Giessen coupled-channel results for pion and photon ... NSTAR III-A Parallels/Shklyar... · Giessen...
Transcript of 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
Vitaly Shklyar Giessen coupled-channel results for pion and photon induced reactions
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
Vitaly Shklyar Giessen coupled-channel results for pion and photon induced reactions
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
Vitaly Shklyar Giessen coupled-channel results for pion and photon induced reactions
(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.
Vitaly Shklyar Giessen coupled-channel results for pion and photon induced reactions
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
Vitaly Shklyar Giessen coupled-channel results for pion and photon induced reactions
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
Vitaly Shklyar Giessen coupled-channel results for pion and photon induced reactions
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
Vitaly Shklyar Giessen coupled-channel results for pion and photon induced reactions
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).
Vitaly Shklyar Giessen coupled-channel results for pion and photon induced reactions
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!
Vitaly Shklyar Giessen coupled-channel results for pion and photon induced reactions
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
Vitaly Shklyar Giessen coupled-channel results for pion and photon induced reactions
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
Vitaly Shklyar Giessen coupled-channel results for pion and photon induced reactions
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
Vitaly Shklyar Giessen coupled-channel results for pion and photon induced reactions
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.
Vitaly Shklyar Giessen coupled-channel results for pion and photon induced reactions
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
...
Vitaly Shklyar Giessen coupled-channel results for pion and photon induced reactions
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)
Vitaly Shklyar Giessen coupled-channel results for pion and photon induced reactions
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
Vitaly Shklyar Giessen coupled-channel results for pion and photon induced reactions
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]
Vitaly Shklyar Giessen coupled-channel results for pion and photon induced reactions
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
Vitaly Shklyar Giessen coupled-channel results for pion and photon induced reactions
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 !
Vitaly Shklyar Giessen coupled-channel results for pion and photon induced reactions
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 + ...
Vitaly Shklyar Giessen coupled-channel results for pion and photon induced reactions
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
Vitaly Shklyar Giessen coupled-channel results for pion and photon induced reactions
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
Vitaly Shklyar Giessen coupled-channel results for pion and photon induced reactions
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
Vitaly Shklyar Giessen coupled-channel results for pion and photon induced reactions