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Possible manifestations of new physics in rare (exotic) decays of orthopositronium (o - Ps) are briefly reviewed. It is pointed out that models with infinite additional dimension(s) of Randall–Sundrum type predict disappearance of orthopositronium into additional dimension(s). The experimental signature of this effect is the invisible decay of orthopositronium. We point out that this process may occur at a rate within two or three orders of magnitude of the present experimental upper limit. We also propose a model with a light weakly interacting boson leading to o - Ps → invisible decays at the experimentally interesting rate. We discuss this in details and stress that the existence of invisible decay of orthopositronium in vacuum could explain the o - Ps decay rate puzzle. Thus, our result enhances the existing motivation and justifies efforts for a more sensitive search for o - Ps → invisible decay in a near future experiment.

A closed analytic expression is given for the spectrum of low energy photons in the annihilation of orthopositronium, which expression sums all the effects of the Coulomb interaction between the electron and the positron. The applicability of the formula is limited only by the condition ω_γ ≪ m_e. In the region ω_γ ≫ m_eα² the Coulomb interaction term gives the leading at low energy one-loop correction, proportional to , to the decay spectrum. The constant in ω_γ radiative term in the one-loop correction to the spectrum is also presented here in an analytic form.

Recent experiments on positronium annihilation have confirmed QED calculations at high orders of α and tested discrete fundamental symmetries. These measurements search for rare modes of annihilation which are distinguished from backgrounds by their specific decay signatures. New developments in beyond Standard Model theory provide motivation for new measurements of such decays. A brief history of searches for rare annihilation modes of Ps is given. Recent experimental and theoretical developments are reviewed. Experiments currently being planned are discussed.

The aim of this brief review is twofold. First, we give an overview of the unprecedented experimental efforts to measure the gravitational acceleration of antimatter; with antihydrogen, in three competing experiments at CERN (AEGIS, ALPHA and GBAR), and with muonium and positronium in other laboratories in the world. Second, we present the 21st Century’s attempts to develop a new model of the Universe with the assumed gravitational repulsion between matter and antimatter; so far, three radically different and incompatible theoretical paradigms have been proposed. Two of these three models, Dirac–Milne Cosmology (that incorporates CPT violation) and the Lattice Universe (based on CPT symmetry), assume a symmetric Universe composed of equal amounts of matter and antimatter, with antimatter somehow “hidden” in cosmic voids; this hypothesis produced encouraging preliminary results. The heart of the third model is the hypothesis that quantum vacuum fluctuations are virtual gravitational dipoles; for the first time, this hypothesis makes possible and inevitable to include the quantum vacuum as a source of gravity. Standard Model matter is considered as the only content of the Universe, while phenomena usually attributed to dark matter and dark energy are explained as the local and global effects of the gravitational polarization of the quantum vacuum by the immersed baryonic matter. An additional feature is that we might live in a cyclic Universe alternatively dominated by matter and antimatter. In about three years, we will know if there is gravitational repulsion between matter and antimatter; a discovery that can forever change our understanding of the Universe.

The construction of positronium decay amplitudes is handled through the use of dispersion relations. In this way, emphasis is put on basic QED principles: gauge invariance and soft-photon limits (analyticity).

A firm grounding is given to the factorization approaches, and some ambiguities in the spin and energy structures of the positronium wave function are removed. Nonfactorizable amplitudes are naturally introduced. Their dynamics are described, especially regarding the enforcement of gauge invariance and analyticity through delicate interferences. The important question of the completeness of the present theoretical predictions for the decay rates is then addressed. Indeed, some of those nonfactorizable contributions are unaccounted for by NRQED analyses. However, it is shown that such new contributions are highly suppressed, being of .

Finally, a particular effective form factor formalism is constructed for parapositronium, allowing a thorough analysis of binding energy effects and analyticity implementation.

A simple method to compute QED bound state properties is presented, in which binding energy effects are treated nonperturbatively. It is shown that to take the effects of all ladder Coulomb photon exchanges into account, one can simply perform the derivative of standard QED amplitudes with respect to the external momentum. For example, the derivative of the light-by-light scattering amplitude gives an amplitude for orthopositronium decay to three photons where any number of Coulomb photon exchanges between the e⁺e^- is included.

Various applications are presented. From them, it is shown that binding energy must be treated nonperturbatively in order to preserve the analyticity of positronium decay amplitudes.

Interesting perspectives for quarkonium physics are briefly sketched.

We propose an experiment to search for invisible decays of orthopositronium (o-Ps) with the 90% confidence sensitivity in the branching ratio as low as 10^-8. Evidence for this decay mode would unambiguosly signal new physics: either the existence of extra–dimensions or fractionally charged particles or new light gauge bosons. The experimental approach and the detector components of the proposed experiment are described.

We discuss the C, P, T, CP, CPT symmetries and possible searches for violation of these symmetries in positronium decays.

The aim of this CP symmetry test in positronium is to measure the CP violation amplitude parameter C_CP. This is derived from the measurement of the asymmetry in an angular distribution of the photons from the decay of the ortho-positronium in a magnetic field. The Standard Model prediction for C_CP is a value of the order of 10^-9. Thus the observation of a larger C_CP value would be signal of physics beyond the Standard Model. A previous measurement has found C_CP consistent with zero, with an uncertainty of ~ 10^-2. We have investigated the possibility of using the existing ETHZ-INRM-IN2P3 BGO crystal detector, set-up for positronium physics studies, to improve the sensitivity on the C_CP measurement. Preliminary calculations indicate that, using such an apparatus, with some modification, in a magnetic field of 4 kGauss, C_CP could be measured with an uncertainty in the range between ~ 10^-4 and ~ 10^-3, depending mainly on the uncertainty in the asymmetry measurement and the angular resolution of the photon detectors. If C_CP is less than ~ 10^-4, the experimental technique outlined here appears to be inadequate to observe a CP violating effect and new techniques or different observables must be exploited for better sensitivity.

Using the Gammasphere array of high-purity germanium detectors at the 88" Cyclotron at Lawrence Berkeley National Laboratory, we have made several measurements to test discrete fundamental symmetries in positronium annihilation. We tested charge conjugation symmetry (C) by searching for decays of ortho- and para-positronium to the "wrong" number of photons. We measured the five-photon annihilation mode of ortho-positronium, finding agreement with tree-level QED calculations at order α⁸. In a second experiment, we searched for decays of polarized ortho-positronium which violate the combined symmetry operation CPT. We improved existing limits on this CPT test by roughly a factor of ten. We are studying the feasibility of an experiment to search for "invisible" decays of ortho-positronium. Invisible decays could be caused by extra dimensions (invoked in string theories). General requirements for an experiment sensitive to decay branching ratios of order 10^-9 are discussed.

As an unstable light pure leptonic system, positronium is a very specific probe atom to test bound state QED. In contrast to ordinary QED for free leptons, the bound state QED theory is not so well understood and bound state approaches deserve highly accurate tests. We present a brief overview of precision studies of positronium paying special attention to uncertainties of theory as well as comparison of theory and experiment. We also consider in detail advantages and disadvantages of positronium tests compared to other QED experiments.

High-order perturbative corrections to positronium decays and hyperfine splitting are briefly reviewed. Theoretical predictions are compared to the most recent experimental data. Perspectives of future calculations are discussed.

In order to fulfill Low's theorem requirements, a new lowest order basis for bound state decay computations is proposed, in which the binding energy is treated non-perturbatively. The properties of the method are sketched by reviewing standard positronium decay processes. Then, it is shown how applying the method to quarkonia sheds new light on some longstanding puzzles.

The intrinsic decay rate of orthopositronium formed in SiO₂ powder is measured using the direct 2γ correction method such that the time dependence of the pick-off annihilation rate is precisely determined. The decay rate of orthopositronium is found to be 7.0396±0.0012(stat.)±0.0011(sys.)μs^-1, which is consistent with our previous measurements with about twice the accuracy. Results agree well with the O(α²) QED prediction, and also with a result reported very recently using nanoporous film.

Following recent theoretical results, it is suggested that positronium (Ps) might undergo spontaneous oscillations between two 4D space–time sheets whenever subjected to constant irrotational magnetic vector potentials. We show that these oscillations that would come together with o-Ps/p-Ps oscillations should have important consequences on Ps decay rates. Experimental setup and conditions are also suggested for demonstrating in nonaccelerator experiments this new invisible decay mode.

We consider hard three-loop nonlogarithmic corrections of order $m{\alpha }^7$ 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.

We show that due to the large coupling constant of the monopole–photon interaction the annihilation of monopole–antimonopole and monopolium into many photons must be considered experimentally. For monopole–antimonopole annihilation and lightly bound monopolium, even in the less favorable scenario, multiphoton events (four and more photons in the final state) are dominant, while for strongly bound monopolium, although two photon events are important, four- and six-photon events are also sizable.

While our visible Universe could be a 3-brane, some cosmological scenarios consider that other 3-branes could be hidden in the extra-dimensional bulk. Matter disappearance toward a hidden brane is mainly discussed for neutron — both theoretically and experimentally — but other particles are poorly studied. Recent experimental results offer new constraints on positronium or quarkonium invisible decays. In the present work, we show how a two-brane Universe allows for such invisible decays. We put this result in the context of the recent experimental data to constrain the brane energy scale $M_B$ (or effective brane thickness $M_B^{-1}$) and the interbrane distance $d$ for a relevant two-brane Universe in a $SO(3,1)$-broken 5D bulk. Quarkonia present poor bounds compared to the results deduced from previous passing-through-walls-neutron experiments for which scenarios with $M_B<2.5\times 10^{17}$ GeV and $d>0.5$ fm are excluded. By contrast, positronium experiments can compete with neutron experiments depending on the matter content of each brane. To constrain scenarios up to the Planck scale, positronium experiments in vacuum cavity should be able to reach $\text{Br}(\text{o-Ps}\to \text{invisible})\approx 10^{-6}$.

Experiments suggest that localization via self-trapping plays a central role in the behavior of equilibrated low mass particles in both liquids and in supercritical fluids. In the latter case, the behavior is dominated by the liquid-vapor critical point which is difficult to probe, both experimentally and theoretically. Here, for the first time, we present the results of path-integral computations of the characteristics of a self-trapped particle at the critical point of a Lennard-Jones fluid for a positive particle-atom scattering length. We investigate the influence of the range of the particle-atom interaction on trapping properties, and the pick-off decay rate for the case where the particle is ortho-positronium. We find that, at the critical point, the transition from the self-trapped inhomogeneity to the density of the surrounding fluid is more gradual than in the liquid, or dense gas, away from the critical point. In addition the "shell structure" in fluid density surrounding the droplet is effaced.

In this paper, we study the relativistic effect on the wave functions for a bouncing particle in a gravitational field. Motivated by the equivalence principle, we investigate the Klein–Gordon and Dirac equations in Rindler coordinates with the boundary conditions mimicking a uniformly accelerated mirror in Minkowski space. In the nonrelativistic limit, all these models in the comoving frame reduce to the familiar eigenvalue problem for the Schrödinger equation with a fixed floor in a linear gravitational potential, as expected. We find that the transition frequency between two energy levels of a bouncing Dirac particle is greater than the counterpart of a Klein–Gordon particle, while both are greater than their nonrelativistic limit. The different corrections to eigen-energies of particles of different nature are associated with the different behaviors of their wave functions around the mirror boundary.