1. Measurement of direct photon emission in K+ →π+π0γ ---Spectroscopic studies for various K+ decay channels --- S. Shimizu for the KEK-PS E470 collaboration
KEK-PS E470　collaboration
Japan Osaka Univ.
KEK
Univ. of Tsukuba
Russia Institute for Nuclear Research
Canada TRIUMF
Univ. of British Columbia
Univ. of Saskatchewan
Univ. of Montreal
Dafne2004, 8 June 2004

2. 1. Contents 2. Introduction 2. Introduction 3. Physics motivation
4－6. Experimental setup
7－8. Study of Kπ2γ decay in E470
9－11. Study of Ke4 decay in E470
12. Summary
2. Introduction
The decay spectra of K-mesons offer a fertile ground to probe various fundamental theories of weak interactions (scalar, vector, and/or tensor types), symmetries (CP- and T- violations), and strong interaction models such as QCD inspired Chiral perturbation theories.
At KEK, E470 collaboration have been heavily involved in the study of K+ decays for testing T- violation(E246). In addition to the T-violation study, we have made important contributions to the spectroscopic studies of K+ →π0 μ+ ν (Kμ3) and K+ →π0 e+ ν (Ke3) decays using the E246 detector system. The Kμ3 and Ke3 data were taken in 2 days as special runs of E246. We continue to collect data in 40 days for the spectroscopic studies of decay channels with relatively small branching ratio (Br=　 ) such as K+ →π+ π0γ (Kπ2γ), K+ → π0 π0 e+ ν (Ke4), and so on (E470). The E470 data were recorded by well-understood E246 detector system with reasonable up-grading.
In this poster, we would like to show the results of the Kπ2γ and Ke4 analyses.

3. 3. Direct photon emission in K+ →π+π0γ decay
2 processes in K+ →π+π0γ decay　(Kπ2γ) γ γ IB DE
Internal Bremsstrahlung (IB)
Since the Kπ2 decay is hindered due to the ΔI=1/2 rule, the IB contribution to the Kπ2γ decay is also suppressed.
2. Direct Emission (DE)
The direct γ emission in Kπ2γis sensitive to important aspects of the low energy hadronic interactions of mesons. The DE component consists of magnetic(M1) and electric(E1) transitions, which can be separated by measuring interference pattern with IB.
　　Purpose
I.F. average
In-flight exp. average
(1.8 ±0.4)　x 10-5
’00 BNL
(0.47±0.1) x 10-5
No Interference Term was observed
→ Pure M1 process
i.e.
Measurement of DE branching ratio and
DE-IB interference pattern

4. 4. Experimental setup (End view)
Stopped K+
Large solid angle for γ detection (75% of 4π）
High momentum resolution
for charged particle detection (3% at 205 MeV/c)
　Rotational symmetry of the 12 identical gaps
Superconducting toroidal magnet

5. 5. Experimental setup (Side view)
Pb-plastic γ veto counter
newly installed in E470 exp.
Particle identification
Time of Flight
Momentum determination
Toroidal spectrometer
K+ Identification
Cherenkov counter
γ detection
CsI(Tl) calorimeter
768 segmentation
P ＝660 MeV/c
Active K+ stopper
256 segmentation
Because,
Spectra distortions due to detector misalignment are cancelled, and kinematic resolution in the flame is better for stopped kaons.
Systematic errors are greatly suppressed.

6. 6. Experimental setup (Photos)aa

7. 7. Analysis of K+ →π+π0γ decay
We observed ～4k Kπ2γ　events by extending the Tπ region (Tπ＞35 MeV) below the Kπ3　upper threshold (Tmax＝55 MeV), where the DE component should be significantly enhanced.
The experimental distribution ρ(θπγ,θπγ,Eγ） was fitted to a simulation spectrum of IB[1+α(DE/IB)+β(INT/IB)] with α and β being free parameters. ＋
compare
ρExp (θπγ,θπγ,Eγ） 　　　　　　ρMC (θπγ,θπγ,Eγ） ＋ ＋
Red. χ2＝1.27
(α,β) fit
α＝[ ] x 10－2
β＝[－ ] x 10－2
　　　　　　　　
－0.38
－0.83

8. 8. Branching ratio of K+ →π+π0γ decay
M.Aliev et al.
Phys. Lett. B554,7 (2003)
Results
Exp＝IB [1+ α(DE/IB)+ β(INT/IB)]
（α,β) fit　 α＝[　　 ]x 10－2
β＝[－ ]x 10－2
β＝ α＝[0.76±0.31(stat.)±0.23(syst.)] x 10－2
－0.38
－0.83
Following the analysis procedure of the previous experiments, we assumed β＝0 and determined the partial branching ratio in the region of 55<Tπ<90 MeV as,
BR(DE) ＝[ 0.32±0.13(stat.)±0.10(syst) ] x 10－5
by normalizing it to the theoretical value of the IB branching ratio.
Conclusion
Our branching ratio is consistent with the previous stopped K+ measurement.
This work
DE-IB interference term is not observed.

9. 9. Measurement of K+ →π０π０ e+νdecay (Ke400）
Physics motivation
ππ scattering information can be extracted by analyzing ππ spectra of Ke4 decays.
Ke400 decays are clean sources of π-π　pairs at low energy from which one can deduce the s-wave zero-isospin scattering length (a00, L=0, I=0) for model of hadron dynamics.
Previous a00 [1/mπ] studies
K+ →π＋π－ e+ν　decay (Ke4+－）
a00=0.216±0.013±0.005
Analysis is very complicated. The Ke400 can offer complimentary information for the a00 value.　　
πN→ππN
a00=0.204±0.014±0.008
Analysis is very difficult, because results strongly depend on models.
life time measurement of ππ atom （Dirac）
goal: 5% error in a00
PRL 87, (2001)
PRC58, 3431(1998)

10. 10. Principle of a00 determination
Characteristics of Ke400
Because of symmetry arguments, the kinematices of Ke400 can be described by only one form factor. On the other hand, Ke4＋－ needs 3 form factors.
only 1 form factor, simple!
Principle of a00 determination
N.Cabibbo et al.
P.R　137, B438(1965)
Cabibbo proposed the　Ke4 analysis procedure which treats the Ke400 form factor is identical with the ππ scattering amplitude. The q dependence of the phase shift δ(q) is given by the Chew-Mandelstam effective range formula.
Ke4 hadron current
　ππ scattering
F∝T00

11. 11. ππ scattering length and Ke4 branching ratio
Previous Ke400 Experiments
SJNP 44,68 (1986)
SJNP 48, 1032(1988)
Total 37 events have been observed using in-flight K+ technique. The branching ratio was determined by assuming flat distribution over whole phase space.
Bｒ(Ke400) = [2.0±0.5 ] x 10－5
Results
S.Shimizu et al.
PRD
We observed 218 Ke4 events. The experimental distribution ρ(θππ, q2） was fitted to the simulation spectrum with a00 being a free parameter.
Red. χ2＝　0.91
a00 = 0.45±0.43 [1/mπ]
Bｒ(Ke400) = [2.29±0.17(stat)±0.29(syst) ] x 10－5
While the large error precludes a meaningful comparison with results from other channels, the feasibility of determining the parameter of significant importance with much more statistics is assured.

12. 12. Summary
Spectroscopic studies for Kμ3, Ke3, Kπ2γ, and Ke4 decays have been successfully performed using a stopped K+ beam in conjunction with a superconducting toroidal spectrometer at KEK. Due to higher kinematical resolution and rotational symmetry of the experimental apparatus, many systematic errors are drastically reduced. The results of the KEK E470 experiment are summarized as follows.
K+ →π0 e+ ν
Exotic scalar and tensor couplings were not found, which is consistent with SM and inconsistent with the previous Ke3 experiment.
K+ →π0 μ+ ν
λ0 was obtained by measuring the Γ(Kμ3)/Γ(Ke3) ratio. The result is consistent with a ChPT prediction.
K+ →π+ π0 γ
Branching ratio of Direct photon emission was consistent with the previous stopped K+ experiment. DE-IB interference term was not found.
K+ →π0 π0 e+ ν
We established the Ke4 decay can be used to determine the π-π scattering length.
Future plan at J-PARC
K+ beam with high intensity and good quality enable us to perform spectroscopy of various K+ decays with high accuracy. We are preparing interesting experiments for the next generation.