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Magentic Moment of the ∆+-Resonance via γp→ pπoγCrystal Ball, TAPS collaborations
Introduction
Experiment
Results
Conclusions
PhD theses of: B. Boillat, BaselE. Downie, GlasgowS. Schumann, Mainz
B. Krusche, Gordon Conference on Photonuclear Reactions, Tilton, New Hampshire, August 2008
magnetic moments of baryons
anomalous magnetic moments of the nucleon: first hint for nucleon sub-structure
magnetic moments are fundamental properties of baryons→ sensitive tests of quark model wave functions
precisely known for octet baryons from spin-precesion experiments
for decuplet baryons only possible for Ω−
prediction for ∆ baryons in SU(3) isospin symmetry: µ∆ = Q∆ × µp
some predictions from more realistic models: experimental status:
model µ∆++/µN µ∆+/µN
µ∆ = Q∆ × µp 5.58 2.79rel. QM (Schlumpf ’93) 4.76 2.38lattice (Leinweber ’92) 4.9±0.6 2.5±0.3χPT (Butler et al. ’94) 4.±0.4 2.1±0.2χQSM (Kim et al. ’98) 4.73 2.19
LC-SM (Aliev et al. ’00) 4.4±0.8 2.2±0.4
µ∆++/µN : (UCLA ’78:)4.7-6.7, 6.9-9.8, 5.6-7.5, 3.7-4.2
µ∆++/µN : (SIN ’91:) 4.52±0.95
µ∆+/µN : (Mainz ’92:)2.7±1.3(stat.) ±1.5(sys.) ±3.(theo.)
B. Krusche, Gordon Conference on Photonuclear Reactions, Tilton, New Hampshire, August 2008
principle of experiment
• principle:M1 re-alignment photon fromγp→∆+ →∆+γ′→ pγ′πo
sensitive to µ(∆+)
• problem:wanted process:
but background from many otherdiagrams (bremsstrahlung):
→ sophisticated models←for extraction of µ(∆+) needed
B. Krusche, Gordon Conference on Photonuclear Reactions, Tilton, New Hampshire, August 2008
models for the γp→ pπoγ reaction
principle: start with model for γp→ pπo, then add radiative photonsdifferent approaches:• Machavariani and Faessler: Born approximation with different models for ∆-propagator
• Chiang, Drechsel, Vanderhaeghen, Yang: unitary model with on-shell πN re-scattering
example: result for γp→ pπo tree level approximation on-shell re-scattering
150 200 250 300 350 400 4500
50
100
150
200
250
300
350
Ahrens
MacCormick
σ tot [
µb]
Eγ
lab [MeV]
• Pascalutsa and Vanderhaeghen: chiral effective field theory
v ; +t ; v v +(b) ( )(a) k0 k0
B. Krusche, Gordon Conference on Photonuclear Reactions, Tilton, New Hampshire, August 2008
MAMI accelerator in Mainz
4. Stage: Harmonic Double Sided Microtronmaximum energy: 1.5 GeV
B. Krusche, Gordon Conference on Photonuclear Reactions, Tilton, New Hampshire, August 2008
experimental setup - Crystal Ball and TAPS and...Crystal Ball detector:672 NaI crystals covering full azimuthal angle for polar angles between 20 - 160o
TAPS derector:510 BaF2 crystals covering forward polar angles down to 4o
TAPS-Veto detector, MWPC, and ∆E-detectorfor charged particle identification
10 cm
B. Krusche, Gordon Conference on Photonuclear Reactions, Tilton, New Hampshire, August 2008
TAPS Crystal Ball - at MAMI
B. Krusche, Gordon Conference on Photonuclear Reactions, Tilton, New Hampshire, August 2008
analysis first step: single πo production
identification with invariant mass and missing mass
comparison to previous results
0
5
10
15
20
25
30
0 30 60 90 120 150 180
dσ/d
Ω[µ
b/sr
]
Boillat 08, preliminary
Leukel 01
Θπ[deg]*
325-375 MeV
0
5
10
15
0 30 60 90 120 150 180
dσ/d
Ω[µ
b/sr
]
Boillat 08, preliminary
Leukel 01
Θπ[deg]*
375-425 MeV
0
2
4
6
8
10
0 30 60 90 120 150 180
dσ/d
Ω[µ
b/sr
]
Boillat 08, preliminary
Leukel 01
Θπ[deg]*
425-475 MeV
B. Krusche, Gordon Conference on Photonuclear Reactions, Tilton, New Hampshire, August 2008
analysis pπoγ first step
accept events with exactly three photons and one proton
identification with πo invariant mass and πoγ missing mass ?
background visible e.g.:
polar angle ofradiative photon:beam relatedelm. backgroundat forward angles
angular differencebetween radiativephoton andπo photons:cluster split-off
B. Krusche, Gordon Conference on Photonuclear Reactions, Tilton, New Hampshire, August 2008
main experimental background from:
total cross sections:
• γp→ pπoγ : 0.05 - 0.07 µb
• γp→ pπo: 60 - 310 µb
• γp→ pπoπo: 0.01 - 1 µb
10-5
10-4
10-3
10-2
10-1
1
10
10 2
10 3
250 300 350 400 450 500
σ[µb
]
γp→pπo
γp→pπoπo
γp→pπoγ
Eγ[MeV]
• γp→ pπo:backround from cluster ‘split-off’:one ‘fake’ photon
• γp→ pπoπo:backround from cluster ‘fusion’:one ‘lost’ photon
B. Krusche, Gordon Conference on Photonuclear Reactions, Tilton, New Hampshire, August 2008
Reaction identification
background suppression with serveral cuts optimized with Monte Carlo simulationsπoγ missing mass spectra before cuts:
data MC: γp→ pπoγ MC: γp→ pπo MC: γ → pπoπo
B. Krusche, Gordon Conference on Photonuclear Reactions, Tilton, New Hampshire, August 2008
Reaction identification
background suppression with serveral cuts optimized with Monte Carlo simulationsπoγ missing mass spectra before cuts:
data MC: γp→ pπoγ MC: γp→ pπo MC: γ → pπoπo
πoγ missing mass spectra after cuts:
reduction factors: 1.6 82. (negligible) 25. (0. -10.% of signal)
B. Krusche, Gordon Conference on Photonuclear Reactions, Tilton, New Hampshire, August 2008
Experimental results compared to model predictions
angular distributions of re-orientation photon
0
2
4
6
8
0 30 60 90 120 150 180
dσ/d
Ω[n
b/sr
]
Boillat 08, preliminary
Kotulla 02
Pascalutsa 05, κ=3Pascalutsa 05, κ=2
Pascalutsa 05, κ=0
Θγ[deg]*
325-375 MeV
0
2
4
6
8
10
0 30 60 90 120 150 180
dσ/d
Ω[n
b/sr
]
Boillat 08, preliminary
Kotulla 02
Pascalutsa 05, κ=3Pascalutsa 05, κ=2
Pascalutsa 05, κ=0
Θγ[deg]*
375-425 MeV
0
5
10
15
0 30 60 90 120 150 180
dσ/d
Ω[n
b/sr
]
Boillat 08, preliminary
Kotulla 02
Pascalutsa 05, κ=3Pascalutsa 05, κ=2
Pascalutsa 05, κ=0
Θγ[deg]*
425-475 MeV
energy distributions of re-orientation photon
0
0.5
1
1.5
2
0 50 100 150
dσ/d
Eγ[n
b/M
eV]
Boillat 08, preliminary
Kotulla 02
Pascalutsa 05, κ=3
Pascalutsa 05, κ=2
Pascalutsa 05, κ=0
Pascalutsa 07, κ=3
Eγ[MeV]
325-375 MeV
0
0.5
1
1.5
0 50 100 150 200
dσ/d
Eγ[n
b/M
eV]
Boillat 08, preliminary
Kotulla 02
Pascalutsa 05, κ=3
Pascalutsa 05, κ=2
Pascalutsa 05, κ=0
Pascalutsa 07, κ=3
Eγ[MeV]
375-425 MeV
0
0.5
1
1.5
0 50 100 150 200
dσ/d
Eγ[n
b/M
eV]
Pascalutsa 05, κ=3
Pascalutsa 05, κ=2
Pascalutsa 05, κ=0
Pascalutsa 07, κ=3
Boillat 08, preliminaryKotulla 02
Eγ[MeV]
425-475 MeV
compared to chiraleffective field theorycalculations:
Pascalutsa andVanderhaeghen ’05:
LO-calculationµ∆+ = (1 + κ)µN
κ = 1,2,3 (..., - -, —)
Pascalutsa andVanderhaeghen ’07:
NLO-calculation(with Born-terms)κ = 3 —
B. Krusche, Gordon Conference on Photonuclear Reactions, Tilton, New Hampshire, August 2008
Ratio in soft-photon limit
normalization to soft photon limit: connects γp→ pπo and γp→ pπoγ′ for Eγ′ → 0
limEγ′→0
(
dσ
dEγ ′
)
=1
Eγ ′σo σo =
∫
dΩπo
(
dσ
dΩπo
)
α
2πF(t)
R(Eγ) =Eγσo×
dσdEγ
for data: σo from(
dσmeasdΩπo
)
for model: σo from(
dσcalcdΩπo
)
0
0.2
0.4
0.6
0.8
1
0 50 100 150
R
Boillat 08, preliminary
Kotulla 02
Pascalutsa 05, κ=3
Pascalutsa 05, κ=2
Pascalutsa 05, κ=0
Pascalutsa 07, κ=3
Eγ[MeV]
325-375 MeV
0
0.5
1
1.5
2
0 50 100 150 200
R
Boillat 08, preliminary
Kotulla 02
Eγ[MeV]
375-425 MeV
0
1
2
3
0 50 100 150 200
R
Boillat 08, preliminary
Kotulla 02
Eγ[MeV]
425-475 MeV
B. Krusche, Gordon Conference on Photonuclear Reactions, Tilton, New Hampshire, August 2008
Beam asymmetry Σ: linearly polarized photons
first result for photon beam asymmetry Σ (S. Schumann)
B. Krusche, Gordon Conference on Photonuclear Reactions, Tilton, New Hampshire, August 2008
Summary and Outlook
Preliminary, precise results for angular and
energy distributions of γp→ pπoγ′.
Final results within next few months.
First results for photon beam asymmetry of γp→ pπoγ′.
No value yet for magnetic dipole moment due to
discrepancies between model calculations.
Reaction γp→ nπ+γ′ is under analysis
(better test of bremsstrahlung terms in models.)
B. Krusche, Gordon Conference on Photonuclear Reactions, Tilton, New Hampshire, August 2008