

p

E2+

p

E3-

p

M0+

p

M1+

p

M2-

p

M2+

p

M3-

p

1.2 1.4 1.6 1.8 2

√S [GeV]

-1

0

1

2

0

5

Am

plitu

de [

mfm

]

0

0.5

1

0

5

-2

0

-2

0

2

Am

plitu

de [

mfm

]

-0.5

0

0.5

1.2 1.4 1.6 1.8 2

√S [GeV]

-1

0

1

2

neutron multipoles

-20

-10

0

Re[A]Im[A]

-2

0

E0+

n

E1+

n

E2-

n

E2+

n

E3-

n

M0+

n

M1+

n

M2-

n

M2+

n

M3-

n

1.2 1.4 1.6 1.8 2

√S [GeV]

-1

0

-10

-5

0

Am

plitu

de [

mfm

]

-0.5

-0.25

0

-6

-4

-2

0

2

0

2

4

6

-1

0

1

Am

plitu

de [

mfm

]

-2

-1

0

1

1.2 1.4 1.6 1.8 2

√S [GeV]

-1

0

1

Combined analysis of (π, γ)N → (π, γ)N gives a strongconstraint on extracted resonance parameters

Vitaly Shklyar , Giessen coupled-channel model for baryon resonance analysis p. 21


Giessen coupled-channel results for pion and photon ... NSTAR III-A Parallels/Shklyar... · Giessen...

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