introduction experiment results conclusions · introduction experiment results conclusions phd...

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.)


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


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


MAMI accelerator in Mainz

4. Stage: Harmonic Double Sided Microtronmaximum energy: 1.5 GeV


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


TAPS Crystal Ball - at MAMI


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

]


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

]


Leukel 01

Θπ[deg]*

425-475 MeV


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


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


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


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)


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

]


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

]


Kotulla 02


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

]


Kotulla 02


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]


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]


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 —


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


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


Kotulla 02

Eγ[MeV]

375-425 MeV

0

1

2

3

0 50 100 150 200

R


Kotulla 02

Eγ[MeV]

425-475 MeV


Beam asymmetry Σ: linearly polarized photons

first result for photon beam asymmetry Σ (S. Schumann)


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.)


introduction experiment results conclusions · introduction experiment results conclusions phd...

Documents