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

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!

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

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

QED Consistency : Fine structure a

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, 111804 (2001). Effective Lagragean predicts sidereal time change of muonium frequency.

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

mm/me (or mm/mp) accuracy

Relationship of muon percise measuremnet by K.Jungmann μ 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

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

Breit Rabi Diagram m e

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

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

Los Alamos experimental set up

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

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

Old Muonium Method Delay time gate shows more sharp resonance !

Results of Los Alamos Experiment n12=1897539800(35)Hz (18ppb), n34=2565762965(43)Hz (17ppb) Dn=4463302765(53)Hz (12ppb), mm/mp=3.18334513(39) (120ppb) Combine the pervious results Dn=4463302776(51)Hz (12ppb), mm/mp=3.18334524(37) (120ppb) (93% Error comes from statistical error) Muon mass determination Where, gm=2(1+am) am=0.01165923(8.5) (gm error 4ppb) 　　　　meB/mp=1.521032202(15) (1ppb) mm/me=206.768277(24) (120ppb)

Sources of uncertainty at Los Alamos Experiment

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

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∞＝10973731.568639(91)m-1(0.09ppt)　 　　　　　　　　（Ｃｓ　atomic beam interferometory） a-1=137.03599958(52) (3.8ppb) 　　　　　　　　（from electron g-2） mm/me=206.7682670(55) (27ppb), mm/mp=3.183345396(94) (30ppb) This value is used for the determination of g-2.

Summary of Los Alamos Experiment 　　　　Dn=4463302776(51)Hz (12ppb), 　　mm/mp=3.18334524(37) (120ppb)　　 　・old muonium method 　←Pulsed muon beam is ideal ! 　・Total muon 1013 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 possible @J-PARC/MUSE!!

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 MUSE @MLF 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） 1.8×106/s@120kW World strongest pulsed muon ! （1.5×107/s@1MW）

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

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. ⇒ 3.0×107/s(@1MW) Small Ｑ

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+ 4×108/s Design work Y.Ikedo, K.Nakahara et al. Collaborated with J-PARC cryogenic section

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

Expectes Statics at J-PARC MUSE Beam Intensity @Super Omega　 4 ×108/s Beam structure　Pulsed Total　Beam Time 100 days Total Muon 　 3.4　×　1015 300 times statics ! This is ideal ! Beam Intensity @D2 0.9×107/s　＠0.3ＭＷ(next few years) 3.0×107/s　＠１ＭＷ(goal) 50 days run makes 15 times higher statics.

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)

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 !

mm/mp Direct Measuremnet K.M.Crowe et al., Phys.Rev.D5,2145 (1972) mm/mp=3.1833467(82) (2600ppb) E.Klempt et al., Phys.Rev.D25,652 (1982) Liq.Br中でのmSR mm/mp=3.1833432(17) (530ppb) Uncertainty of magneti field（ppm) Stroboscopic measurement