Positronium Hyperfine Splitting Research Articles

Hadrons as QCD Bound States

Bound state perturbation theory is well established for QED atoms. Today the hyperfine splitting of Positronium is known to𝒪(α7logα). Whereas standard expansions of scattering amplitudes start from free states, bound states are expanded around eigenstates of the Hamiltonian including a binding potential. The eigenstate wave functions have all powers ofα, requiring a choice in the ordering of the perturbative expansion. Temporal (A0= 0) gauge permits an expansion starting from valence Fock states, bound by their instantaneous gauge field. This formulation is applicable in any frame and seems promising even for hadrons in QCD. The𝒪(αs0) confining potential is determined (up to a universal scale) by a homogeneous solution of Gauss’ law.

Hyperfine splitting in muonium and positronium

Calculation of hard three-loop corrections of order [Formula: see text] to hyperfine splitting in muonium and positronium is reviewed. All these contributions are generated by the graphs with photon, electron and/or muon loop radiative insertions in the two-photon exchange diagrams. We calculate contributions of six gauge invariant sets of diagrams.

Measurement of positronium thermalization in isobutane gas for precision measurement of ground-state hyperfine splitting

The thermalization parameter of positronium in pure isobutane gas was measured in order to take into account the thermalization effect on precision measurements of the ground-state hyperfine splitting (HFS) of positronium. The momentum-transfer cross section was measured to be for positroniums with kinetic energy below 0.17 eV. Using this value, our new HFS experiment revealed that the positronium thermalization effect on HFS was as large as . In this article, we show the details of Ps thermalization measurement, which have not been published before, and also its effect on HFS.

Hard three-loop corrections to hyperfine splitting

We consider hard three-loop nonlogarithmic corrections of order [Formula: see text] to hyperfine splitting in muonium and positronium. All these contributions are generated by the graphs with photon, electron and/or muon loop radiative insertions in the two-photon exchange diagrams. We calculate contributions of six gauge invariant sets of diagrams.

Hard three-loop corrections to hyperfine splitting in positronium and muonium

We consider hard three-loop corrections to hyperfine splitting in muonium and positronium generated by the diagrams with closed electron loops. There are six gauge-invariant sets of such diagrams that generate corrections of order $m\alpha^7$. The contributions of these diagrams are calculated for an arbitrary electron-muon mass ratio without expansion in the small mass ratio. We obtain the formulae for contributions to hyperfine splitting that in the case of small mass ratio describe corrections for muonium and in the case of equal masses describe corrections for positronium. First few terms of the expansion of hard corrections in the small mass ratio were earlier calculated for muonium analytically. We check numerically that the new results coincide with the sum of the known terms of the expansion in the case of small mass ratio. In the case of equal masses we obtain hard nonlogarithmic corrections of order $m\alpha^7$ to hyperfine splitting in positronium.

Higher order corrections to the hyperfine splitting of positronium

The positronium ground state hyperfine splitting (hfs) has long been of interest as a high-precision test of our understanding of binding in QED. The positronium hfs is particularly sensitive to recoil effects (because the ratio of masses is one) and to virtual electron-positron annihilation, but positronium is insensitive to strong and weak interaction effects. Consequently, the comparison between theory and experiment for the positronium hfs, and more generally the positronium spectrum, tests different aspects of the theory compared to comparisons in other exotic atoms. For the past fifteen years there has been a persistent discrepancy between predicted and measured values of the positronium hfs of about four standard deviations (although a new experimental result is consistent with present theory). Recent experimental work is leading to new high-precision measurements, and the calculation of order- α 3 corrections has begun. The status of the positronium hfs problem and a discussion of recent progress is the topic of this contribution.

Hard nonlogarithmic corrections of ordermα7to hyperfine splitting in positronium

We consider hard three-loop nonlogarithmic corrections of order $m{\ensuremath{\alpha}}^{7}$ to hyperfine splitting in positronium. All these contributions are generated by the graphs with photon and/or electron loop radiative insertions in the two-photon exchange diagrams. We calculate contributions of six gauge-invariant sets of diagrams. The total result for all these diagrams is $\mathrm{\ensuremath{\Delta}}E=\ensuremath{-}1.2917(1)m{\ensuremath{\alpha}}^{7}/{\ensuremath{\pi}}^{3}=\ensuremath{-}5.672\text{ }\text{ }\mathrm{kHz}$.

New precision measurement of hyperfine splitting of positronium

The ground state hyperfine splitting of positronium ΔHFS is sensitive to high order corrections of quantum electrodynamics (QED) in bound state. The theoretical prediction and the averaged experimental value for ΔHFS have a discrepancy of 15 ppm, which is equivalent to 3.9 standard deviations (s.d.). A new precision measurement which reduces the systematic uncertainty from the positronium thermalization effect was performed, in which the non-thermalization effect was measured to be as large as 10±2 ppm in a timing window we used. When this effect is taken into account, our new result becomes ΔHFS=203.3942±0.0016(stat.,8.0 ppm)±0.0013(sys.,6.4 ppm) GHz, which favors the QED prediction within 1.2 s.d. and disfavors the previous experimental average by 2.6 s.d.

The sub-THz direct spectroscopy of positronium hyperfine splitting

The positronium hyperfine splitting is a good target to study Quantum Electrodynamics in the bound state. There is a discrepancy between precision measurements and a theoretical calculation. We are planning to directly measure the positroinum hyperfine structure for the first time. A gyrotron oscillator is used as a novel radiation source in terahertz region. A Fabry-Pérot resonator is also developed to increase photon density. We have already observed the direct transition at 202.9 GHz. The direct measurement of the order of 100 ppm will be performed within about a year.

Precise measurement of positronium hyperfine splitting using the Zeeman effect

Positronium is an ideal system for the research of the quantum electrodynamics (QED) in bound state. The hyperfine splitting (HFS) of positronium, ΔHFS, gives a good test of the bound state calculations and probes new physics beyond the Standard Model. A new method of QED calculations has revealed the discrepancy by 15 ppm (3.9σ) of ΔHFS between the QED prediction and the experimental average. There would be possibility of new physics or common systematic uncertainties in the previous all experiments. We describe a new experiment to reduce possible systematic uncertainties and will provide an independent check of the discrepancy. We are now taking data and the current result of ΔHFS = 203.395 1 ±0.002 4 (stat., 12 ppm) ±0.001 9 (sys., 9.5 ppm) GHz has been obtained so far. A measurement with a precision of O(ppm) is expected within a year.

First observation of o-Ps to p-Ps transition and first direct measurement of positronium hyperfine splitting with sub-THz light

Positronium is an ideal system for the research of the bound state QED. The hyperfine splitting of positronium (Ps-HFS, about 203 GHz) is an important observable but all previous measurements of Ps-HFS had been measured indirectly using Zeeman splitting. There might be the unknown systematic errors on the uniformity of magnetic field. We are trying to measure Ps-HFS directly using sub-THz radiation. We developed an optical system to accumulate high power (about 10 kW) radiation in a Fabry-Perot resonant cavity and observed the positronium hyperfine transition for the first time.

Measurement of positronium hyperfine splitting with quantum oscillation

Interference between different energy eigenstates in a quantum system results in an oscillation with a frequency which is proportional to the difference in energy between the states. Such an oscillation is observable in polarized positronium when it is placed in a magnetic field. In order to measure the hyperfine splitting of positronium, we perform the precise measurement of this oscillation using a high quality superconducting magnet and fast photon-detectors. A result of 203.324±0.039(stat.)±0.015(sys.) GHz is obtained which is consistent with both theoretical calculations and previous precise measurements.

Precise Measurement of Hyperfine Splitting of Positronium Using the Zeeman Effect

The ground state hyperfine splitting of positronium, , is sensitive to high order corrections of QED. A new calculation up to O( ) has revealed a 3.9 discrepancy between the QED prediction and the experimental results. This discrepancy might either be due to systematic problems in the previous experiments or to contributions beyond the Standard Model. We propose an experiment to measure employing new methods designed to remedy the possible systematic errors which may have affected the previous experiments. Our experiment will provide an independent check of the discrepancy. The prototype run has been performed and a result of = 203.3804 0.0022 (stat., 11 ppm) 0.0081 (sys., 40 ppm) GHz has been obtained. Compensation magnets to obtain O(ppm) magnetic field uniformity has been developed. The final run will start soon and a measurement with a precision of O(ppm) is expected within a few years.

Experiment for the first direct measurement of the hyperfine splitting of positronium

Positronium is an ideal system for the research of the bound state QED. The hyperfine splitting of positronium (Ps-HFS: about 203 GHz) is a good tool to test QED and also sensitive to new physics beyond the Standard Model via a quantum oscillation between an ortho-Ps and a virtual photon. Previous experimental results show 3.9 σ (15 ppm) discrepancy from the QED calculation. All previous experiments used an indirect method with static magnetic field to cause Zeeman splitting (a few GHz) between triplet states of ortho-Ps, from which the HFS value was derived. One possible systematic error source of the indirect method is non-uniformity of the static magnetic field. We are developing a new direct Ps-HFS measurement system without static magnetic field. In this measurement we use a gyrotron, a novel sub-THz light source, with a high-finesse Fabry-Pérot cavity to obtain enough radiation power at 203 GHz. The present status of the optimization studies and current design of the experiment are described.

Measurement of positronium hyperfine splitting with quantum oscillation

It is well known that a coherent system can bring a quantum interference between different energy eigenstates into an observable oscillation. Since an energy difference and a frequency are related with each other by the equation ΔE = ℏω we can make use of the oscillation to measure the energy difference of quantum states. In this experiment, the hyperfine splitting of positronium is measured using the quantum oscillation. The result is 203.324±0.044(stat.)±0.028(sys.) GHz. This value is consistent with the theoretical calculations.

Precise measurement of HFS of positronium using Zeeman effect

The ground state hyperfine splitting of positronium, ΔHFS, is sensitive to high order corrections of QED. A new calculation up to O(α3) has revealed a 3.9 σ discrepancy between the QED prediction and the experimental results. This discrepancy might either be due to systematic problems in the previous experiments or to contributions beyond the Standard Model. We propose an experiment to measure ΔHFS employing new methods designed to remedy the systematic errors which may have affected the previous experiments. Our experiment will provide an independent check of the discrepancy. The measurement is in progress and a result of ΔHFS = 203.385 ± 0.011 GHz (58ppm) has been obtained from the prototype run. A measurement with a precision of O(ppm) is expected within a few years.

Probing the energy structure of positronium with a 203 GHz Fabry-Perot Cavity

Positronium is an ideal system for the research of the bound state QED. The hyperfine splitting of positronium (Ps-HFS: about 203 GHz) is sensitive to new physics beyond the Standard Model via a vacuum oscillation between an ortho-Ps and a virtual photon. Previous experimental results of the Ps-HFS show 3.9 σ (15 ppm) discrepancy from the QED calculation. All previous experiments used an indirect method with static magnetic field to cause Zeeman splitting (a few GHz) between triplet states of ortho-Ps, from which the HFS value was derived. One possible systematic error source of the indirect method is the static magnetic field. We are developing a new direct measurement system of the Ps-HFS without static magnetic field. In this measurement we use a gyrotron, a novel sub-THz light source, with a high-finesse Fabry-Perot cavity to obtain enough radiation power at 203 GHz. The present status of the optimization studies and current design of the experiment are described.

Precise measurement of HFS of positronium

The ground state hyperfine splitting in positronium, ΔHFS, is sensitive to high order corrections of QED. A new calculation up to O(α3) has revealed a 3.9 σ discrepancy between the QED prediction and the experimental results. This discrepancy might either be due to systematic problems in the previous experiments or to contributions beyond the Standard Model. We propose an experiment to measure ΔHFS employing new methods designed to remedy the systematic errors which may have affected the previous experiments. Our experiment will provide an independent check of the discrepancy. The measurement is in progress and a preliminary result of ΔHFS = 203.399±0.029 GHz (143 ppm) has been obtained. A measurement with a precision of O(1) ppm is expected within a few years.

The first direct measurement of the hyperfine splitting in positronium

Positronium is an ideal system for the research of the QED. The hyperfine splitting of positronium (Ps-HFS) is sensitive to the new physics beyond the Standard Model via a vacuum oscillation. Previous experimental results of the Ps-HFS show 3.5 σ discrepancy from the QED calculation, and it might be caused by uncertainties of the indirect method with static magnetic field and a few GHz RF. We developed a new direct measurement system of the Ps-HFS without static magnetic field, using a sub-THz gyrotron and a quasi-optical Fabry-Perot cavity. Status (hopefully the first result) of the direct positronium hyperfine transition observation will be presented.

Precise measurement on HFS of positronium

Positronium is an ideal system for the research of the QED. The hyperfine splitting of positronium is sensitive to the higher order correction of the QED and to the new physics beyond the Standard Model via a vacuum oscillation. The new method of QED calculations has revealed the 3.5σ discrepancy between the QED prediction and the previous measurements. It might be because of the new physics or the experimental systematic uncertainties (the effect of unthermalized Ps and the nonuniformity of the magnetic fields). We present the results of the first run and the future plan of our new precise measurement on HFS without these uncertainties.