1. QNP2018 @KEK, Tsukuba, Japan, November 13-17, 2018
Measuring space-time properties of excited nucleons below 1.2 GeV using Bose-Einstein Correlations
Qinghua HE for FOREST Collabration
1 Department of Nuclear Science and Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing , China
2 Research Center for Electron Photon Science, Tohoku University, Sendai , Japan

2. 2 or more than 2 identical bosons
How to measure ultra-short lifetime excited nucleon
How to measure ultra-short lifetime excited nucleon γ N N N*
𝜋 0
source size of a multi-pion emitter
2 or more than 2 identical bosons
𝜋 0
how to measure the size of particles
Electron scattering electron-proton elastic scattering (Orsay, Stanford, Saskatoon, Mainz)
Hydrogen spectroscopy
Hadron scattering
Muonic hydrogen
from the measured energy difference between the 2P and 2S states of muonic hydrogen
r_p^\mu= (39) fm
r_p^e=0.8775(51) fm …
BEC provides a tool to measure the space-time properties of the boson emission source.
Bose-Einstein correlations (BEC)
𝜋 0
𝜋 0

3. Symmetrized two-particle wave function
Bose-Einstein correlations (BEC)
Size ?
Symmetrized two-particle wave function
(assume plane wave function of propagation)
Bose-Einstein (BE) correlations provide a measure of the space-time properties of the boson emission source.
This symmetrization results in an enhanced probability of emission if the two bosons have similar momenta.
enhancement
space-time properties

4. Analysis of Bose-Einstein correlations
The BE correlations are measured in terms of a correlation function, which depends on the four-momentum difference of two pions Q.
Two particle correlation function
p1,2: four momentum of the two identical particles.
μ: boson’s mass
completely chaotic:
Assumption:
a spherical emission volume with a Gaussian density distribution
plane wave function of propagation
completely coherent:
Normalized Fourier transform of source density ρ(x):
N: normalized factor
r0 : emitter radius
λ2 : chaoticity parameter (0≦ λ2 ≦1)
0: completely coherent case
1: totally chaotic limit

5. Experimental procedure to observe BEC effects
Measure the spectra of Q (momenta difference) and compared it to that in a reference sample free of BE effects
signal sample
reference sample
A valid reference sample should be identical to the real data (signal sample) in all aspect but free of BEC.
The reference sample is constructed by taking two π0 from different events, namely event mixing

6. Difficulties in BEC analysis at low energies with low multiplicities
(1) Event mixing method
low energies
low multiplicities
high energies
high multiplicities
strongly disturbed by non-BEC factors of exclusive reactions with a low multiplicity such as global conservation laws and decays of resonances
weakly disturbed by non-BEC factors of exclusive reactions with a low multiplicity such as global conservation laws
Complicated kinematical constraints
Simple kinematical constraints
(2) Resonance decay effects

7. Event Mixing Technique
Appropriate mixing cuts should be applied in the mixing
Missing mass consistency (MMC) cut
The third particle’s mass in the mixed event should be the same as the original event.
where 𝑚 𝑋 𝑚𝑖𝑥 and 𝑚 𝑋 𝑜𝑟𝑖 are the missing particle mass for the mixed event and that for the original event, respectively
Missing mass consistency (MMC) cut : 𝑚 𝑋 𝑚𝑖𝑥 − 𝑚 𝑋 𝑜𝑟𝑖 < 𝑀 𝑐𝑢𝑡
Pion energy (PE) cut: Events with pion energy higher than a given level are rejected
Energy sum order (ESO) cut: 𝐦𝐢𝐧 E 𝒔𝒖𝒎 𝒐𝒓𝒊,𝟏 , E 𝒔𝒖𝒎 𝒐𝒓𝒊,𝟐 < E 𝒔𝒖𝒎 𝒎𝒊𝒙 <𝐦𝐚𝐱 E 𝒔𝒖𝒎 𝒐𝒓𝒊,𝟏 , E 𝒔𝒖𝒎 𝒐𝒓𝒊,𝟐
no overlapping photon clusters (Used to correct the detection efficiency) ……

8. Appropriate mixing cuts in event mixing:
Event Mixing Technique
Appropriate mixing cuts in event mixing:
MMC + PE cuts
Fig. Fitted values of r0 (a) and λ2 (b) obtained by event mixing in a single and a multi mixing (up to 10 times) mode at six incident photon energies 𝐸 𝛾 =1.0, 1.03, 1.06, 1.09, 1.12, and 1.15 GeV for the γp→ π 0 π 0 p events. For comparison, the values of r0 and λ2 for the generated sample with BEC effects are also shown.
Fig. The ratio of the Q distribution of the generated BEC/noBEC sample, NBEC(Q), to that from the mixed events, NMix(Q) (filled circles). The ratio of NBEC(Q) to the Q distribution of pure phase space sample, NPS(Q), is also shown (open triangles) in each panel for comparison.
[1] Q. He, et al., Prog. Theor. Exp. Phys. 2017, (2017); [2] Q.-H. He, et al., Chinese Phys. C 40, (2016).

9. Measuring space-time properties of excited nucleons below 1
Measuring space-time properties of excited nucleons below 1.2 GeV using Bose-Einstein Correlations
γp→π0π0p
Using FOREST ELPH
1.2 GeV
Proton

10. FOREST Experiment

11. 4π Electromagnetic detector complex FOREST
EM Calorimeter
SCISSORS III
192 CsI; θ: 4o-24o, φ:full
Res. : 1GeV
Backward Gamma
252 Lead/Scintillating fiber modules;
θ: 30o-100o, φ:full
Res. : 1GeV
Rafflesia II
62 Lead Glass modules;
Res. : 1GeV
Plastic Scintillator
SPIDER (2 layers × 24 modules
IVY (18 modules)
LOTUS (12 modules) γ

12. Identification of γp→π0π0p
fig
π0→2γ
Two neutral clusters with Δt=[-1.5,1.5] ns.
Invariant mass = Mπ0
m2γγ =2Eγ1Eγ2(1−cosθγ1γ2)
Proton γ
Delayed charged cluster wrt. the average time of the selected 2 pairs of coincident photons (t4γ)
Miss mass MX of γp→π0π0X is equal to the proton mass
p/π

13. Invariant mass and missing mass
The best combinations of the two paris of photons
Missing mass distribution of the hypothesis γp→π0π0X

14. BEC results for FOREST data (exclusive)
γp→2π0p (FOREST 2009D)
fit:

15. BEC results for FOREST data (inclusive)
γp→2π0X (FOREST 2009D)
γd→2π0X (FOREST 2009D)

16. Preliminary Results r0 = 0.91 ± 0.01(stat.)±0.04(syst.) fm

17. Resonance decay effects correction
γp→π0Δ→π0π0p process is dominant in γp→π0π0p π0 ∆+ p p π0
Q. He, PhD Thesis, Tohoku University, 2014

18. Resonance decay effects correctionQ q N Δ
𝜋 0
S wave meson emission due to an energetic quark
Δ→π0N decay originated by an energetic quark Q N q Δ Q
𝜋 0
𝑃 2
−𝑃 2
We here discuss how to use BEC effects between two identical neutral π to measure the spatial size of Δ(1232) using π^0Δ events obtained in double neutral pion photoproduction at an incident photon energy around 1 GeV. In this process, \pi^0 and \Delta are produced at the same time at first. Then the \Delta decays into \pi^0 N. If there is an overlap of the \Delta and the first \pi^0 wave function, some information on the size of \Delta is obtainable through \pi^0\pi^0 BEC in the \Delta rest frame under the following considerations.
H. Shimizu, ELPH Annual Report, 2017

19. Space-time coordinates of Δ at rest
Resonance decay effects correction
3-dimentional correlation function
𝐶 𝐵𝐸𝐶 𝑞, 𝑝 2 =1+𝜆 exp − 𝛼 2 𝑞 exp − 𝛽 2 𝑞 𝑧 𝐽 0 (𝛽 𝑞 𝑟 ),
q: 3-D relative momentum of two pions at rest Delta frame Δ
1st 𝜋 0
2nd 𝜋 0 O x y A B
𝑞 2 = 𝑞 𝑟 2 + 𝑞 𝑧 2
𝑞 = 𝑞 𝑟 ,0, 𝑞 𝑧 in cylindrical coordinates
𝛽= 1 2 𝑝 2
𝑝 2 : the momentum vector of 𝜋 0 decaying from Δ in the rest Δ frame
Space-time coordinates of Δ at rest
𝐽 0 (𝛽 𝑞 𝑟 )= sin⁡(𝛽 𝑞 𝑟 ) 𝛽 𝑞 𝑟 , 0-order Bessel function
H. Shimizu, ELPH Annual Report, 2017

20. Resonance decay effects correction
BGOegg data is better for further BEC analysis
High intensity：
Multi (ex. 4) laser injection
w/ large aperture beam-line
& Laser beam shaping
~107 photons/s（LEPS ~106 ）
Backward Compton Scattering
Spring-8
Large acceptance EM calorimeter BGOegg
N. Muramatsu, Beijing, 19 July, 2018

21. Summary
An event mixing method for low-multiplicity BEC analysis is developed
Preliminary BEC results on FOREST experiments are obtained
Resonance decay effects on BEC analysis should be taken into consideration
BEC analysis for BGOegg experimental data is on the way

22. Thanks for your attention

23. Back up

24. Total cross section NX : yield Nbeam : number of the incident photons.
Ntarget : number of target particles
εdet : detection efficiency
ΓX→Y : branching ratio of pπ0π0→p4γ
（Γpπ0π0→pγγγγ = Γπ0→γγΓπ0→γγ = 0.976).
The detection efficiency is estimated with a GEANT4-based simulator RFS package (by T. Ishikawa).

25. Total cross section Syst. Error: 11%
证实了在第二和第三共振区对 γp → 2π0p 反应的主要贡献就是 ∆ 的级联衰变 γp → ∆(1232)π0 → pπ0π0

26. 大立体角电磁量能器BGOegg 264 升；1.9吨 1320块BGO晶体（22层，每层60个） 自支撑结构（晶体间只有ESR反射包裹材料）
极角：24o-156o
两种PMT：H11334 (metal package type) 和H6524 (head on type)
BGO晶体220 mm长（20X0），棱锥形。
Energy resolution
Position resolution
1.3% at 1 GeV
3 mm at 0.8 GeV

27. π,η,ππ,πη,ηη,ω光生反应 BGOegg将要开展的物理实验 η’介子在核子环境中的质量改变 强子质量起源自发手征对称破缺
寻找η’-mesic nuclei
12C(γ,P) η’11B
重子共振态
π,η,ππ,πη,ηη,ω光生反应
π0π0玻色爱因斯坦关联
[1] H. Nagahiro, M. Takizawa, and S. Hirenzaki, Phys. Rev. C 74, (2006).