1. PHySES Positronium Hyperfine Structure of the first Excited State:
Measurement of the 𝑆 1 → 2 1 𝑆 0 transition in vacuum
Michael W. Heiss

2. Motivation: Positronium HFS
Ps is purely leptonic system
Free from
QCD effects
weak force effects
Precision test bench for
bound state QED
Very precise measurements in 1970s and 1980s
Almost 4 sigma discrepancy with most recent QED result
(well, almost)
𝑉𝑒𝑟𝑡𝑒𝑥 ∼ ⋅ ⋅ 𝛼 𝑆 16 𝜋 2 ∼ ⋅
𝑉𝑒𝑟𝑡𝑒𝑥 ∼ ⋅2
𝑉𝑒𝑟𝑡𝑒𝑥 ∼
𝑃𝑟𝑜𝑝𝑎𝑔𝑎𝑡𝑜𝑟∼ 𝑀𝑒 𝑉 2 − 𝑀𝑒 𝑉 2
𝑃𝑟𝑜𝑝𝑎𝑔𝑎𝑡𝑜𝑟∼ 𝑀𝑒 𝑉 2
Source: Ishida et al., New Precision Measurement of Hyperfine Splitting of Positronium. 2014
Michael W. Heiss

3. Zeeman splitting in Ps In a static magnetic field:3γ 2γ
In a static magnetic field:
parallel spin states are unaffected
antiparallel spin states pick up ∆E
The | 1,0> state mixes with the | 0,0> state
magnetic quenching
We can induce transitions between different 𝑚 𝑍 ‘s instead of different 𝐽‘s
Compare: ∆ 𝑚𝑖𝑥 ≈4 𝐺𝐻𝑧 (at 1 𝑇)
vs ∆ 𝐻𝐹𝑆 ≈203 𝐺𝐻𝑧 3γ 2γ
Michael W. Heiss

4. Difficulties: Indirect measurements3γ 2γ
one calculates ∆ 𝐻𝐹𝑆 from:
Δ mix ≈0.5⋅ Δ HFS 𝑞 2 −1
where: 𝑞∝ 𝐵 Δ HFS
needs very high B-Fields (~ 1 𝑇)
to quench efficiently
to see a large effect when the microwave is on
Disadvantages
some theoretical uncertainty
inhomogeneities in the fields contribute
directly to systematic errors 3γ 2γ
Michael W. Heiss

5. Review: First direct measurement
Notoriously difficult (Δ𝜈=203 𝐺𝐻𝑧)
no off-the-shelf sources
no off-the-shelf resonators
behavior somewhat between microwave and light
Multiple resonators required
need to be changed for every frequency point
Needs very high MW power
very rudimentary power estimation
measured the heat absorbed by a pot of water
Source: Miyazaki et al., First Millimeter-wave Spectroscopy of the Ground-state Positronium. 2015
Michael W. Heiss

6. Difficulties: Dense gas measurements
In dense gases
gas acts as 𝑒 + target
𝑒 + can ionize a gas atom
𝑒 + picks up the 𝑒 − and forms Ps
Advantage: no need for a beam
Disadvantages:
E field of gas atoms → Stark effect
Needs extrapolation to vacuum
Uncertainties in the Ps thermalization
High MW powers strongly interfere with Ps production in gases
Source: Ishida et al., New Precision Measurement of Hyperfine Splitting of Positronium. 2014
Michael W. Heiss

7. Idea: Use vacuum HFS transition in 2s state
Transition in vacuum
no extrapolation necessary
need a beam
need different converter
Direct transition
no theoretical uncertainty
needs no static B field
need 486nm laser
Commercially available
Signal Generators: 200mW
TWT Amplifiers: 100’s of W
Michael W. Heiss

8. PHySES: Schematic overview of the experiment
Michael W. Heiss

9. PHySES: Laser excitation 1s-2s
Pulsed laser setup
Multi-purpose system
HFS spectroscopy
1s-2s spectroscopy
Stark deceleration of Rydberg states
Extensive Simulation
≈ 1% of Ps available for HFS
limited by
photoionization
oscillation back to ground state
Michael W. Heiss

10. PHySES: Microwave HFS transition
Confocal 25.4 GHz
two spherical mirrors
impedence matched coupling hole
waveguide signal feed (TWT amplified)
Quality factor
𝑄= 𝜈 0 ∆𝜈
𝑄=2𝜋 𝑒𝑛𝑒𝑟𝑔𝑦 𝑠𝑡𝑜𝑟𝑒𝑑 𝑒𝑛𝑒𝑟𝑔𝑦 𝑙𝑜𝑠𝑡 𝑏𝑦 𝑐𝑦𝑐𝑙𝑒
Design value: 𝑄 ≈ 50000
Simulation results:
HFS transition probability ≈ 3.5%
Michael W. Heiss

11. PHySES: Event signature
Experimental signature (pPs decay)
2 matching back-to-back 511 keV photons
temporal coincidence in opposite detector modules
intersection of connecting line with target region
energy cut
Dominant background (oPs decay)
misidentification of 3 photon decays as 2 photon decays
very small angle between 2 of the 3 photons
one photon very soft
Ground state positronium
removed by time of flight (separation of converter and cavity)
𝑚 𝑃𝑠 =1022 𝑘𝑒𝑉
𝐸 𝛾 ≈511 𝑘𝑒𝑉
𝐸 𝛾 ≈0 𝑘𝑒𝑉
𝑚 𝑃𝑠 =1022 𝑘𝑒𝑉
𝐸 𝛾 =511 𝑘𝑒𝑉
𝑚 𝑃𝑠 =1022 𝑘𝑒𝑉
𝐸 𝛾 ≈255.5 𝑘𝑒𝑉
𝐸 𝛾 ≈511 𝑘𝑒𝑉
𝑚 𝑃𝑠 =1022 𝑘𝑒𝑉
∑𝐸 𝛾 =1022 𝑘𝑒𝑉
Michael W. Heiss

12. PHySES: Detector – AxPET
AxPET demonstrator
provided by the group of Prof. Dissertori
very good temporal and spatial resolution
6 layers per module
8 LYSO crystals
26 wavelength shifters
204 MPPC & bias voltage supply channels
3 temperature probes
Reinstrumentation was necessary
old DAQ could not be reused (no energy measurement)
original cabling solution extremely noisy
Source: Beltrame et al., The AX-PET demonstrator – Design, construction and characterization. 2011
Michael W. Heiss

13. PHySES: Simulation results
C++/GEANT4/Mathematica
average rate of 4x105 e+/s
30% Ps conversion efficiency
optimization for S/N
~3% detection efficiency
1 misidentified oPs event for ~40 signal events
projected sensitivity:
± 5 ppm (stat) ± 3 ppm (syst)
Michael W. Heiss

14. PHySES: Estimation of systematics
Ps formation and transition in vacuum
no systematic errors from gas
Ps formation with thin silica films very stable
Direct transition not using Zeeman splitting
no systematic errors from static magnetic field
Systematic errors few ppm
Michael W. Heiss

15. PHySES: Current status I
Pulsed positron beam and Ps conversion
stable operation
minor flux issues
Laser system
switched to 486 nm generation
aligning, testing and optimizing 2s excitation
Microwave system
completed first tests of confocal resonator
surprisingly stable
Q ≈ , coupling efficiency ≈ 90%
Amplifier stopped working, further tests required
Michael W. Heiss

16. PHySES: Current status II
Detector system
preliminary tests with new DAQ successful
assembling new parts for reinstrumentation
testing and calibration will begin shortly
Vacuum chamber
final design is a work in progress
linear piezo actuator stage
thermal and vibrational decoupling of mirrors
Michael W. Heiss

17. PHySES: Outlook Laser Microwave DAQ Simulation
Optical cavity locked to CW laser
Possible improvements somewhat limited
Microwave
investigate effect of cooling on the coupling efficiency
significant increase in Q factor possible by LN2 cooling
waveguide-type resonator could also be reconsidered
DAQ
test neural network analysis approach to increase S/N
Simulation
effort to consolidate all stages of the simulation for reliable error estimations
Michael W. Heiss

18. Thank you for your attention
Michael W. Heiss