1. 　　　　　Possibility of precise
　　　　　　　measurements
of muonium HFS at J-PARC MUSE
K.Shimomura (KEK)

2. First reported at 1960, 50 years old this year!
持出厳禁
Ｍｕｏｎｉｕｍ
Ｈｙｄｒｏｇｅｎ
Ｍｕｏｎｉｕｍ
Ｐｏｓｉｔｉｖｅ　Ｍｕｏｎ
Proton
Electron
Electron
First reported at 1960, 50 years old this year!

3. Muonium Energy Level Fine Structure explained by Dirac
Classic Lamb Shift
QED
Tomonaga, Shwinger,
Feynman
Not included QED weak hadronic correction

4. Muonium Pure leptonic bound system, free from finite size effect.
Good example for testing QED,
HFS,1s-2s, Lamb shift
Muonium ground state hyperfine interval measurement is related to
Determination of fine structure constant a
Test of CPT and Lorentz Invariance
related muon g-2 experiment

5. QED Consistency : Fine structure a

6. Test of CPT and Lorentz Invariance (V. W. Hughs et al. , Phys. Rev
Test of CPT and Lorentz Invariance (V. W. Hughs et al., Phys. Rev. Lett. 87, (2001).
Effective Lagragean predicts sidereal time change of muonium frequency.

7. Why Muonium HFS measurement is so important？
g-2 E821(BNL) 0.5ppm 3s deviation
-measurement of the deviation of muon spin direction(ws)
and muon momentum direction(wc) wa∝(g-2)/2=am　
　 -The ratio to proton NMR frequency is important!
　mm/mp accuracy from direct measurement 0.12ppm　
W. Liu et al., Phys. Rev. Lett. 82, 711 (1999). q
am an independent precise muon mass measurement is required ⇒
From g-2 strage ring
From Muonium HFS

8. mm/me (or mm/mp) accuracy

9. Relationship of muon percise measuremnet by K.Jungmannμ
g-2
→ hadronic contributions
→ weak contributions
→ New Physics
μμ, α, gμ
QED mμ
QED
2 ・ mμ ・ c
・ σ →
μμ = gμ ・
e ・ h -
μ+ e-
ΔνHFS, n=1
→ μμ
→ α
→ QED corrections
→ weak contributions
μ+ e-
Δν1S-2S
→ mμ
→ QED corrections mμ
QED

10. Muonium Hamiltonian Ｉm muon spin J electron spin
mmB muon Bohr magneton　　 meB electron Bohr magneton
g’m　 gyromagnetic ratio of electron in bound muonim
gJ　 gyromagnetic ratio of muon in bound muonim
Dn ground state muonium hyperfine constant

11. Breit Rabi Diagram m e

12. m+
OFF Resonance
F.G. Mariam et al., Phys. Rev. Lett. 49, 993 (1982).

13. m
ON Resonance
F.G. Mariam et al., Phys. Rev. Lett. 49, 993 (1982).

14. Los Alamos experimental set up

15. W. Liu et al., Phys. Rev. Lett. 82, 711 (1999).

16. Only TMmn0 modes have no z axis dependence for cylindrical or rectangular cavity.
TM110 for n12
=c2*((j11/p*R)2+(0/h)2)1/2=1897.5MHz
TM210 for n34
=c/2*((j21/p*R)2+(0/h)2)1/2=2565.8MHz
j11=3.832,j21=5.136　R=9.6cm

17. Old Muonium Method
Delay time gate shows
more sharp resonance !

18. Results of Los Alamos Experiment
n12= (35)Hz (18ppb), n34= (43)Hz (17ppb)
Dn= (53)Hz (12ppb), mm/mp= (39) (120ppb)
Combine the pervious results
Dn= (51)Hz (12ppb), mm/mp= (37) (120ppb)
(93% Error comes from statistical error)
Muon mass determination
Where, gm=2(1+am) am= (8.5) (gm error 4ppb)
　　　　meB/mp= (15) (1ppb)
mm/me= (24) (120ppb)

19. Sources of uncertainty at Los Alamos Experiment

21. Statics at Los Alamos Experiment
Beam intensity　 a few ×　107/s
Beam structure　Quasi DC
4ms　ON 10ms OFF
Therefore actual beam intensity 107/s
1 run 10s×120 step
Total　1270 run
（magnetic field scan 200 run, Micro wave scan　1070 run）
Total Muon 　 1013

22. How to improve the accuracy of mm/mp?
Comparison between theoretical and experimental value of Dn
where,　recoil term 800kHz(120ppm) and so on are included.
R∞＝ (91)m-1(0.09ppt)　
　　　　　　　　（Ｃｓ　atomic beam interferometory）
a-1= (52) (3.8ppb)
　　　　　　　　（from electron g-2）
mm/me= (55) (27ppb), mm/mp= (94) (30ppb)
This value is used for the determination of g-2.

23. Summary of Los Alamos Experiment
　　　　Dn= (51)Hz (12ppb), 　　mm/mp= (37) (120ppb)　　
　・old muonium method
　←Pulsed muon beam is ideal !
　・Total muon statiscal error is dominant（93%）
　→ If we will get100 times muon, one order improvement is possible !
　・Muonium is formed at Kr gas
　→Intense low energy (＜4MeV) beam is requiered !
→only

24. Status of J-PARC MUSE @MLF Pulsed proton beam3GeV,333mA,1MW 25Hz
持出厳禁
ミュオン施設
Status of J-PARC Pulsed proton beam3GeV,333mA,1MW 25Hz
2cm carbon graphite target
SuperOmega
Proton
Energy
(ＧeV)
Beam
Intensity
(mA)
Structure
Muon Intensity
m+ / s
KEK-MSL
0.5 5
Pulsed
2.5 x 104
RAL
0.8
200
1.5 x 106
PSI
3000 DC
~5×108
J-PARC(D) 3
333
1.5 x 107
SuperOmega
4 x 108
Current Beam Intensity（４MeVsurface）
World strongest pulsed muon !

25. Acceptance estimation at D2 by G4Beamline
G4Beamline model of D2 beam line
28 MeV/c μ
Acceptance for Injection Part:40 msr
Beam Loss at Q-triplet

26. Improvement for D line extraction
About 50% Loss due to small Q (20cm).
→We fabricated new two quadrupole magnets, and will install at this summer. ⇒
Small Ｑ

27. The Super Omega Muon Beamline
Build the highest intensity pulsed muon beamline in the world
Capture both cloud - and surface +
400mSr (J-PARC SC BL: ~40 mSr)
Consists of three sections:
Normal conducting capture solenoid (installed!)
Superconducting transport solenoid (Final design stage)
Axial focusing magnet
(Design stage)
Surface m ×108/s
Design work Y.Ikedo, K.Nakahara et al.
Collaborated with J-PARC
cryogenic section

28. Possible Setup for Muonium HFS measurement J-PARC MUSE
Capture Solenoid
～ 0.3T　400mSr　 １ｍ
Axial focusing coils
Beam focus
　Superconducting
Curved Solenoid
～２Ｔ　beam transport efficiently　　
　 Reduce B.G.(n,g)
　 P/N Muon selection by Dipoles
Muonium HFS Detector Solenoid
～1.7Ｔ　ppm accuracy　　
　 Highky segmented detctors
Micro Wave Kr

29. Expectes Statics at J-PARC MUSE
Beam Omega　 4 ×108/s
Beam structure　Pulsed
Total　Beam Time 100 days
Total Muon 　 3.4　×　1015
300 times statics !
This is ideal !
Beam
0.9×107/s　＠0.3ＭＷ(next few years)
3.0×107/s　＠１ＭＷ(goal)
50 days run makes 15 times higher statics.

30. Issues Magnetic Field 1.7T? Higher Field helps the accuracy of mm/mp.
持出厳禁
Issues　
Magnetic Field
1.7T?
　　Higher Field helps the accuracy of mm/mp.
However, the decay positron orbit is confined.
⇒ Need optimization.
　Required Uniform Region
1ppm accuracy 20ｃｍ diamater,20ｃｍ length
Stability　10-7~10-8/h
Consider about muon stopping region and
cavity (shape,size) 　 Detector
Scintillating fiber? ＧEM?
Kr Pressure Shift
Mu in vacuum (from SiO2)

31. Summary Determination of fine structure constant a
Muonium ground state hyperfine interval measurement is related to
Determination of fine structure constant a
Test of CPT and Lorentz Invariance
Also important for precise determination of mm/mp
New generation of Muonium HFS measurements should be started at J-PARC MUSE as soon as possible !

33. mm/mp Direct Measuremnet
K.M.Crowe et al., Phys.Rev.D5,2145 (1972)
mm/mp= (82) (2600ppb)
E.Klempt et al., Phys.Rev.D25,652 (1982)
Liq.Br中でのmSR
mm/mp= (17) (530ppb)
Uncertainty of magneti field（ppm)
Stroboscopic measurement