PWA talk short - yukawa.kyoto-u.ac.jptetsuo.hyodo/ExHIC2016/Fabbietti2.pdf · 7 Kaonic’Cluster N...
39
Partial Wave Analysis of Strangeness Production at GeV Energies Laura Fabbietti Robert Münzer, Shuna Lu, Technische Universität München Excellence Cluster – Origin of the Universe
Transcript of PWA talk short - yukawa.kyoto-u.ac.jptetsuo.hyodo/ExHIC2016/Fabbietti2.pdf · 7 Kaonic’Cluster N...
Partial Wave Analysis of Strangeness Production at GeV Energies
Laura FabbiettiRobert Münzer, Shuna Lu, Technische Universität München
Excellence Cluster – Origin of the Universe
2
Strangeness Production
p p p
K+
Λ
• Important Ingredient for Transport Models• Understand Production Mechanism to look for Exotics (ppK-‐)
3
Strangeness Production
p N*Λ
K+
Resonance JP Mass (𝑮𝒆𝑽 𝒄𝟐⁄ ) Γ ( 𝑴𝒆𝑽 𝒄𝟐⁄ )
N*(1650) 1 2⁄ * 1.655 0.150
N*(1710) 1 2⁄ + 1.710 0.100
N*(1720) 3 2⁄ + 1.720 0.250
N*(1875) 3 2⁄ * 1.875 0.220
N*(1880) 1 2⁄ + 1.870 0.235
N*(1895) 1 2⁄ * 2.090 0.090
N*(1900) 3 2⁄ + 1.900 0.0250
4
Strangeness Production
p ΛFinal State InteractionAka: scattering length andeffective range
p N*Λ
K+
NΣ
pΛ
Conversion Processes
5
Strangeness Production
p
Λ
K+
N NK
Kaonic Bound States
6
Partial Wave Analysis
𝐴 : reaction amplitude A ∝ 𝐴 ∝ 𝐴/01 (s) (Transition amplitude of wave 𝛼)𝑘 : 3-‐momentum of the initial particle in the CM𝑠 − 𝑃8 ∶ 𝑘: + 𝑘8 8
𝑑ϕ 𝑃,𝑞:,𝑞8,𝑞@ : invariant three-‐particle phase space
Cross-‐section DecompositionA. Sarantsev et.al., Eur.Phys J A 25 2005
Parameterization of the Transition
Bonn-‐Gatchina PWA Framework
Constant amplitude
Phase
Energy dependent amp.
𝑑𝜎 = 2𝜋 D 𝐴 8
4 𝑘 𝑠 𝑑ϕ 𝑃, 𝑞:,𝑞8, 𝑞@ , 𝑃 = 𝑘: + 𝑘8
𝐴/01 𝑠 = 𝑎:1 + 𝑎@1 𝑠 𝑒HIJ𝑎:1
𝑎81
𝑎@1
7
Kaonic Cluster
N NK
Theoretical Predictions
Binding Energy (BE):10-100 MeVMesonic Decay (Γm)30-110 MeVNon-Mesonic Decay (Γnm)4-30 MeV
Property Value
charge +1strangeness -1
participants ppK−, pnK0
JP 0−
Table 0.1: Overview of different predictions for the binding energy BE, mesonic- m and non-mesonic nm decaywidths of the KNN (in MeV), inspired from [Gal13, Gal10]. The symbols (♣,♡) mark different works bythe same authors.
Chiral, energy dependent
var. [DHW09, DHW08] Fad. [BO12b, BO12a] var. [BGL12] Fad. [IKS10] Fad. [RS14]
BE 17–23 26–35 16 9–16 32m 40–70 50 41 34–46 49nm 4–12 30
Non-chiral, static calculations
var. [YA02, AY02] Fad. [SGM07, SGMR07] Fad. [IS07, IS09] var. [WG09] var. [FIK+11]
BE 48 50–70 60–95 40–80 40m 61 90–110 45–80 40–85 64–86nm 12 ∼20 ∼21
8
Kaonic Cluster
Physical Background:p + p Λ + p + K+
p + p N*+ + p
Λ + K+
N*+ -‐ Resonances J. BeringerPhys.Rev. D86 (2012)
p + pppK-‐ + K+
Λ + p
Λ(1405) + p + K+
N NK
Resonance JP Mass (𝑮𝒆𝑽 𝒄𝟐⁄ ) Γ ( 𝑴𝒆𝑽 𝒄𝟐⁄ )
N*(1650) 1 2⁄ * 1.655 0.150
N*(1710) 1 2⁄ + 1.710 0.100
N*(1720) 3 2⁄ + 1.720 0.250
N*(1875) 3 2⁄ * 1.875 0.220
N*(1880) 1 2⁄ + 1.870 0.235
N*(1895) 1 2⁄ * 2.090 0.090
N*(1900) 3 2⁄ + 1.900 0.0250
9
Total Data Set
Hades Data Ebeam=3.5 GeV Had. Wall Data Ebeam=3.5 GeV FOPI Data Ebeam=3.1 GeV
No Peak VisibleNo Signal?R. Münzer, PhD Thesis, TUM 2014
E. Epple, PhD Thesis, TUM 2014
10
Phase Space Simulation
Experimental Data
pp p K+ Λ Phase Space
Masses
CMS An
gle
G.-‐J.-‐A
ngle
Hel. -‐A
ngle
dN/dcosθ
[events/0.07]
dN/dcosθ
[events/0.07]
dN/dcosθ
[events/0.07]
dN/dcosθ
[events/0.07]
dN/dcosθ
[events/0.07]
dN/dcosθ
[events/0.07]
dN/dcosθ
[events/0.07]
dN/dcosθ
[events/0.07]
dN/dcosθ
[events/0.07]
dN/dM
[events/ 25 MeV
c-‐2]
dN/dM
[events/ 36 MeV
c-‐2]
dN/dM
[events/ 21 MeV
c-‐2]
11
Four Best PWA Solutions
Measured DataPWA solutions
Inside HADES acceptance
DataPWA
CMS An
gle
G.-‐J.-‐A
ngle
Hel. -‐A
ngle
12
PWA ResultsExperimental DataExperimental Data
Solution ASolution BSolution CSolution DSolution E
CMS An
gle
G.-‐J.-‐A
ngle
Hel. -‐A
ngle
dN/dcosθ
[events/0.07]
dN/dcosθ
[events/0.07]
dN/dcosθ
[events/0.07]
dN/dcosθ
[events/0.07]
dN/dcosθ
[events/0.07]
dN/dcosθ
[events/0.07]
dN/dcosθ
[events/0.07]
dN/dcosθ
[events/0.07]
dN/dcosθ
[events/0.07]
13
Four Best PWA Solutions
DataPWA
dN/dM[events/ 25 MeVc-‐2]
dN/dM[events/ 36 MeVc-‐2]
dN/dM[events/ 21 MeVc-‐2]
FOPI
HADES
DataPWA
14
ppK-‐ Upper Limit DeterminationΓ = 20 MeVc-‐²Γ = 35 MeVc-‐²Γ = 50 MeVc-‐²
2+0+ 1-‐
Γ (MeVc-‐2) Cross Section (μb)
20 7.6 ± 1.2 -‐ 3.5 -‐ 22.4 ± 3.6 -‐ 10.7
35 6.3 ± 1.7 -‐ 0.6 -‐ 9.5 ± 2.6 -‐ 0.9
50 10.2 ± 1.8 -‐ 4.5 -‐ 11.6 ± 3.4 -‐ 0.6
60 11.2 ± 1.9 -‐ 5.0 -‐ 33.8 ± 5.2 -‐ 16.9
80 11.4 ± 2.7 -‐ 3.8 -‐ 35.9 ± 5.7 -‐ 17.4
Upper Limit Cross Sectionp + p -‐> p + K+ + ΛTotal Cross Section
Interpolated from literature
15
Upper Limit
6.3 Comparison With Other Results
Table 6.9: The extracted cross section of the acceptance corrected histograms.All given in [μb].
Histogram Sol. No. 6/9 Sol. No. 1/8 Sol. No. 3/8 Sol. No. 8/8
CMSΛ 36.88±0.36 37.79±0.37 36.41±0.35 35.95±0.35CMSp 38.27±0.47 39.41±0.53 36.43±0.47 36.3±0.44CMSK+ 38.8±0.32 39.57±0.33 37.68±0.3 36.7±0.3
GJ-Angle RF-pK 37.25±0.35 38.18±0.37 36.16±0.34 35.29±0.33GJ-Angle RF-KΛ 38.15±0.36 39.11±0.37 37.21±0.34 36.74±0.34GJ-Angle RF-pΛ 40.41±1.06 41.67±1.09 40.75±1.10 39.7±1.15H-Angle RF-pΛ 37.63±0.37 38.47±0.38 36.97±0.36 36.14±0.35H-Angle RF-pK 37.23±0.40 37.91±0.41 36.38±0.38 35.51±0.38H-Angle RF-KΛ 37.75±0.42 38.36±0.44 37.22±0.42 36.24±0.40
IM(ΛK+) 38.72±0.35 39.57±0.36 37.83±0.34 37.01±0.33IM(pK+) 38.25±0.34 39.27±0.35 37.52±0.33 36.59±0.32IM(Λp) 38.07±0.38 38.83±0.40 37.35±0.36 36.41±0.36
Average 38.12±0.43 - - -
corresponding model. The model is normalized to the experimental data in theindicated range inside the brackets. To obtain the total production cross sec-tion each histogram was integrated. The experimental data are summed insideof the indicated range. Outside of this range the extrapolated model value istaken for the integration. The resulting cross section is quoted in each his-togram. Table 6.9 summarizes the results of the integration of all the presentedhistograms of Appendix G.3. The average cross section obtained with sol. No.6/9 is written in the last row of Table 6.9. The systematic error is constructed bythe maximum deviations to this value, marked in bold. The uncertainty due tothe normalization to p+p elastic events gives an additional error of 2.67 μb. Alast error comes from the fact that the data contain a certain amount of statisticnot associated to pK+Λ production. This amount is roughly 6% as described inSection 4.1.3. The overall total production cross section, thus, reads as:
σpK+Λ = 38.12± 0.43+3.55−2.83 ± 2.67(p+p-error)−2.9(background) μb. (6.12)
6.3 Comparison With Other Results
The extracted pK+Λ cross section of this work can be compared to the crosssections at other beam energies. Figure 6.14 shows in both panels the pK+Λ
153
5 Is There a New Signal? - A Statistical Analysis
seem astonishingly high. Unlike in many analyses where the observed yieldin a "bump" is directly connected to a production yield this can not be donewhen considering interference. When two sources interfere the final yield cannot be attributed clearly to one or the other source only from observing theinterference pattern. The percentages quoted in Figures 5.8, 5.10 and 5.12are, thus, attributed to an initial yield before interference as a final yield is notclearly defined in this approach. Only in case of absent interference one couldobserve directly a signal with 5% signal strength as compared to the total pK+Λproduction cross section.
For an upper bound on the production amplitude the most conservative case ata mass point is the one that sets the limit. To summarize the results of Figures5.8, 5.10 and 5.12 the highest percentage of cross section still accepted byCLs is shown in Figure 5.13 as gray bands. One sees that the upper limit asa function of the kaonic cluster mass is rather structure-less. While a kaoniccluster produced via Wave A and B seems to allow a higher yield by still beingconsistent with the data, a production of a kaonic cluster via Wave C is strongerconstrained to about half the production strength as compared to the two othercases. The larger the width of the produced state the more yield is consistentwith the data.
Figure 5.13: The upper limit on the production of a KNN in the measured reactionat a CLs limit of 95%. The limit is quoted in percentage of total pK+Λproduction cross section. The three figures show the limit for allthree transition amplitudes. This is obtained from the HADES data-set for a simulated width of 30, 50, and 70 MeV.
128
70 MeV50 MeV30 MeV
Measured total cross-‐section:
Upper limit of ppK-‐ Cross Section:
Γ (MeVc-‐2) Cross Section (μb)
0+ 1.9 – 3.9
1-‐ 2.1 – 4.2
2+ 0.7 – 2.1
Production Cross Section Λ(1405)
9.2 ± 0.9 ± 0.7 +3.3 -‐1.0 μb
HADES coll. (G. Agakishiev et al.) Phys. Lett. B742 (2015) 242-248.
Multi-‐PWA
17 17
Data Sets
Experiment EB [GeV] pK+ΛStatistics
Status
COSY-‐TOF 1.96 ~160k In Preparation (not used in the analysis)
DISTO 2.15 121 k Available
COSY-‐TOF 2.16 43 k Available
COSY-‐TOF 2.16 ~90k In Preparation (not used in the analysis)
DISTO 2.5 304 k Available
DISTO 2.85 424 k Available
FOPI 3.1 0.9 k Single PWA
HADES 3.5 21 k Single PWA
18
COSY-‐TOF Spectrometer
Acceptance: 1°-‐60° (polar), 2π (azimuthal)Sec. Vertex: 𝜎N,O < 1𝑚𝑚, 𝜎R < 3𝑚𝑚
𝜎STU = 300𝑝𝑠𝜎WW(YZ) = 16 𝑀𝑒𝑉/𝑐8
19
DISTO Spectrometer
Acceptance: 23°-‐43° (polar), 2π (azimuthal)𝜎Y = 5%
𝜎WW(YZ) = 30 𝑀𝑒𝑉/𝑐8
20
1. Solution for HADES+FOPI+DISTO25 – Energy Range wide enough for energy dependence– High energy for higher N*-‐Resonances– Three datapoint to pin down set– Easier to make manual changes in parameter set
2. Include Stepwise further data sample1. Cosy216 / DISTO21 / DISTO28– Inclusion do not require further manual modification of data
parameter set.
Combined Analysis
21
Parameter Scan
Solution A B C D E
Loglike -‐67142 -‐67018 -‐66878 -‐66504 -‐66405
χ8
𝑛𝑑𝑓 (𝑛𝑑𝑓 = 4547)9,50 9,98 9,98 10,01 10,34
N*(1650) + + + + +
N*(1710) + + + + +
N*(1720) + + + + -‐
N*(1875) + + -‐ -‐ +
N*(1880) + + + + +
N*(1895) + + + + +
N*(1900) -‐ + + -‐ +
Σ𝑁 (0+) + + + + +
Include different N* Resonances pKΛ non resonant up to F wave *
26
FOPI
26
Χ2 / ndf (ndf=428)
PWA 0.91
27
HADES
27
Χ2 / ndf (ndf=428)
PWA 2.14
28
HADES -‐ WALL
28
Χ2 / ndf (ndf=428)
PWA 1.86
29
Total Cross Section
Value:𝐶: = 4.03 ± 0.57 108𝐶8 = 1.49 ± 0.04𝐶@ = 1.43 ± 0.39
𝜎YZl = 𝐶: 1 −𝑠m
𝑠m + 𝜖8
oI 𝑠m𝑠m + 𝜖
8
op
R.Muenzer et al.,Hyperfine 233, 159-166 (2016)
30
Branching Ratio
4.3 A Partial Wave Analysis for p+K++Λ Production
where S is the total spin of the p+p system, L is the orbital momentum betweenthe two protons and J is the total angular momentum.
The final state is manifold. As explained in Section 2.4, the final pK+Λ statemay contain several intermediate particles. The most prominent ones are N∗+
resonances that subsequently decay into K+ and Λ, see Reaction (2.6). The PDG[8] contains a list of N*-resonances but not all of them are well established.Within this thesis no conclusion can be drawn about the precise contributionof the different N∗+-resonances to the investigated final state and hence nocross section of the latter will be extracted. Thus, all N*-resonances belowthe mass of 2100 MeV/c2 that have a measured K+Λ branching above 1% wereconsidered as possible contribution to the K+Λ yield. Table 4.1 lists the selectedN*-resonances, their quantum numbers, masses, widths and branching ratiosinto K+Λ. Especially the branching in K+Λ is not well known in most of thecases.
Table 4.1: Selected N*-resonances with their properties [8].
Notation in PDG Old notation Mass [GeV/c2] Width [GeV/c2] ΛK/A %
N(1650) 12
−N(1650)S11 1.655 0.150 3-11
N(1710) 12
+N(1710)P11 1.710 0.200 5-25
N(1720) 32
+N(1720)D13 1.720 0.250 1-15
N(1875) 32
−N(1875)D13 1.875 0.220 4±2
N(1880) 12
+N(1880)P11 1.870 0.235 2±1
N(1895) 12
−N(1895)S11 1.895 0.090 18±5
N(1900) 32
+N(1900)P13 1.900 0.250 0-10
Using this table, one can construct several allowed transitions from a p+p initialto a N∗++p final state. As an example, one transition will be discussed here.A proton has the following quantum numbers JP = 1/2+, where J is the totalspin of the particle and P is its parity. A system of two protons can, therefore,have a total spin S = 0 or S = 1. If one considers the S = 0 combination andassumes no orbital momentum between the two particles (L = 0), the quantumnumbers of the system are JP = 0+. This state can also be characterized inthe spectroscopic notation (Equation (4.18)). Then, in this example, the p + pcombination is in the state 1S0.
If one considers, further, a final state of an N∗(1650) with the quantum num-bers JP = 1/2− produced together with a proton, one has to build all possible
97
31
Cross Section
Non Resonant-‐Resonant: 20-‐80
32
Initial State
33
Final State Interaction in PWA
33
[15] Haidenbauer et al.Nuclear Physics A,915,24-‐58 (2013)[16] G. Alexander et a., Phys. Rev. 173,1452 (1968).[17] M.Roeder et al., Eur. Phys. J. A49, 157 (2013)[18] Hauenstein 2014
Scattering Length
Effective Range of System𝐴8qr = st
:+uI0vwIHxy
v +zwHxyv wI{ U w,0v,|}
𝑎Ylr
𝑟r
𝛼s = −1.43 ± 0.36 ± 0,09 𝑓𝑚 𝛼/ = −1,88 ± 0,38 ± 0.10𝑓𝑚𝑟s = 1.31 ± 0.24 ± 0,16 𝑓𝑚 𝑟/ = 1.04 ± 0.78 ± 0.15𝑓𝑚
Source 1S 0 a⇤�p
[fm] 1S 0 r⇤�p
[fm] 3S 1 a⇤�p
[fm] 3S 1 r⇤�p
[fm] < a⇤�p
> [fm]This work �1.43 ± 0.36 ± 0.09 1.31 ± 0.24 ± 0.16 1.88 ± 0.38 ± 0.10 1.04 ± 0.78 ± 0.15NLO2 [15] -2.91 2.78 -1.54 2.72 -1.883
LO2 [15] -1.91 1.40 -1.23 2.13 -1.43
[16] �1.8+2.3�4.2 - �1.6+1.1
�0.8 - -[17] - - - - �1.25 ± 0.08 ± 0.03[18] - - �1.310.32
�0.49 ± 0.3 ± 0.16 - �1.233 ± 0.014 ± 0.3 ± 0.12
Table 3: Scattering length and e↵ective range extracted from the combined PWA fit and reference values from theoretical calculation and previous measurement(see text for details).
[6] L. Fabbietti, Strange Baryonic Res-onances and Resonances Coupling to Strange Hadrons at SIS Energies, in11th Conference on Quark Confinement and the Hadron Spectrum (Confinement XI) St. Petersburg, Russia, September 8-12, 2014,2015.
[7] G. Agakishiev et al., Phys. Rev. C84, 014902 (2011).[8] G. Agakishiev et al., Eur. Phys. J. A50, 82 (2014).[9] J. Weil and U. Mosel, EPJ Web Conf. 52, 06007 (2013).
[10] G. Agakishiev et al., Phys. Lett. B742, 242 (2015).[11] G. Agakishiev et al.[12] B. Sechi-Zorn, B. Kehoe, J. Twitty, and R. A. Burnstein, Phys. Rev. 175,
1735 (1968).[13] F. Eisele, H. Filthuth, W. Foehlisch, V. Hepp, and G. Zech, Phys. Lett.
B37, 204 (1971).[14] G. Alexander et al., Phys. Rev. 173, 1452 (1968).[15] J. Haidenbauer et al., Nucl. Phys. A915, 24 (2013).[16] G. Alexander et al., Phys. Rev. 173, 1452 (1968).[17] M. Rder et al., Eur. Phys. J. A49, 157 (2013).[18] F. Hauenstein, Proton-Lambda Final State Interaction and Polarization
Observables Measured in the pp pKLamda Reaction at 2.7GeV/c BeamMomentum, PhD thesis, 2014.
[19] M. Maggiora et al., Nucl.Phys. A835, 43 (2010).[20] M. Maggiora, Nucl.Phys. A691, 329 (2001).[21] M.Roeder, Final state interactions and polarization observables in the
reaction pp!pK+⇤ close to threshold, Dissertation, Ruhr UniversitatBochum, 2011.
[22] F. Balestra et al., Phys.Rev.Lett. 83, 1534 (1999).[23] R. Munzer, Search for the kaonic bound state ppK
� - Exclusive analysisof the reaction p+p! pK+⇤ at the FOPI experiment at GSI,Dissertation, TU Munchen, 2014.
[24] E. Epple, Measurable consequences of an attractive KN interaction.,Dissertation, TU Munchen, 2014.
[25] A. Anisovich and A. Sarantsev, Eur.Phys.J. A30, 427 (2006).[26] K. Ermakov et al., Eur.Phys.J. A47 (2011).[27] A. Sarantsev, private Communication, 2013.[28] K. A. Olive et al., Chin. Phys. C38, 090001 (2014).[29] K. Brinkmann, V. Nikonov, A. Sarantsev, and M. Schulte-Wissermann,
The analysis of the pp!pK+⇤ data at beam momenta 2950,3059 and3200 MeV, Draft from 2013, 2013.
[30] S. Abd El-Samad et al., Eur.Phys.J. A49, 41 (2013).[31] S. Wycech, private communication, 2014.[32] E. R. E. Roderburg, J. Ritman, private communication, 2014.[33] S. Abdel-Samad et al., Phys.Lett. B632, 27 (2006).[34] S. Abd El-Samad et al., Phys.Lett. B688, 142 (2010).[35] M. Abdel-Bary et al., Eur.Phys.J. A46, 27 (2010).[36] S. Abd El-Samad et al., Eur.Phys.J. A49, 41 (2013).[37] K. Fuchs and H. So↵el, Geophysics, in Landolt-Bornstein, New Series,
volume V/2, page 417(a) and 468(b), Springer-Verlag, Heidelberg, 1985.[38] A. Sibirtsev, W. Cassing, G. Lykasov, and M. Rzyanin, Nucl.Phys.
A632, 131 (1998).[39] R. Muenzer et al., Hyperfine Interaction 233, 159 (2016).
[MeV]Λ,+p,K
- Ms100 200 300 400 500 600 700 800 900
b)
µ(σ
0123456789
(x2)0
S1
0P3
(a)
[MeV]Λx,P+p,K
- Ms100 200 300 400 500 600 700 800 900
b)
µ(σ
0
5
10
1520
25
3035
40
45
(x3)2D1
1P3
2P3
(b)
[MeV]Λ,+p,K
- Ms100 200 300 400 500 600 700 800 900
b)
µ(σ
0
2
4
6
8
10
12
14
16
2F
3
(c)
Figure 4:
7
34
The ΣN Cusp Effect
34
At Threshold : 2130 MeVc-‐2
Quantum Number of Cusp: 0+ / 1+ (L=0,2)
Spectral Function: Breit Wigner
Flatté
S.Abd El-‐Samad, Eur.Phys.J A49(2013)
Coupled Channel:
NΣ
pΛ
35
Previous Observations
36
Cusp Spectral Function
37
Data Set
38
Results
39
• Combined Analysis for COSY & DISTO & HADES & FOPI completed
• Systematical Analysis performed • Excitation Function for N* and pKL extracted• Scattering Length p-‐Λ separate for Singlet and Triplet• Cusp Wave included too ( not discussed here)• Common upper limit for Kaonic Bound states to come soon
Summary and Outlook
