Study of few-body problems at WASA

Wasa-at-Cosy

ContentContent

• General overviewGeneral overview– decaysdecays– dd dd 00

– -mesic helium-mesic helium

• The ABC effectThe ABC effect– dd–

See talk A. Winnemoeller Friday 18:40

The ABC effectThe ABC effect

ABC effectABC effect

• ExperimentallyExperimentally– low-mass enhancement in Mlow-mass enhancement in M

– observed in many fusion reactionsobserved in many fusion reactions– accompanied with accompanied with ΔΔΔΔ excitations excitations

• TheoreticallyTheoretically– originates from originates from t-t-channel channel ΔΔΔΔ excitation excitation– expected double-hump structure in Mexpected double-hump structure in M

(not supported by experimental observations)

pn d00

2D x-section2D x-section

s

M

Total x-sectionTotal x-section

pn d+-

pn d00

(+0)=(I=1)(+-)=0.5(I=1)+2(I=0)(00)=(I=0)=0.2(I=1)

pp d+0

t - channel

Total x-sectionTotal x-section

MeV 50

GeV 38.2

M

d threshold

mass

Total x-sectionTotal x-section

MeV 50

GeV 38.2

M

d threshold

mass

Qualitative descriptionQualitative description

GeV 38.2RM MeV 60

22

2

)(

q

qF

GeV 3.0

21)(

2)(

1

DDqFiMM R

n

p

n

Δ

Δ

d

π

π+

Δ

Δ

dπ

πp

Total xsection slices: qualitative Total xsection slices: qualitative descriptiondescription

Total xsection slices: qualitative Total xsection slices: qualitative descriptiondescription

Total xsection slices: qualitative Total xsection slices: qualitative descriptiondescription

Total xsection slices: qualitative Total xsection slices: qualitative descriptiondescription

Total xsection slices: qualitative Total xsection slices: qualitative descriptiondescription

Total xsection slices: qualitative Total xsection slices: qualitative descriptiondescription

Total xsection slices: qualitative Total xsection slices: qualitative descriptiondescription

Total xsection slices: qualitative Total xsection slices: qualitative descriptiondescription

Total xsection slices: qualitative Total xsection slices: qualitative descriptiondescription

Total xsection slices: qualitative Total xsection slices: qualitative descriptiondescription

Total xsection slices: qualitative Total xsection slices: qualitative descriptiondescription

Total xsection slices: qualitative Total xsection slices: qualitative descriptiondescription

Total xsection slices: qualitative Total xsection slices: qualitative descriptiondescription

Total xsection slices: qualitative Total xsection slices: qualitative descriptiondescription

Total xsection slices: qualitative Total xsection slices: qualitative descriptiondescription

Total xsection slices: qualitative Total xsection slices: qualitative descriptiondescription

Total xsection slices: qualitative Total xsection slices: qualitative descriptiondescription

Total xsection slices: qualitative Total xsection slices: qualitative descriptiondescription

Total xsection slices: qualitative Total xsection slices: qualitative descriptiondescription

Total xsection slices: qualitative Total xsection slices: qualitative descriptiondescription

Dalitz plot (peak region)

pn pn d d0000 and pp and pp d d++00 (p-spectator) (n-spectator)

++00 invariant mass T invariant mass Tpp 1GeV1GeV

pp 2He pp d

ABC in ABC in 33HeHe

00

M HeM 3

M.Bashkanov et. al, Phys. Lett. B637 (2006) 223-228

He3

He3

(I=0,1)

(I=0)

pdpd33HeHeππππ, T, Tpp=0.89 GeV=0.89 GeV

dd dd 44He He Invariant Mass Invariant Mass

1.117 GeV

0.9 GeV 1.05 GeV

See talk A. Pricking Tuesday 17:30

ConclusionConclusion• ABC effect due to narrow ABC effect due to narrow s s -channel -channel

resonance with resonance with – – –

• More data next yearMore data next year– -decays-decays– dd dd 00

– dd dd ( ()) 3He+N+ 3He+N+

MeV 90GeV 38.2 MM

MeV 50

)3or 1(0)( PJI

*

*

OutlookOutlook

•Finish data analysisFinish data analysis

•Perform Partial Wave Analysis Perform Partial Wave Analysis (J(JPCPC))– Do we need polarization?Do we need polarization?

•Analysis of Analysis of

•MeasureMeasure

•Measure Measure pnpn elastic scattering elastic scattering

ONd 1614

dd

MultipletMultiplet1010=35282710

*

*

Y()=2I()=0

Kim Maltman, Nucl. Phys. A501 (1989) 843

Data analyzed so farData analyzed so far

•Tp = 1.0 GeV : 70 kEvents(80%) Tp = 1.0 GeV : 70 kEvents(80%) • Tp = 1.1 GeV :Tp = 1.1 GeV :

•Tp = 1.2 GeV : 26 kEvents(15%)Tp = 1.2 GeV : 26 kEvents(15%)• Tp = 1.3 GeV :Tp = 1.3 GeV :

•Tp = 1.4 GeV : 47 kEvents(25%)Tp = 1.4 GeV : 47 kEvents(25%)

Angular distribution (in the Angular distribution (in the peak)peak)

Dalitz plotDalitz plot

Additional corrections and Additional corrections and cross-checkscross-checks

Angular distribution (in the Angular distribution (in the peak)peak)

Total x-sectionTotal x-section

Tp = 1.0 GeVTp = 1.2 GeVTp = 1.4 GeV

Corrections for Fermi-Corrections for Fermi-motionmotion

Cross-checks at pn Cross-checks at pn dd000000

CW: pn d d000000

WaC: pn WaC: pn d d000000

Check of resolutionCheck of resolution

30 PS

ResolutionResolution

• In pn In pn d d000000 the the width width 30MeV 30MeV

• From MC, X-section resolution in From MC, X-section resolution in pn pn d d000 0 30MeV 30MeV

pn pn d d0000 and pp and pp d d++00 (p-spectator) (n-spectator)

pp pp d d++00 analysis analysis

pp pp d d++00 analysis analysis

++00 invariant mass invariant mass

Total xsection slices: Total xsection slices: qualitative descriptionqualitative description

Parameters of a new stateParameters of a new state

MR = 2.385 GeV = 53 MeV

Total x-sectionTotal x-section

Tp = 1.0 GeVTp = 1.2 GeVTp = 1.4 GeV

ΔΔΔΔ versus versus ΔΔ

HeM 3

He3

He3

He3

He3

*N

0

0

pdpd33HeHeππππ, T, Tpp=895 MeV=895 MeV

ΔΔΔΔ

22

2

)(

q

qF

π

N

Δπ

NΔ

π N

Δ

π

N

Δ

Large π π invariant mass

Small π π invariant mass

qppppppq NN 212211)()(

pn pn d dππππ,, T Tpp=1.03 GeV=1.03 GeV

00

M HeM 3

M.Bashkanov et. al, Phys. Lett. B637 (2006) 223-228

He3

He3

(I=0,1)

(I=0)

pdpd33HeHeππππ, T, Tpp=0.89 GeV=0.89 GeV

ΔΔΔΔ Resonance Resonance

21)(

2)(

1

DDqFiMM R

p

n

p

n

Δ

Δ

d

π

π

Δ

Δ

dπ

π

+

ΔΔΔΔ resonance in differential resonance in differential distributionsdistributions

Δ

Δ

π

π

Δ

π

π

Δ

Δ

π

π

Δ

+

Parameter of F(q) is fitted here

pdpd33HeHeππππ

qΔΔ q

ΔΔΔΔ resonance parameters resonance parameters

)MeV 37(22GeV 39.2 MM R

MeV 80

22

2

)(

q

qF GeV 19.0

Consistent description for d and Consistent description for d and 33He He casecase

With ΔΔ resonance

Without ΔΔ resonance

pd pd 33He He pn pn d d Tp=0.895 GeV

Tp=1.03 GeV

Tp=1.35 GeV

Angular distributionsAngular distributions

00

ΔΔ

bound ΔΔ

pea

kfu

ll

pd pd 33He He Tp=0.895 GeV

Angular distributionsAngular distributions

ΔΔ

bound ΔΔ

pn pn d d Tp=1.03 GeV

Quantum numbers of the Quantum numbers of the resonanceresonance

From Fermi-statistics: J=1From Fermi-statistics: J=1++,3,3++ if L if LΔΔΔΔ=0=0

3S1 (d) : S wave only3D1 (d) : S + D waves3D3 (d) : no S wave

pn pn R R d d 0000

1+

3+

pn pn d d 0000

I=0,1

I=0 I=0,2

I=0

ppppdd++00

no ABC

* (k1 x k

2)

Tp=1.1 GeV

Control channel (NO ABC expected)

Data collected for Data collected for pnpndd0000

• TTpp=1.0, 1.1, 1.2, 1.3, =1.0, 1.1, 1.2, 1.3, 1.4 GeV1.4 GeV

• To cover full To cover full resonance regionresonance region

• To have overlaps To have overlaps between different between different energies, due to Fermienergies, due to Fermi

• To reduce To reduce systematical errors.systematical errors.

Results from dd Results from dd +X +X beamtimebeamtime

Collected energies: Td= 0.8, 0.9, 1.01, 1.05, 1.117, 1.2, 1.25, 1.32, 1.4 GeV

Phase shiftsPhase shifts

pn pnElastic scattering

OutlookOutlook

• Wasa-at-CosyWasa-at-Cosy

• Nov07-Dec07 dd Nov07-Dec07 dd runsruns

• Feb08 pd runsFeb08 pd runs

ΔΔΔΔ - FSI - FSI

2

2

20

2

2

111

qqra

R

s

fmR 1.1

fmfmas 10

16

fmr 20

Energy dependence of the Energy dependence of the lowlow--mass enhancementmass enhancement

unbound (ΔΔ)

bound ΔΔ 27 MeV bound (ΔΔ) 27 MeV

FSIFSI

p

n

p

n

p

n

n n

p

n

p

n

p

n

p p

n

dp

n

dpn

dpn

+ + + + …

+ + +…

2

2

20

2

2

111

qqra

R

s

33SS11 phase shifts phase shifts

33DD33 phase shifts phase shifts

ΔΔΔΔ resonance parameters resonance parameters

)MeV 27(22GeV 41.2 MM R

GeV 09.0

22

2

)(

q

qF GeV 165.0

Effect of collision dampingEffect of collision dampingWithout collision damping

With collision damping

ΔΔ resonance resonance

MeVM 1232

MeV100s

h 2310

π

N

Δ 2cos31

π

N

Δ π

N

Δ

L=1

Total x-section for Total x-section for dpN

ΔΔ resonance

ABC channels (I=0)

No ABC (I=1)

First step into the ABCFirst step into the ABC• Alexander Abashian, Alexander Abashian,

Norman E. Booth and Norman E. Booth and Kenneth M. Crowe, Kenneth M. Crowe, Phys. Rev. Lett. Phys. Rev. Lett. 55, 258 (1960), 258 (1960)

5.113 He

X Hepd 3

labHe

P3

π

2 π Phase SpaceGeV 743.0pT

All of ABCAll of ABC

dXnp Xpd He3

Xdd He4

No ABC effect!

ABC effect

ΔΔ resonance resonance

MeVM 1232

MeV100s

h 2310

π

N

Δ 2cos31

π

N

Δ π

N

Δ

L=1

F. Plouin et. al. Nucl. Phys. A302 (1978), 413-422

ABC and ABC and ΔΔΔΔ models models

labdP

ππ

π π π

π π

F. Plouin, P. Fleury, C. Wilkin PRL 65 (1990) 692

ΔΔΔΔ versus Reality versus Reality

Total x-section for Total x-section for dpN ABC channels (I=0)

No ABC (I=1)

pp d+0

NNΔΔ state in pp state in pp+d pp

Total x-section for Total x-section for dpN ABC channels (I=0)

No ABC (I=1)

pp d+0