427

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First Observation of Positronium Hyperfine Splitting Transition - Particle Physics at a

Frequency Frontier -

Akira Miyazaki Department of Physics, Graduate School of Science

and International Center for Elementary Particle Physics (ICEPP),

The University of Tokyo, 7-3-1 Hongo, Bunkyo-kv., Tokyo, 133-0033, Japan

miyazaki@icepp.s.u-tokyo.ac.jp

Abstract

Positronium is an ideal system for the research of QED in a bound state. The hyperfine splitting of positronium (Ps-HFS: about 203 GHz) is a good tool to test QED, and is also sensitive to new physics beyond the Standard Model. Previous experimental results of Ps-HFS show 3.9 u (15 ppm) discrepancy from the QED prediction up to 0 (a3 lnl/a) . A first direct Ps-HFS measurement without one of the systematic uncertainties is proposed in this paper. This measurement needs progress of technology in sub-THz region. The technology for sub-THz and THz is still under development, which is called terahertz gap. Technological innovation can create a new probe for the totally unexpected. By developing three key de­vices in sub-THz region, the direct transition between ortho-positronium and para-positronium was observed for the first time with 5u. The current status and future prospect are explained.

1 Introduction

Positronium (Ps), the electron-positron bound state, is a purely leptonic system. Since it is free from any hadronic interactions, positronium is a good target to precisely study Quantum Electrodynamics (QED) in a bound state system. The energy difference between ortho-positronium (o-Ps, 35 1 state) and para­positronium (p-Ps, 1 So state) is called hyperfine splitting of positronium (Ps­HFS). The Ps-HFS value is approximately 203 GHz (0.84 meV) .

Measurements of the Ps-HFS have been performed in the 70's and 80's [1]!2]. The results were consistent with each other, and a combined accuracy of 3.3 ppm was obtained. They were consistent with a 0 ( a 2 ) prediction of the QED calcu­lation available at that time. In 2000, the corrections up to 0 (a3 1n 1/a) have been calculated using NonRelativistic QED (NRQED), which is given by

.C.ifFs = .C.ifFso {1- ~ (32 + ~ ln 2) + ~a2 ln ~ 1r 21 7 14 a

+ (;) 2 [133:: _ ~~~~ 7r2 + ( ~ + 282417r2 ) ln 2 _ 155: ( (3)]

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---ln2 -+C-ln-+D - + ... , 3 a 3 1 a 3 1 ( a ) 3 }

2n a 7r a 7r (1)

where the coefficient C is calculated as C = ~; - 678 ln 2 "' -2.6001, and D is estimated as an error of the current calulation according to hyperfine splitting of muonium. The new prediction is Ll~FS =203.391 69(41) GHz [3]. This cal­culated value differs from the measured value of D.~$8 =203.388 65(67) GHz by 3.9a as shown in Fig. 1. This discrepancy may be due to common system­atic uncertainties in the previous measurements or to new physics beyond the Standard Model as show in Fig. 2 or Fig. 3.

Experimental Theory average (Kniehl et al., 2000)

Mills et al. 19

Ritter et al.. 1984

203.385 203.387 203.389 203.393 203.395

Figure 2: fermion X.

HFS [GHz]

Figure 1: The discrepancy of Ps-HFS value.

.. >.- ___ .:._·---<·-..

Contribution of unknown Figure 3: Contribution of unknown pseudo-scalar ao.

In all previous measurements, the Ps-HFS value was not directly measured, since 203 GHz was too high to be produced and controlled. Zeeman splitting of o-Ps has been measured instead. A static magnetic field makes Zeeman mixing between mz = 0 spin state of o-Ps and p-Ps. As a result, the energy level of mz = 0 state of o-Ps becomes higher than mz = ±1 states. This Zeeman splitting, which is approximately proportional to Ps-HFS, is a few GHz under about 1 Tesla magnetic field. A static magnetic field is applied in a RF-cavity where positronium is produced. Zeeman transition from o-Ps of mz = ±1 to o­Ps of mz = 0 has been observed. Therefore, the non-uniformity of the magnetic field might be a common systematic uncertainty in all previous experiments.

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o-Ps I= 142ns, 3y decay

Stimulated Transition (Ml)

p-Ps 't= 0.125ns, 2y decay

Figure 4: A schematic of the direct transition.

198 200 202 204 206 208 210

Frequency (GHz)

. Figure 6: The calculated timing spec-Figure 5: The calculated resonance tra of two 1-ray annihilation. The red curve of two 1-ray annihilation with- line is background p-Ps contribution out any timing selection. The power and the blue one is transited p-Ps. The of 203 GHz is 10 kW. power of 203 GHz is 10 kW.

We are planning to measure directly the Ps-HFS transition without any magnetic fields. Figure 4 shows a schematic of the direct transition. A very strong RF-field of 203 GHz gives rise to a transition from o-Ps to p-Ps. Para­positronium decays into two 1-rays promptly, whereas o-Ps decays into three 1-rays. A signal of two 1-rays indicates the transition. Figure 5 shows the expected resonance of the probability of two 1-decay when the input frequency is swept. Because of spin statistics, 25% of initial positronium is p-Ps, which becomes background. The transition events can be distinguished from such background events by selecting delayed events as shown in Fig. 6.

The direct transition from o-Ps to p-Ps has a very small spontaneous emission rate of 3.37 X w-s s-1 [4] . Because, this transition is Ml-transition, and the Ps­HFS is extremely large. Therefore, a powerful electromagnetic wave of 203 GHz is essential so as to stimulate the direct transition.

The frequency of 203 GHz is just intermediate between optical light and radiowave. There were no high power light sources for spectroscopy in sub-THz region. Our first aim was to observe the direct transition from o-Ps to p-Ps. We developed the following three new sub-THz devices.

1. A sub-THz to THz light source called gyrotron,

2. An efficient transportation system of gaussian converter,

3. A Fabry-Perot cavity with high-finesse.

These are explained in the next section.

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2 Optical system

2.1 Gyrotron

Figure 7: A photograph of gyrotron.

Figure 8: Transportation system.

A gyrotron[5] is a novel high power RF -source for sub-THz to THz frequency region. It has been developed in the field of nuclear fusion, and is dedicated to spectroscopic measurement this time. It contains an electron gun, super­conducting magnet, and open RF-cavity. An electron emitted from the gun is accelerated and gyrating inside the cavity. The relativistic cyclotron motion of the electrons coherently stimulates the strong RF-field inside the cavity. The frequency of RF is monochromatic, and is approximately the same as that of the cyclotron motion. This phenomenon is called cyclotron-maser resonance.

We developed a gyrotron (Fig. 7) operated at f = 203 GHz with B = 7.34 Tesla, -y ~ 1.04. The stable power of 250 W is obtained at the output window of the gyrotron. The frequency spread is expected to be less than 1 MHz. The resonant mode is TE031-mode. The transverse mode of in an output section of the gyrotron is azimuthally polarized TE03-mode. The mode inside a Fabry-Perot cavity is, unfortunately, a linearly polarized gaussian mode. The original gyrotron output cannot couple with a Fabry-Perot cavity. That's why a mode conversion is essential to use gyrotron power efficiently.

2.2 Gaussian Converter

The transportation system is composed of three parabolic mirrors called MO, Ml and M2 as shown in Fig. 8. The first parabolic mirror MO converts polarization from azimuthal to linear [6]. Ml and M2 change the shape of power distribution from hi-gaussian to gaussian. Then the plain mirror M3 reflects radiation and introduces it into the Fabry-Perot cavity. The mirror M3 is made of h!j.lf mirror so as to sample radiation from the gyrotron and reflected radiat ion from the Fabry-Perot cavity. This transportation system is the key device which connects microwave t echnology inside waveguides and optical technology in free space.

The power profile is successfully converted into gaussian mode. The trans­formation efficiency is 30%, since the output mode of TE03-mode is strongly

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disturbed by an output taper, a large hole connected to a vacuum pump, and RF-window of gyrotron. The efficiency will become over 80% by optimizing the mode purity in the future.

2.3 Fabry-Perot cavity

Pyroelectric detector is used to monitor transmission power of the cavity ---·

Au mesh mirror R = 99.3%, T = 0.5%

· (width=2001Jm, gap=1501Jm)

Figure 9: A photograph of the test setup of Fabry-Perot cavity.

0 510 515 520 525 530 535

mirror position h•m]

:::> 0.2~

0.18 Q; ~

0.16 ~

0.14 al 0.12 ~

Q)

0.1 a:

0.08 540

Figure 10: A photograph of the observed resonance of the Fabry-Perot cavity.

Photons produced at the gyrotron are transported and accumulated in a Fabry-Perot cavity. The cavity consists of two opposing mirrors as shown in Fig. 9. A golden mesh mirror evaporated on a quartz substrate is used for the input side of the cavity in order to smoothly introduce photons from the gyrotron. A copper concave mirror is used on the other side to transversely stabilize the resonance. The length of the cavity is controlled with a piezo stage under the concave mirror. One can sweep the cavity length around a couple of wavelengths (1.47 mm for 203 GHz), and precisely control it within 0(100) nm as well, since the piezo stage can switch the operating mode between rough­motion and precise-motion.

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Transmitted power is measured through a small hole on the concave mirror. Reflected power is monitored from the outside of the cavity, just behind the half mirror M3 in the transportation system. A pyroelectric detector is used as a power monitor. Figure 10 shows a resonance observed in our cavity. A trans­mitted power increases at the resonance, whereas a reflected power decreases. The performance of the cavity can be estimated by two parameters: finesse F and input coupling C.

Finesse F is a parameter of resonance-sharpness, which is given by

A F= 2r' (2)

where r is the width of the resonance, and A = 1.4 7 mm is wavelegth of 203 GHz. r is measured as l.1J.tm, which results in F = 650.

Input coupling C is given by

C = 1 _ Vpeak

Vbaseline (3)

Vpeak is a voltage at peak decreasing from Vbaseline which is the voltage of the baseline of the reflected power. An input coupling of 67% is achieved.

The gain G of the cavity can be approximately calculated with these two parameters:

F G=C-rv140 .

1f (4)

The accumulated power and its stability are shown in Fig. 11. The output power of 250 W from the gyrotron reduces to 70 W as propagating through transportation system. The input power to the cavity is stabilized by a feedback control which adjusts heater temperature of an electron gun in the gyrotron. The input power of 70 W times gain G is the accumulated power in the cavity, which is about 10 kW. The achieved power is stabilized by a feedback control of cavity length.

235 12 230~

1 ~10 -

225 ,.,

~ ~ 220 §: Q; 8 Q; 215~ ~ ~

210 ~ ~6~ ,., - 205 ~ - ::; ·~ 4~ 200 Q; l) 195-m

2 190 J:

0 185

Elapsed Time [hour]

Figure 11: Accumulated power and its stability.

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3 Positronium assembly and [-ray detectors

I signal"' two back-to-back 511keV y rays with long lifetime (T = 142ns) i 203GHz Gaussian Beam 22Na W source (lMBq)

laBr 3(Ce) crystal scintillator -energy resolution FWHM 4%@SllkeV -time constant 16ns -time resolution 200ps (FWHM)@ SllkeV

Form Ps by stopping e• in gas (N2 :i-C4H10=0.9atm:O.latm)

Figure 12: Schematic view of positronium assembly and 1-ray detectors.

Figure 13: A photograph of the assembly.

Figure 12 and Fig. 13 show a schematic view and a photograph of the positro­nium assembly and signal detection system, respectively. Gyrotron power is introduced to the cavity via the mesh mirror, and is accumulated inside the Fabry-Perot cavity. This cavity is placed inside a gas chamber filled with a gas mixture of 0.9 atm nitrogen and 0.1 atm isobutane. The positron is emitted from a 22Na f3+ -source, which is located 20 mm above the cavity. In order to generate start timing, the emitted positrons pass through a plastic scintillator, with thickness of 100 J.Lm . A lead collimator is placed under the plastic scintil­lator so as to select the positrons which go into the cavity. It also works as a shield to protect LaBr3 (Ce) scintillators from pileup 1-rays.

A positron forms a positronium with an electron in the gas molecule. Para­positronium annihilates into two 1-rays of 511 keY immediately, whereas o-Ps

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remains with lifetime of 142 ns to decay into three 1-rays, whose energy spectra are continuous and less than 511 ke V. A signal of the transition from o-Ps to p-Ps under 203 GHz is a delayed-two-1-ray event. Four LaBr3 crystal scintillators, which have good energy resolution of 4%@511 keV (FWHM), surround the chamber to detect 1-rays. Two 1-decay can be easily separated from three ,_ decay with both the energy information and back-to-hack topology. The LaBr3 scintillators also have good timing resolution of 200 ps@511 keV (FWHM) . Delayed events (i.e. signal of transition) is easily separated from prompt events using delayed coincidence of two signals from LaBr3 and plastic-scintillator.

4 Analysis and Result

Three major selections are applied to improve S/N: (i) Timing selection (ii) Pileup rejection (iii) Energy selection.

( i) Figure 14 shows a typical spectrum of time difference between signals from LaBr3 and plastic-scintillator. A large peak at 0 ns is called prompt annihilation, which contains the events that positronium is not formed or that p-Ps is formed . They are two 1-decay, and become background. An exponential structure from 50 ns to 400 ns is a contribution of o-Ps. Since the direct transition is from o-Ps, the events from 100 ns to 320 ns were selected in order to reject the above background.

(ii) The events from 400 ns to 1200 ns are mainly pileup events of plastic­scintillator signal, which extrapolatively exist under o-Ps events selected by above timing selection. This background is about 100 times lager than the transition signal. Pileup events is significantly reduced by discarding events in which plastic-scintillator signal synchronizes LaBr3 signal within 50 ns. The result of this selection is shown in Fig. 15, where o-Ps events is drastically enhanced.

(iii) The upper side of Fig. 16 shows the energy spectra combined of all LaBr3 detectors. The gyrotron is operated with duty ratio 30% and repetition rate 5 Hz. The events with and without power are normalized by livetime. The lower side of Fig. 16 shows the spectrum subtracted off events from on events. The excess of power-on events around 511 keV indicates the direct transition. In order to distinguish the transited events from non-transited o-Ps events, the events in 511 keV ± 2 a are counted to calculate the transition rate. The detection rate is 3.99 ± 0.71 mHz. The direct transition is firstly observed with significance of Sa-level. Einstein A coefficient (spontaneous emission rate) is estimated to be 3.9 ( + 1.8-1. 7) x w-8 s- 1 , which is consistent with QED calculation of 0 (a) .

The systematic errors are listed in Table 1. It is estimated that the large systematic error of e+ tagging rate is due to photons from black-body radia­tion of the mesh mirror by 10 kW RF-field. Therefore, the plastic scintillator is optically shielded for the next measurement in Sep. 2011. The normaliza­tion problem is due to a trouble of one of the CAMAC modules used for data acquisition, and is solved now.

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Signal region Prompt annihilation

106

....,. 105

::> ~

" ::> 104 8

103

0

+-+ Timing Window

.....__

200 400 600 BOO 1 000 time[ns]

-

r

"' "' !B "' " 0 0

.. . \sefqr~r~j~ctioq ... ••••.•••• :;: on!vili!evb ·

reduces 1/20

z Afterrej~ction·

time [ns]

Figure 14: Time spectrum of Positron- Figure 15: Pileup rejection of plastic­ium decay and timing window. scintillator signal. Ortho-Ps events are

enhanced after this selection(red his­togram)

Table 1: The summary of systematic errors

Source Systematic error LaBra energy resolution Zero point of the timing spectra e+ tagging rate normalization Quadrature sum

0 ' 2i Livetime: 14 days

With power 0· . Without power....---

! 007!

... ~·-- ·- --- - -- ~--- - ---·

3.0% 0.3% 7.7% 3.1% 8.8%

~~1)--~,.~,---~M,--,,$=-~~~-..,.~o--"•oo~-..,~~-o~~,--~,~~~~· l!tbt:&nno•gyjl.oV)

~ - ·-·~ ··, :::::::·#:~~: . ·--· ' · ~ ~ ~

;. ::.;:l. , ')(''

; ~'"' . . .

o,;~o) l!Oi Iii.

Figure 16: (Upper)Energy spectrum after t iming selection and pileup rejec­tion. (Lower) A spectrum subtracted off events from on events.

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5 Conclusion and future prospect

There is a large discrepancy between a theory and experiments in the Ps-HFS value. We suspect that non-uniformity of a static magnetic field is one of the common systematic uncertainties in previous experiments. The direct measure­ment without any magnetic fields is proposed, and a gyrotron, mode converter, and Fabry-Perot cavity have been developed. We took data for two weeks at fixed frequency of 203 GHz. The direct transition from o-Ps to p-Ps was for the first time observed with 5o--level.

In order to measure the whole resonance of the direct transition, the input frequency must be swept within a few GHz range around 203.4 GHz, whereas the gyrotron used in this experiment is monochromatic (called gyromonotron). Tunability is an extremely challenging issue in sub-THz region. A new device called reflective gyro-BWO was proposed recently [7]. In terms of the dispersion relation, the resonance occurs at a cross point of cyclotron motion of electrons and resonant frequency of a cavity (R(z) is radius, and i!.nn = 7.016) as shown in Fig. 17. The output frequency is tuned by changing the magnetic field . We have made the prototype of gyro-BWO as shown in Fig. 18, and testing the basic performance in Sep. 2011.

These experiments are performed in collaboration with T. Yamazaki, T . Sue­hara, T. Namba, S. Asai, T. Kobayashi, H. Saito, T . Idehara, I. Ogawa and S. Sabchevski.

Figure 17: Backward wave interaction.

References

Figure 18: A photograph of the reflective gyro-BWO.

[1] A. P. Mills, Jr. et al. Phys. Rev. Let t. 34 (1975) 246; A. P. Mills, Jr. et al. Phys. Rev. A 27 (1983) 262.

[2] M. W. Ritter , et al. Phys. Rev. A 30 (1984) 1331.

[3] B. A. Kniehl and A. A. Penin, Phys. Rev. Lett. 85 (2000) 5094.

[4] V. V. Burdyuzha,et al. Astro. Lett.25 (1999) 3.

[5] T . Idehara, et al. IEEE Trans. Plasma Sci. 27 (1999) 340.

[6] I. Ogawa, et al. Int . J. Elec. 83 (1997) 5.

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[7] N. C. Chen, et al. Appl. Phys. Lett. 96 (2010) 161501.

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