1. An Experimental study on the K-pp
bound state by using the d(π+, K+) reaction.
Yudai Ichikawa for the J-PARC E27 collaboration
Kyoto University / JAEA
2014/3/12
第11回ハドロンスクウェア 1

2. Introduction Kaonic nuclei K-pp bound state
A bound state of antikaon and nucleus due to a strong interaction.
K-pp bound state
KNN(Total charge; +1, I=1/2)
Expected to be the simplest kaonic nuclei.
Theoretical prediction of B.E. and Γ depend on the KN interaction and the calculation method. 2

3. Past experiments for K-pp
FINUDA
DISTO
reaction
Stopped K- absorption
on 6, 7Li+12C
p + Tp=2.85GeV
method
Invariant mass of back-to-back
Λp pairs
p+p→X+K+ （missing mass）
X→Λ+p （invariant mass）
B.E
105 ± 5 MeV
Width
118 ± 8 MeV -
M.Agnello et al., PRL 94, (2005)
T.Yamazaki et al., PRL 104, (2010)
K-+p+p~2.37GeV/c2
K-+p+p~2.37GeV/c2
T.Yamazaki et al.,
PRL 104, (2010)
M.Agnello et al., PRL 94, (2005) 3

4. J-PARC E27 experiment d(π+, K+)X reaction (Pπ+= 1.69GeV/c) π+
K-pp is produced via a Λ(1405) doorway.
K1.8 Beam
π+ + n → Λ(1405) + K+
Λ(1405) + p → K-pp
(→quasi free Λ* ） K+
Target π+
Y.Akaishi, T.Yamazaki, Phys. Rev. C (2007) 4

5. →Coincidence measurement.
d(π+, K+)X reaction (Pπ=1.69GeV/c)
Simulated inclusive missing mass spectrum of quasi-free hyperon productions.
There are a lot of background process in this reaction.
B.G.
QF Σ
Black : all components
K-pp
threshold
QF Λ
K-pp signal will be hidden by other QF processes at inclusive spectrum.
→Coincidence measurement. Σ+
QF Y* + πYN
FINUDA, DISTO
K-pp
Σ+(1385) Σ0
Λ(1405) Λ*
Missing Mass[GeV/c2] 5

6. RCA for B.G. suppression Coincidence measurement!! K-pp → Λ + p p+π-
d（π+,K+）K-pp π+
(Range Counter Array) 6

7. RCA for B.G. suppression K-pp→ Λ p →p π-
6units, 5 layers ( cm) of plastic scintillator.
TOF: 50cm, θxz:39°–122°(L+R)
Momentum coverage for proton: 300~800MeV/c
Geometrical coverage ~ 26%
→We suppress the B.G. by tagging a proton at RC-2, 3.
→More strongly suppress by tagging two protons.　
K-pp→ Λ p
　　 　 　　　　　→p π-
RC-1L, R
RC-2L, R
RC-3L, R
QF=π+ “n”→ Λπ0 K+
　　　　　　 → p π-
(proton spectator)
RC-1L, R
RC-2L, R
RC-3L, R 7

8. Summary of the data taking
We have carried out the data taking as first stage in June, 2012.
Goal
Inclusive d(π+,K+)X < Mx <2.5GeV/c2.
The first measurement of this reaction and this missing mass region.
p(π+,K+)X data (same beam momentum)
Check the contribution of “p” in “d”
Check the feasibility of coincidence measurements.
One proton tag/ two proton tag (with RCA)
Beam time summary
Same pbeam run
Calibration run 8

9. Preliminary results of this data9

10. Spectrometer performance
GeV/c (Calibration)
The K+ momentum is same region as the
d(π+,K+)K-pp reaction.
Missing mass resolution of Σ+
2.4MeV (FWHM)
Missing mass resolution of d(π+, K+)X
reaction
X = K-pp(B.E=100MeV),
Resolution = 2.4MeV(FWHM)
X = ΣN threshold cusp(2.13GeV/c2),
Resolution = 3.0MeV(FWHM)
Cross section
Cross section is consistent with
old data (D. J. Candlin et al.).
2.4 MeV
Missing Mass[GeV/c2]
dσ/dΩ of Σ+[μb/sr] 10
Scattering angle[degree] 10

11. p(π+, K+)X at Pπ+ = 1.69GeV/c Target = LH2
~ In order to check the contribution of “p” in “d”.~
The same beam momentum was selected for d target run. 11

12. Cross sections of old data.
Process
Cross section[μb]
Error[μb]
π++p → Σ+K+
470 39
π++p → Σ(1385)+K+
124 20
π++p → ΛπK+
40.0 28
π++p → ΣπK+
6.0
・Ref. Y.Pan et al. PRD 2, 3(1970) 、
Y.Pan and F. Forman NPB (1970)
This experiment was performed by using the bubble chamber. 12

13. Acceptance of p(π+, K+)X reaction.
Scattering angle θpiK(Lab)[deg]
The Acceptance of p(π+, K+)X reaction at pπ=1.69GeV/c
Missing Mass[GeV/c2]
The region of XMass=1.2~1.45GeV/c2 have a flat acceptance. 13

14. p(π+,K+)X Missing Mass spectrum (Pπ+=1.69GeV/c)
Σ+ production
- ΔM = 3.2 MeV (FWHM)
- RCA coincidence probability
- Proton: 2.9±0.1%(data), ±0.02%(sim)
- π＋: ±0.3%(data), ±0.05%(sim)
Σ+(1385) and Yπ production
- Obtained spectrum can be fitted with two-components(Σ+(1385)and Yπ).
(χ2/ndf = 2.51)
Black : Data
Blue : Sum of fit
Green :Σ+(1385)
Red : Yπ Σ+
Counts / 1MeV
Σ(1385)+
Zoom
Missing Mass [GeV] 14

15. d(π+, K+)X at Pπ+ = 1.69GeV/c Target = LD215

16. Elementary cross section from old data
Process
Cross section[μb]
Error[μb]
π++p → Σ+K+
470 39
π++p → Σ(1385)+K+
124 20
π++p → ΛπK+
40.0 28
π++p → ΣπK+
6.0
π++n → ΛK+
175 15
π++n → Σ0K+
121 10
π++n → Λ(1405)K+
20.6
1.0
π++n → Σ(1385)0K+
76.7
π++n → ΛπK+
13.7
1.8
π++n → ΣπK+
19.3
・Ref(p-target). Y.Pan et al., PRD 2, 3(1970) 、Y.Pan and F. Forman NPB (1970)
・Ref(n-target). D. W. Thomas et al., NPB 56, 15(1973)
These experiments were performed by using the bubble chamber. 16

17. Acceptance of d(π+, K+)X reaction.
The Acceptance of d(π+, K+)X reaction at pπ=1.69GeV/c
Scattering angle θpiK Lab[deg]
Missing Mass[GeV/c2]
The region of Xmass=2.16~2.48GeV/c2 have a flat acceptance. 17

18. d(π+, K+)X inclusive spectrum
Quasi-free B.G.
Λ, Σ
Y* ：Σ (1385)+/0,
Λ (1405)
Λπ, Σπ
There are a lot of B.G.
→It is difficult to identify the
K-pp bound state from
inclusive spectrum.
In the Λ and Σ region,
observed spectrum is almost consistent with simulation.
ΣN-ΛN Cusp
Excess is observed around GeV/c2.
Peak shift
Y* peak shift to lower mass
side ~ 30 MeV/c2.
Black: Simulation for the B.G.
(quasi-free Hyperon production)
Red: Data
Σ0 + p = GeV/c2
Σ+ + n = GeV/c2
ΣN-ΛN Cusp
Σ+/0
counts/0.5 MeV
Zoom Λ
preliminary
Y*s
K-+p+p~2.37GeV/c2 18

19. π+ d→K+ X at 1.4GeV/c @Saclay
ΣN-ΛN
Cusp
Mt≧1
Mt≧2
ΣN->ΛN
Conversion
Mt≧3
(Σ)
Pigot et al., NPB 249 (1985) 19

20. d(π+, K+)X inclusive spectrum
Quasi-free B.G.
Λ, Σ
Y* ：Σ (1385)+/0,
Λ (1405)
Λπ, Σπ
There are a lot of B.G.
→It is difficult to identify the
K-pp bound state from
inclusive spectrum.
In the Λ and Σ region,
observed spectrum is almost consistent with simulation.
ΣN-ΛN Cusp
Excess is observed around GeV/c2.
Peak shift
Y* peak shift to lower mass
side ~ 30 MeV/c2.
Black: Simulation for the B.G.
(quasi-free Hyperon production)
Red: Data
Σ+/0
Peak shift Λ
preliminary
Y*s
K-+p+p~2.37GeV/c2 20

21. d(γ, K+π-)X reaction at Eγ=1.5-2.4 GeV
Spring-8 LEPS
A. O. Tokiyasu et al., Phys. Lett. B 728C, (2014).
can be fitted
(data and simulation 　　
are consistent.)
Peak shift is not observed in this reaction. 21

22. d(π+, K+)X inclusive spectrum
Quasi-free B.G.
Λ, Σ
Y* ：Σ (1385)+/0,
Λ (1405)
Λπ, Σπ
There are a lot of B.G.
→It is difficult to identify the
K-pp bound state from
inclusive spectrum.
In the Λ and Σ region,
observed spectrum is almost consistent with simulation.
ΣN-ΛN Cusp
Excess is observed around GeV/c2.
Peak shift
Y* peak shift to lower mass
side ~ 30 MeV/c2.
Black: Simulation for the B.G.
(quasi-free Hyperon production)
Red: Data
preliminary
Σ+/0
→Coincidence analysis
to suppress these B.G. Λ
preliminary
Y*s
K-+p+p~2.37GeV/c2 22

23. PID performance of RCA P π Emitted proton is selected by RCA.
Proton is well separated from pion
stopped at 4th layer
Cut parameter
stop layer
1/β
PID function (dE/dx)
1/β P π
escape before stop
PID function ( ≡ (dEi + dEi-1)α - dEiα × cosθ )
i : stop layer 23

24. Coincidence spectra p Coincidence preliminary Inclusive Proton
Missing Mass[GeV/c2]
Counts/6MeV
p Coincidence
Black: p selection
Green: mis-ID
Red: Black-Green
Proton selection:
Proton(Momproton>~300MeV/c)
Proton
selection
preliminary
Inclusive
preliminary
Counts/6MeV
Proton
selection
Missing Mass[GeV/c2]
Counts/6MeV
π Coincidence
Proton selection:
π±(main) + e± + γ
preliminary
Missing Mass[GeV/c2] 24

25. π Coincidence analysis
π coincidence probability (Rπ)
Rπ = (π coincidence spectrum) / (Inclusive spectrum)
Rπ ∝ (π emission BR) x (π detection efficiency)
QFΣ
QFY* + πYN
QFΛ
1 pion
2 pions
preliminary Rπ
π Coincidence(Simulation) Λ Σ0 Σ+
Σ*+
Σ*0 Λ*
Black: Simulation
(for QF B.G.)
Red: Data
QFΛ and QFΣ emit 1 pion
QFY* and πYN emit 2 pions
Rπ reflects π emission probability, therefore the ratio in QFY* + πYN region is higher than those in the other regions.
Rπ is almost consistent between
data and simulation(quasi-free). 25

26. 1p Coincidence method QF=π+ “n”→ Λπ0 K+ → p π- (proton spectator)
Proton(>=300MeV/c) from QF processes can reach only RC-1L, R.
QF=π+ “n”→ Λπ0 K+
　　　　　　 → p π-
(proton spectator)
RC-1L, R
RC-2L, R
RC-3L, R 26

27. 1p Coincidence for RC-2L, R
RC-2L, R are almost free from QF backgrounds.
Excess due to ΣN-ΛN cusp is clearly observed ~ 2.13GeV/c2.
Broad Enhancement is observed around 2.3GeV/c2.
There is a proton emitting source involving two nucleons
(non quasi free) in high emission probability.
A possible explanation of the observed structure is K-pp.
RC-2L, R
<1P coincidence spectrum>
1 p hit in the RC-2L, R is required.
<1P coincidence probability>
P coin spectrum / Inclusive
ΣN-ΛN
Cusp
K-pp ??
Rp/6MeV
/Inclusive 27

28. 2p Coincidence analysis
2 protons coincidence spectrums show the same tendency
as 1proton coincidence spectrum.
In order to apply the acceptance correction for protons, we have to know the final state.
Detection efficiency depends on the final state.
η2p
<Detection efficiency of RCA> Λp
Σ0p
Λπ0p
Σπp
d(π+, K+)X;
Red: X->Λp,
Pink: X->Σ0p,
Green:X->Λπ0p,
Sky: X->Σπp,
<2P coincidence spectrum>
2 protons hit in the RCA is required.
<2P coincidence probability>
2P coin spectrum / Inclusive
ΣN-ΛN
Cusp
K-pp ?
Rp/6MeV
/Inclusive 28

29. Determination of final state
Hyperon masses of final state are reconstructed by
2p coincidence analysis.
　 d(π+, K+)X; X→Y+p1, (Y→π + p2 (+…))
Y=Λ, Σ0, Λπ, Σπ
MY2= (Eπ + Md – EK – Ep1)2 –(pπ – pK – pp1)2
Pp1 > Pp2 at X rest frame. (In this frame, PY=Pp1).
Same analysis was performed for simulation.
→ Template fit.
We set the 3 regions at the missing mass spectrum
(2p coincidence histogram)
①MM<2.22GeV, ②2.22<MM<2.35GeV, ③MM>2.35GeV
Cusp region
Enhance region
Y* region 29

30. Calculation of momentum vector of proton
RCA doesn’t have a tracking devise.
Originating point
Vertex point of (π+, K+) react.
σvtx=(4.4, 2.7, 1.6, 1.5, 1.6, 1.6, 1.6)[cm] for
θpiK(Lab)= (2-4, 4-6, 6-8, 8-10, 10-12, 12-14, 14-16)[deg]
RC hit position (estimated from 1st layer)
RC size of 1st layer is (10×100×1[cm3]).
XZ; assume the center of the counter.
Y; time difference between up and down (σY ~ 1.1[cm]).
Absolute value of momentum
Calculated from TOF (proton mass is assumed) .
Time resolution is ~150ps.
Simulation use the same calculation method and include these resolutions.

31. Determination of final state
Hyperon masses of final state are reconstructed by
2p coincidence analysis.
　 d(π+, K+)X; X→Y+p1, (Y→π + p2 (+…))
Y=Λ, Σ0, Λπ, Σπ
MY2= (Eπ + Md – EK – Ep1)2 –(pπ – pK – pp1)2
Pp1 > Pp2 at X rest frame. (In this frame, PY=Pp1).
Same analysis was performed for simulation.
-> Template fit.
We set the 3 regions at the missing mass spectrum
(2p coincidence histogram)
①MM<2.22GeV, ②2.22<MM<2.35GeV, ③MM>2.35GeV
ΣN-ΛN
Cusp
K-pp ?
<2P coincidence probability>
2P coin spectrum / Inclusive ① ② ③
Rp/6MeV
Cusp region
Enhance region
Y* region 31

32. The final state of X (2p coin events).① ② ③
Enhance
region Y* ① ② ③
Cusp
region
The final state of X (2p coin events).
Hyperon masses are reconstructed by 2p coin analysis.
・d(π+, K+)X; X→Y+p1, (Y→π + p2 (+…))
※MY2= (Eπ + Md – EK – Ep1)2 –(pπ – pK – pp2)2
2.1<MM<2.22[GeV/c2]
2.22<MM<2.35[GeV/c2] ① Λ ② Σ0
χ2/ndf=4.95 Λ
χ2/ndf=0.65
Black: Data ,
Red: X->Λp,
Pink: X->Σ0p,
Green:X->Λπ0p,
Sky: X->Σπp,
Blue: Sum Λπ
MM<2.35[GeV/c2]
η2p
<Detection efficiency of RCA> Λp
Σ0p
Λπ0p
Σπp ③ Σ0
χ2/ndf=0.66 Σπ Λ Λπ 32

33. Summary and Future work
<Inclusive analysis>
We have obtained d(π+, K+) at 1.69 GeV/c for the first time.
In the Λ and Σ region, observed spectrum is almost reproduced by the
simulation which is based on the quasi-free processes.
ΣN-ΛN cusp structure and peak shift of Y* are observed.
<Coincidence analysis>
In proton coincidence, the ΣN-ΛN cusp structure and an broad enhancement around 2.3 GeV/c2 are clearly observed.
→ A possible explanation of the observed structure is K-pp.
→ The detail studies on detection efficiencies are in progress.
Hyperon masses are reconstructed from 2 protons analysis .
→The final states are determined.
<Future work>
Apply the acceptance correction for protons which detected by RCA. 33

34. Back up 34

35. Fermi-motion in deuteron
Bonn meson-exchange model
300MeV/c Cut off
R. Machleidt, K. Holinde and Ch. Elster, Phys. Rept. 149, 1-89 (1987). 35

36. Ymass calculation (Kinematics)
π+ + d -> X + K+
Four-momentum of X is determined by π+, d, K+ .
(PμX = Pμπ+ + Pμd – PμK+)
X-> p1 + p2 + X2
Momentum of p1 and p2 are measured with RCA
Pp1 > Pp2 at X1 rest frame.
In this frame, PY=Pp1.
Y (PμY = Pμp2 + PμX2 = PμX – Pμp1 ) 36

37. 1p Coincidence analysis
RC-1L(a)
RC-1R(a)
RC-1L(b)
RC-1R(b)
RC-2L
RC-2R
RC-3L
RC-3R
Missing Mass[GeV] Rp
Black:Simulation(QF),
Red:Data
preliminary
Forward
Backward L R
Proton(>=300MeV/c) from QF processes
can hit only RC-1L, R.
RC-1L(a)
RC-1L(b)
RC-1R(a)
RC-1R(b)
RC-1L, R
RC-2L, R
RC-3L, R
QF=π+ “n”-> Λπ0 K+
　　　　　　-> p π- π0 K+
(proton spectator) 37 37

38. B.G. suppression of 1proton tag
Proton from QF processes can
reach only RC-1L, R.
Quasi-free process(B.G.)
K-pp(Signal)
RC-1L, R
RC-2L, R
RC-3L, R
QF=π+ “n”→ Λπ0 K+
　　　　　　 → p π-
(proton spectator)
K-pp→ Λ p
　　　 　 → p π-
RC-1L, R
RC-2L, R
RC-3L, R 38

39. B.G. suppression of 2protons tag
K-pp decay
B.G. (quasi-free)
K-pp → Λ + p1, K-pp → Σ0 + p1, p2 + π- Λ + γ, p2 + π-
π+ + d → Λ* + K+ + p1s,
Λ* → Σ + π,
Σ+ → p2 + π0
P1s< 250MeV/c
B.G.(quasi-free);
momentum of spectator proton
(p1s) is smaller than 300MeV/c.
QF background are more strongly
suppressed by 2 protons tag. 39

40. Data taking of pilot run
We performed a data taking in June 2012.
GeV/c : 7.6 days, 3.3 × 1011 π
GeV/c : 0.6 days, 7.6 × 109 π
calibration : 2 days
3M π+/spill (6s cycle)
irradiated pion number (d target)
5E+10
1E+11
1.5E+11
2E+11
2.5E+11
3E+11
3.5E+11
Irradiated π number (d target)
proposal : 40 days,
5M π+/ spill
⇒ taken data : ~10 %
6/18 0:00 6/20 0:00 6/22 0:00 6/24 0:00 6/26 0:00 6/28 0:00 6/30 0:00 7/2 0:00
date 40

41. Seg1L, 1R acceptance difference
θpiK[degree]
θpiK[degree]
Missing Mass[GeV]
Missing Mass[GeV]
Missing Mass[GeV]
Missing Mass[GeV]

42. Tagging efficiency(Acceptance) Final state = Λp
Missing Mass[GeV]
Missing Mass[GeV]
Missing Mass[GeV]
Missing Mass[GeV]
Missing Mass[GeV]
Missing Mass[GeV]

43. Tagging efficiency(Acceptance) Final state = Σ0p
Missing Mass[GeV]
Missing Mass[GeV]
Missing Mass[GeV]
Missing Mass[GeV]
Missing Mass[GeV]
Missing Mass[GeV]

44. Tagging efficiency(Acceptance) Final state = Σ+π-p
Missing Mass[GeV]
Missing Mass[GeV]
Missing Mass[GeV]
Missing Mass[GeV]
Missing Mass[GeV]
Missing Mass[GeV]

45. Tagging efficiency(Acceptance) Final state = Λπ0p
Missing Mass[GeV]
Missing Mass[GeV]
Missing Mass[GeV]
Missing Mass[GeV]
Missing Mass[GeV]
Missing Mass[GeV]

46. mis-ID of RC Simulation Data Black: proton Blue：π+ Red : π-
Proton is selected by range and β.
Data
PID function
Red: proton (±3σ)
Green: side band (3σ ~ 6σ)
　　　linear background (from π)

47. range : beta correlation
4th
3rd
2nd ・p
1st ・π
proton momentum
~250 MeV/c
~600 MeV/c

48. PID function
i-1 Layer
i Layer
y position of RC
Path length

49. PID of high momentum proton (All layers have hit)
1.54<1./β<2.4
Red：proton stops at last layer
Green : proton doesn’t stop last layer
(penetrate event)
dE of Layer5[MeV]
PID function

50. Differential cross section for d(π+,K+) reaction
θLab= 2 - 4°
θLab= 4 - 6°
dσ/dΩ/dm[ub/sr/2MeV]
dσ/dΩ/dm[ub/sr/2MeV]
Missing Mass[GeV]
Missing Mass[GeV]
θLab= 6 - 8°
θLab= °
dσ/dΩ/dm[ub/sr/2MeV]
dσ/dΩ/dm[ub/sr/2MeV]
Missing Mass[GeV]
Missing Mass[GeV]
θLab= °
θLab= °
dσ/dΩ/dm[ub/sr/2MeV]
dσ/dΩ/dm[ub/sr/2MeV]
Missing Mass[GeV]
Missing Mass[GeV]
θLab= °
preliminary
dσ/dΩ/dm[ub/sr/2MeV]
Missing Mass[GeV] 50

51. Result from CLASS for Λ(1405)
<abstract>

53. 53

54. chisqr 2_4deg=12.7784 4_6deg=20.2207 6_8deg=20.5354 8_10deg=16.0251
2_4deg=
4_6deg=
6_8deg=
8_10deg=
10_12deg=
12_14deg=
14_16deg= 54

55. Differential cross section of QFΛ and QFΣ0 d(π+,K+) @1.7 GeV/c
We checked differential cross section by comparing our data with some old data.
π+ ”n” → K+ Σ0 at 1.7 GeV/c
calculated by
π+ d → Σ+/0 K+ ー π+ p → Σ+ K+
π+ ”n” → K+ Λ at 1.7 GeV/c 55

56. p(π+, K+)X spectrum (each θpiK)56

57. p(π+, K+)X spectrum (each θpiK)57

58. Breit-Wigner for Σ(1385)+
Ref. G. Agakishiev. et al. PRC 85, (2012)

59. Σ(1385)+ Mass & Width Ref; PDG
We use the (Mass= 1380, 1382, 1384MeV)（Width=32, 35, 41, 44, 47, 50MeV）. 59

60. p(π+,K+)X Missing Mass spectrum(1.7GeV/c)
Σ+ production
- ΔM = 3.2 MeV (FWHM)
- RCA coincidence probability
- Proton: 2.9±0.1%(data), 3.5±0.02% (sim)
- π＋: ±0.3%(data), ±0.05%(sim)
Σ+(1385) production
- Mass: 1380MeV, Γ: 32MeV (PDG averaged value: 1383MeV, 36MeV)
Yπ production
(χ2/ndf = 2.51)
Black : Data
Blue : Sum of fit
Green :Σ+(1385)
Red : Yπ Σ+
Counts / 1MeV
Σ(1385)+
Missing Mass [GeV] 60