PHySES Positronium Hyperfine Structure of the first Excited State: Measurement of the 2 3 𝑆 1 → 2 1 𝑆 0 transition in vacuum Michael W. Heiss 24.11.2016

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 ∼ 1 137 ⋅ 1 137 ⋅ 𝛼 𝑆 16 𝜋 2 ∼ 1 137 ⋅ 2 10 5 𝑉𝑒𝑟𝑡𝑒𝑥 ∼ 1 137 ⋅2 𝑉𝑒𝑟𝑡𝑒𝑥 ∼ 1 137 𝑃𝑟𝑜𝑝𝑎𝑔𝑎𝑡𝑜𝑟∼ 1 1 𝑀𝑒 𝑉 2 − 10 10 𝑀𝑒 𝑉 2 𝑃𝑟𝑜𝑝𝑎𝑔𝑎𝑡𝑜𝑟∼ 1 1 𝑀𝑒 𝑉 2 Source: Ishida et al., New Precision Measurement of Hyperfine Splitting of Positronium. 2014 Michael W. Heiss 24.11.2016

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 24.11.2016

Difficulties: Indirect measurements 3γ 2γ one calculates ∆ 𝐻𝐹𝑆 from: Δ mix ≈0.5⋅ Δ HFS 1+ 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 24.11.2016

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 24.11.2016

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 24.11.2016

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 24.11.2016

PHySES: Schematic overview of the experiment Michael W. Heiss 24.11.2016

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 24.11.2016

PHySES: Microwave HFS transition Confocal resonator @ 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 24.11.2016

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 24.11.2016

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 24.11.2016

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 24.11.2016

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 24.11.2016

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 ≈ 30000 , coupling efficiency ≈ 90% Amplifier stopped working, further tests required Michael W. Heiss 24.11.2016

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 24.11.2016

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 24.11.2016

Thank you for your attention Michael W. Heiss 24.11.2016