Precision measurement of the muon mass by 1S-2S laser spectroscopy of muonium

Takahiro Hiraki (on behalf of the collaboration)

MAC/MuSAC 2019

1

Collaboration list- T. Hiraki, H. Hara, Y. Imai, T. Masuda, Y. Miyamoto,

S. Uetake (PI), S. Yamamoto, K. Yoshimura

- Y. Ikedo, N. Kawamura, A. Koda, T. Mibe, Y. Miyake, Y. Oishi,M. Otani, S. Patrick, K. Shimomura, K. Suzuki, T. Yamazaki, M. Yoshida

- C. Zhang, Y. Mao

- K. Ishida

- S. Kamal

2

Okayama university

KEK

Peking university

Riken

University of British Columbia

introduction 3

12𝑆𝑆1/2

22𝑆𝑆1/2

𝐹𝐹 = 1

𝐹𝐹 = 0

𝐹𝐹 = 0𝐹𝐹 = 1

• Muonium (Mu: μ+e-): pure leptonic two-body bound state- possible to precisely calculate transition frequencies

between states such as Mu 1S-2S and hyperfine structure (HFS)- Mu transition frequencies can be written as:

• Mu transition frequencies depends on precisely-measuredfundamental parameters and muon mass (𝑚𝑚𝜇𝜇)

- Current muon mass precision comes from HFS measurement

introduction 4

• goal of this project：measure Mu 1S-2S transition frequency with a precision of 100 kHz

- ~100 improvement from the previous experiment ➡ muon mass precision: 120 ppb→~10 ppb- contribution to CODATA (and PDG) from Japan

• Current theoretical precision of HFS is dominated by muon mass precision

• If this precision is achieved by Mu 1S-2S measurement,theoretical precision of Mu HFS will be 515 Hz → ~40 Hz

- Hadronic vacuum polarization (233 Hz), electroweak effect (65 Hz) can be confirmed with measurement of HFS (by MuSEUM experiment)

M. I. Eides, Phys. Lett. B 795, 113 (2019)

history of muonium 1S-2Syear Japan abroad1987 First laser Mu 1S-2S exp.

S. Chu, A.P. Mills, Jr. A.G. Yodh,K. Nagamine, Y. Miyake, T. Kuga

1999 Mu 1S-2S exp. at RAL- Current best precision

2009 J-PARC start operation- high intensity muon

source available

before 2017 no proposal of Mu 1S-2Sexperiment

new Mu1S-2S project started at PSI

late 2018 this project started2019 budget proposal approved

(科研費基盤S, S. Uetake (PI), K. Shimomura, M. Yoshida,T. Yamazaki, M. Yoshimura)

5

preparation

past Mu 1S-2S experiment 6

V. Meyer et al., Phys. Rev. Lett. 84, 1136 (2000)

• usage of pulse laser causes broad spectra (limit precision)- narrow-linewidth CW laser will greatly improve precision- lower excitation rate is covered by using MLF intense μ beam

244 nm

244 nm

• Current best result was obtained in RAL ~20 years ago

Mu 1S, F=1

Mu 2S, F=1 detuning

Δν1S2S = 2455528941.0 (9.8) MHz

μ++e-detection

to reduce Doppler shift 7

1st order 2nd order

• 2nd order Doppler shift can not be canceled even in the case of counter-propagating excitation

- largest systematic source in our experiment→ It is important to use slow muonium

aerogel target • room-temperature muonium available• We will use laser-ablated aerogel target- Studies have been done by J-PARC μ g-2 group

G. A. Beer et al., PTEP 2014 091C01

𝜇𝜇+

• 1st order Doppler shift can be completely cancelled out by counter-propagating excitation with an optical cavity

mirror mirror

experimental principle 8

• Mu 1S → 2S (CW laser) → μ+ (high-power pulsed laser)• Ionized μ+ guided by slow muon beam line (SMBL)- used in past test experiments in MLF MUSE- now SMBL is at KEK and used for laser ionization test of H atom

244 nmCW laser

cavity

electrostaticmirror

Bendingmagnet

MCPscintillatorlensSOA lens

355 nmpulse laser

schedule 9

Another Mu 1S-2S experiment in PSI ・Different experimental principle- DC μ beam, 2S Mu detection scheme- 2-Phase experiment

P. Crivelli

FY 2019 FY 2020 FY 2021 FY 2022-Hydrogen gas exp. Phase-0 exp.

Phase-1 exp.target: 1 MHz

Phase-2 exp.target: 100 kHz

application tohigh intensity ultra slow muon

Mu distribution study

high-power CW laser development

244 nm pulse laserconstruction

244 nm CW laserconstruction

S2 construction

high-power pulse laser development

MLF S1-type proposal was submitted last year- technical review in 2019 Dec., PAC in 2020 Jan.

experimental area 10

• S2 area (under construction, plan to start in 2020 Nov.)• After initial commissioning studies, Phase-0 exp. will start

J-PARC MLF MUSE

laser system 11

Phase-0

976 nmECDL

Ti:Scavity

SHG CLBO

TaperedAmp.

488 nm 244 nm532 nmNd:YAG

CW→pulse

• backup: dye laser (already available) etc.

Ti:Samp

SHG LBO

25 Hz

976 nm

• pulse laser system- linewidth is broad and this laser cannot be used for

precise measurement of Mu 1S-2S transition- excitation probability is much higher than CW laser and

muonium 1S-2S ionization signal can be quickly confirmed

Setup (plan)

CW

laser system 12

976 nmECDL(+TA)

SHG cavityLBO crystal

SHG cavityCLBO crystal

Mu chambercavity

Yb-dopedfiber amplifier 488 nm 244 nm

frequency comb

Phase-1, Phase-2• continuous-wave (CW) laser system - Compared to usual spectroscopy experiments,

number of Mu is limited and it is important to construct high-power CW laser cavity

- we plan to construct ~30 W (Phase-2) deep UV cavity• Accuracy of laser frequency is also important, and

optical frequency comb will also be used (~2 kHz precision)Setup (under construction)

expected resonance curve 13

500 kW24 h/point

1 MW96 h/point

Phase-1 Phase-2

• statistic uncertainty: ~600 kHz in Phase-1, ~70 kHz in Phase-2• (2nd-order) Doppler shift: 500-600 kHz- If target temperature is controlled with a precision of 5 K,

Doppler shift uncertainty of ~30 kHz can be achieved

summary• Precision frequency measurement of Mu 1S-2S transition• Significant improvement can be achieved by usinghigh-intensity muon beam at MLF MUSE and recent development of laser techniques

- Phase-1 FY2020-2021, f1S2S precision:1 MHz- Phase-2 FY2022-, f1S2S precision:100 kHz• If ~100 kHz precision is achieved,

muon mass precision is improved from 120 ppb to ~10 ppb

14

Backup

15

theory 16

C. Frugiuele et al., Phys. Rev. D 100, 015010 (2019)

Spin-independent force

electron g-2 +muon g-2

Ps 1S-2S

Mu Lamb shift

Mu 1S-2S(1.4 MHz)

Mu 1S-2S(3 kHz)

Due to new particle mediation, binding potential of muonium is modified

new physics using Mu?• If 𝑚𝑚𝜇𝜇 precision of ~ 10 ppb is achieved by this project,

theoretical precision of Mu HFS can be reducedfrom 515 → ~40 Hz

- better than electroweak effect (65 Hz) and new physicseffect might be observed (with MUSEUM experiment)

• If new physics effect would be observed, this might be related to muon g-2 anomaly.

17

M. I. Eides, Phys. Lett. B 795, 113 (2019)

updated analysis of RAL 18

V. Meyer et al., Phys. Rev. Lett. 84, 1136 (2000)

• In the RAL experiment, laser frequency was calibrated by usinga hyperfine component of an R-branch line in 127I2

• Later, those lines were re-calibrated by using an optical frequency comb

Δν1S2S = 2455528941.0 (9.1)(3.7) MHzI. Fan et al., Phys. Rev. A 89, 032513 (2014)Δν1S2S = 2455528940.6 (9.1)(3.7) MHz

V. Meyer et al., Phys. Rev. Lett. 84, 1136 (2000)

- uncertainty of this re-calibration (0.6 MHz) is smaller than muonium statistics and residual Doppler effect of RAL exp.

simulation overview1. S2 area beam injection

- beamline simulation by G4 beamline- absolute flux is estimated by S1 data

2. muonium formation in aerogel- based on past studies by muon g-2 group

3. laser simulation- solve optical Bloch simulation- the same method was used in H 1S-2S experiments

4. downstream beam line transportation and detection- muon transport simulation by using geant4- validated by past experiments

• Background rate will be estimated in Phase-0 experiment

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S2 flux estimation 20

SSL1 [mm×mm]

SSL2[mm×mm]

Collimator efficiency muon flux(500 kW)

note

100×40 40×40 In 5.7×10-4 1.9×105/s current S1100×40 40×40 Out 5.9×10-4 1.9×105/s100×40 240×240 Out 7.2×10-3 2.4×106/s use this setting240×240 240×240 Out 1.1×10-3 3.5×106/s

• The SSL1 slit is common for S1 and S2

• beam widthin the S2beamline

• muon absolute flux at S2:estimate based on S1 data

- 1.2-2.4×106/s (500 kW, w/o slit)• beam profile before injection:- σx=33.2 mm, σy=12.7 mm

• muonium diffusion inside aerogelis simulated by a diffusion model

- This model is validated by pastbeam experiments in TRIUMF

- ~2% muon forms muonium and emit from the aerogel target

S2 beamline simulation 21

emit fromaerogel

total

0mm

2468

simulation by Ce(Peking univ.)

P. Bakule et al., Prog. Theor. Exp. Phys. 2013, 103C01 (2013)

Mesh

Mu profile (S2-line) 22

time

XY X YAerogel target: ~ 78 mm Φ

• Muonium emit from aerogel gradually

• Narrow beam in Y direction is preferablebecause the laser passes through Y=0

• calculate excitation and ionization probability using optical-Bloch equations.

laser simulation 23

Mu 1S

Mu 2S

ionized

244 nm

244 nm

μ++e-

⟩|𝑔𝑔

⟩|𝑒𝑒

aerogel

For each particle, track informationbased on muonium diffusioninside the aerogel is used

laser simulation• Settings

24

efficiency table 25

efficiencystopping inside target 0.47muonium formation 0.52emit out of target 0.082muonium angular momentum for excitation 𝐹𝐹 = 1

0.75

laser ionization 2.0×10-8 (Phase-1)1.8×10-7 (Phase-2)

mesh transmission 0.85muon transportation 0.77MCP detection 0.90analysis selection 0.33

lineshape width better precision of center frequency

is achievable by narrower lineshape

possible systematic sources• Laser linewidth- In RAL experiment, pulsed 244 nm laser was used.- inevitable lineshape uncertainty (~1 MHz)- CW laser and optical frequency comb will be used and < 1 kHz possible

• Residual Doppler effect- largest syst. source in RAL experiment - can be removable by using CW optical cavity

26

mirror mirror

lineshape width better precision of center frequency

is achievable by narrower lineshape

possible systematic sources• DC Stark shift: DC electric field shifts Δν1S2S

- “pulsed” DC field necessary• AC Stark shift: laser field also shifts Δν1S2S

- proportional to 244 nm laser intensity- should be estimated by simulation• Laser power stability: monitor laser power• muon lifetime : principle limitation- width: 72.4×2~145 kHz (FWHM)

27

other systematic sources• DC Stark shift: proportional to 𝐸𝐸2- largely reduced by applying DC fieldafter the pulse laser pass through

- shift uncertainty: ~0.05 kHz (Residual electric field: 0.1 V)

• AC Stark shift: proportional to CW laser intensity- monitor laser power during data taking- estimated shift size: ~30 (3) kHz (Phase-2)• laser frequency stability: 2 kHz

• They are smaller than statistic uncertainty and Doppler shift uncertainty

28

Mu ionization comparison 29

Mu 1S

Mu 2S

ionized

244 nm

244 nm

244 nm

μ++e-

Mu 1S

Mu 2P

ionized

122 nm

355 nm

μ++e-

threshold threshold

• There exists ways to generate ultraslow muon by ionizing Mu

• Currently, Lyman α laser (1S-2P excitation) is used in U-line andis planned to use in E34 (muon g-2) experiment

• Very high-power 244 nm pulse laser is an alternative way togenerate high-intensity ultraslow muon

• From simulation, laser ionization rate with 200 mJ 244 nmpulse laser (with a mirror) seems to be slightly larger than that of 5 μJ 122 nm laser (without a mirror)

Mu ionization comparison 30

Parameters 1S-2P (122 nm, 355 nm) 1S-2S (244 nm pulse)laser intensity 5 μJ (122 nm),

300 mJ (355 nm)200 mJ

laser linewidth 100 GHz (122 nm) narrow (FT-limited)laser duration(FWHM)

1 ns (122 nm)5 ns (355 nm)

5 ns

laser spatial width (D4σ)(at beam waist)

20 mm (xy direction)2 mm (z direction)

20 mm (xy direction)2 mm (z direction)

beam injection position z = 4 mm z = 4 mmmirror position not installed x = 100 mmionization probability 0.0056 0.0066

beamline: S2, target: aerogel

aerogelz

y• For 244 nm pulse laser, it is important toput a mirror for increasing ionization rate

- In the counter-propagating excitationDoppler effect is largely reduced

Laser room 31

• Movable by using a crane• container-type simple room (with interlocks)

External cavity diode laser

• ECDL in Littrow config.• Diffracted light whichback to the DL oscillate

• control temperature byPeltier device

• linewidth：~MHz• power：~40 mW

32

laser diode

grating

Piezo actuator

collimator lens

p

n

diode laser (DL)+

-eh

Tapered Amplifier 33

American Journal of Physics 82, 805 (2014)

25 mW ➡~1W

Yb-doped fiber amplifier 34

976 nmECDL

isolatorASE

Wavelength Division Multiplexing (WDM)

915 nmpump

combinerundopedfiber

Yb-doped fiber

combiner

Yb-doped fiber

ASE rejection

amplified976 nm

30 mW

setup (under construction)

• In order to reduce ASE, only 915 nm and 976 nm component are selected outside the fiber and couple them to fibers again

976 nm laser system 35

fiber fusion 36

• edge of fibers are polished• normal fiber and Yb-doped

fiber is connected by using a fiber splicer

after polish connected area

• We found fiber fusion work is difficult due to bad fiber polish, bad fiber connection etc.

LBO cavity 37

LBO crystal

Similar type cavity will be used

244 nm CW laser cavity 38

x

y

5-pass

aerogel• It is known from past laser studies

deep-uv laser easily damage mirrors- mirrors quickly degrades due to

lack of oxygen gas or hydrocarbon contamination

- flow high purity oxygen gasaround at least cavity mirrors

- The beamline is operated in vacuum, separation by windowor differential pumping is necessary.

• multi-pass CW cavity- Increase Mu excitation rate

PSI 39

P. Crivelli

S2 area plan 40

experimental area 41

Laser room will be constructedaround here (common space with E34 (g-2) group?)

Laser

test experiment using H• 1S-2S ionization experiment of hydrogen atom- similar atom system with muonium

42

Mu 1S

Mu 2S

ionized

244 nm

244 nm

244 nm

μ++e-

pulse

pulse

pulse H 1S

H 2S

243 nm

243 nm

243 nm

H++e-

pulse

pulse

pulse

muonium hydrogen atom

• 1S-2S frequency of hydrogen atom is known precisely (~10Hz)and can be used as a frequency standard

• this can also be used as a downstream beamline test

ionized

Hydrogen test＠Okayama 43

Acknowledgement：Kentaro Kawaguchi (Okayama univ.), Kouzo Hakuta (UEC)

discharge ON

• see H+ ionization signal with changing laser frequency

If microwave dischargecontinues successfully,red light (hydrogen Balmer α, 656.5 nm) can be seen.

Hydrogen test@Okayama• preparatory experiment: 1S-2S ionization of H atom

44

Setup

• H atom is generated by the microwave discharge system• 243 nm laser is generated by using a dye laser (SHG) • Quartz (tube) and Al (nozzle) are used in order to reduce

recombination of H atom

energymeter

H2 gas Microwavecavity

Microwave generator

gasbottle

flowmeter

pressuregauge

nozzle

pressuregauge

Quartztube amplifier oscillo

scope

HV

243 nm

Hydrogen test＠Okayama 45

discharge ONdischarge OFF

HV: -50 Vaveraged pulse height (oscilloscope)

stray light background

H 1S

H 2S

243 nm

243 nm

detuning

observed 1S-2S ionization peak

laser power : ~0.5 mJ

test experiment using H

• Microwave cavity generate H atom from H2 gas• Differential pumping enables us to connect H sourceto the target chamber (pressure < 10-4 Pa)

46

pinhall H2

pump(differential pumping)

laser

microwavecavitytarget

chamber

another laser plan• M.Yoshida (KEK) is developing a pulse laser systemwhich can be used as a backup of the ionization laser forthe E34 experiment

• This laser ionize Mu via 1S-2S transition and so can beused as a laser for our experiment（Phase0, Phase1）

47

976 nmCW SOA

488 nm 244 nm

SHG SHG

• Arbitrary temporal shaping of the 976 nm laser pulse isgenerated by using semiconductor optical amplifier (SOA)

- Linewidth is expected to be narrow

Setup multi-passamplifier