Study of few-body problems at WASA Wasa-at-Cosy. Content General overview General overview – ...
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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