Recent and ongoing experimental work on the positronium spectrum motivates new efforts to calculate positronium energy levels at the level of three loop corrections. We have obtained results for one set of such corrections involving light-by-light scattering of the photons produced in a two-photon virtual annihilation process. Our result is an energy shift $1.58377(8) m α^7/π^3$ for the n=1 singlet state, correcting the ground state hyperfine splitting by -6.95 kHz. We also obtained a new and more precise result for the light-by-light scattering correction to the real decay of parapositronium into two photons.
The hyperfine structure of the ground states in a number of positronium hydrides (TPs, DPs, ${}^{1}$HPs) and MuPs ($μ^{+} e^{-}_2 e^{+}$) is determined with the use of highly accurate variational wave functions. We also evaluate the probabilities of various processes in the MuPs system, including the $(e^{-}, e^{+})$-pair annihilation and its conversion into the charge conjugate system $μ^{+} e^{-}_2 e^{+} \to μ^{-} e^{-} e^{+}_2$.
A detailed presentation is given of the analytic calculation of the single-photon annihilation contributions to the positronium ground state hyperfine splitting to order $m_eα^6$ in the framework of non-relativistic effective theories. The current status of the theoretical description of the positronium ground state hyperfine splitting is reviewed.
We present the complete result for the ${\cal O}(α^7m_e)$ one-photon annihilation contribution to the hyperfine splitting of the ground state energy levels in positronium. Numerically it increases the prediction of quantum electrodynamics by $217\pm 1$ kHz.
We have calculated all contributions to the energy levels of parapositronium at order $m α^7$ coming from vacuum polarization corrections to processes involving virtual annihilation to two photons. This work is motivated by ongoing efforts to improve the experimental determination of the positronium ground-state hyperfine splitting.
Positronium spectroscopy (n=1 hyperfine splitting, n=2 fine structure, and the 1S-2S interval) has reached a precision of order 1 MHz. Vigorous ongoing efforts to improve the experimental results motivate the calculation of the positronium energy levels at order $m α^7$. In this work we present the result for a complete class of such contributions--those involving virtual annihilation of positronium to three photons in an intermediate state. We find an energy shift of $2.6216(11) m α^7/(n π)^3$ for the spin-triplet S state with principal quantum number n.
Ongoing improvements in the measurement of positronium transition intervals motivate the calculation of the $O(m α^7)$ corrections to these intervals. In this work we focus on corrections to the spin-singlet parapositronium energies involving virtual annihilation to two photons in an intermediate state. We have evaluated all contributions to the positronium S-state energy levels that can be written as the product of a one-loop correction on one side of the annihilation event and another one-loop correction on the other side. These effects contribute $ΔE = -0.561971(25) m α^7/π^3$ to the parapo…
Using a four dimensional approach, we show that the singularities for small gluon momenta, which arise in the usual three dimensional treatment of the annihilation decay, disappear if all poles in the relative energy are taken into account correctly in the integration. We obtain an explicit formula for the decay width which involves a non locality originating from the kinetic energy. We calculate not only the familiar logarithmic dependence on the binding energy, but also the constant to be added to the logarithm. For positronium this differs from an earlier result in the literature and leads …
The single photon annihilation contributions for the positronium ground state hyperfine splitting are calculated analytically to order $m_eα^6$ using NRQED. Based on intuitive physical arguments the same result can also be determined by a trivial calculation using results from existing literature. Our result completes the hyperfine splitting calculation to order $m_eα^6$. We compare the theoretical prediction with the most recent experimental measurement.
We approach to the ortho-positronium (o-Ps) as a relativistic two-body problem in $2+1$ dimensions in which o-Ps is composed of two-oppositely charged particles interacting via an attractive Coulomb force. In addition to separation of center of mass and relative coordinates, mapping the background into the polar space-time gives possibility of construction of possible spin eigen-states of o-Ps. This approach makes the energy spectrum complex in order to describe o-Ps that can decay. From the complex energy expression, we find the annihilation energy, binding energy and the life-time of o-Ps, i…
Ortho-Positronium Three-Photon Decays: Physics Constraints and a Closed-Form Energy Method for Annihilation Vertex Reconstruction
IT:U Interdisciplinary Transformation University（IT:U跨学科转型大学）；University of Vienna, Faculty of Physics（维也纳大学物理学院）；National Centre for Nuclear Research（国家核研究中心）；INSA-Lyon, Université Claude Bernard Lyon 1（里昂国立应用科学学院，克洛德·贝尔纳里昂大学）
The rate for complete two-photon annihilation of molecular positronium Ps$_{2}$ is reported. This decay channel involves a four-body collision among the fermions forming Ps$_{2}$, and two photons of 1.022 MeV, each, as the final state. The quantum electrodynamics result for the rate of this process is found to be $Γ_{Ps_{2} \rightarrow γγ}$ = 9.0 $\times 10^{-12}$ s$^{-1}$. This decay channel completes the most comprehensive decay chart for Ps$_{2}$ up to date.
Positronium annihilation amplitudes that are computed by assuming a factorization approximation with on-shell intermediate leptons do not exhibit good analytical behaviour. Using dispersion techniques, we find new contributions that interfere with the known results to restore analytical properties. Those new amplitudes which cannot be obtained using standard factorized amplitude formalism, contribute at order alpha^2. Therefore they have to be evaluated before any theoretical conclusion can be drawn upon the orthopositronium lifetime puzzle.
We consider the production of ultrarelativistic parapositronium and orthopositronium atoms in collisions of high energy electrons with laser photons. Our results demonstrate the opportunity of intensive positronium beam formation with Lorentz-factor 10^6 using laser beam conversion on high energy electrons at the future Electron Linear Accelerators.
We have calculated the contribution to the positronium hyperfine splitting at order $m α^7$ of the light-by-light scattering process in the exchange of two photons between the electron and positron. Our result is $ΔE = -0.235355(8) m α^4 \left ( \fracαπ \right )^3 = -1.034 kHz$. As a check of our approach we confirm earlier evaluations of the analogous correction for a bound system (such as muonium) with unequal masses.
Positronium annihilation amplitudes that are computed by assuming a factorization approximation with on-shell intermediate leptons, do not exhibit good analytical behavior. We propose an ansatz which allows to include binding energy corrections and obtain the correct analytical and gauge invariance behavior of these QED amplitudes. As a consequence of these non-perturbative corrections, the parapositronium and orthopositronium decay rates receive corrections of order alpha^4 and alpha^2, respectively. These new corrections for orthopositronium are relevant in view of a precise comparison betwe…
We examine the implications of including corrections associated with the noncommutative extension of quantum electrodynamics - NCQED - to the decays of the ortho and para positronium (\Trip and \Sing) ground states. In NCQED, the well known charge conjugation argument restricting \Trip decays to an odd number of photons and \Sing decays to an even number of photons no longer obtains. Instead, the dominant two photon decay mode of \Sing is accompanied by a three photon mode. The dominant three photon decay mode of \Trip receives a NCQED correction, but there is no corresponding two photon decay…
Binding energy of the $1^-$ state (ortho-positronium) in QED is calculated using the one-photon exchange Bethe-Salpeter equation in the Feynman and Coulomb gauges for different coupling constants $α$. Calculations show there is a remarkable difference in values of the binding energy for different coupling constants in these two gauges.
A detailed exposition of two-photon decays of P-wave positronium is given to fill an existing gap in the pedagogical literature. Annihilation decay rates of P-wave positronium are negligible compared to the rates of radiative electric dipole transitions to the ground state. This circumstance makes such decays experimentally inaccessible. However the situation is different for quarkonium and the experimental and theoretical research of two-photon and two-gluon decays of P-wave quarkonia is a still flourishing field.
We determine the rates and energy and angular distributions of the positronium decays into a photon and a neutrino-antineutrino pair, Ps-->gamma+nu+anti-nu. We find that both positronium spin states have access to this decay channel, contrary to a previously published result. The low-energy tails of the spectra are shown to be sensitive to the binding effects and agree with Low's theorem. Additionally, we find a connection between the behaviour of the soft photon spectrum in both o-Ps-->gamma+nu+anti-nu and o-Ps-->3gamma decays, and the Stark effect.
Entanglement of three photons from the decay of ortho-positronium is re-analyzed. We use the full three body phase space to write down the entangled states classified according to the spin directions of the ortho-positronium. Even in the case when the spin is perpendicular to the decay plane, we find non-negligible phases entering the entangled state. This has not been noticed before. We advocate a fixed quantization axis of the spin for the sake of generality. A brief discussion of a three dimensional formalism for photons, including correlations, versus a two dimensional one is given.
We compute O(alpha^3 ln alpha) corrections to the decay rates of para- and orthopositronium into two and three photons, respectively. For this calculation we employ the nonrelativistic QED regularized dimensionally and we explain how in this framework the logarithms of the fine structure constant can be extracted.
Positronium is the short-lived atom consisting of a bound electron-positron pair. In the triplet state, when the spins of both particles are parallel, radiative recombination lines will be emitted prior to annihilation. The existence of celestial positronium is revealed through gamma-ray observations of its annihilation products. These observations however have intrinsically low angular resolution. In this paper we examine the prospects for detecting the positronium recombination spectrum. Such observations have the potential to reveal discrete sources of positrons for the first time and will …
Comments on the publication "Discrete symmetries tested at 10e-4 precision using linear polarization of photons from positronium annihilations" by P. Moskal et al
Hard spin-independent three-loop radiative contributions to energy levels in positronium generated by the two-photon-exchange diagrams with one-loop radiative insertions in the fermion lines and exchanged photons are calculated. This is a next step in calculations of all corrections of order $mα^7$ inspired by the new generation of precise $1S-2S$ and $2S-2P$ measurements in positronium.
We consider the decay of positronium to a neutrino-antineutrino accompanied by a single photon. Since the neutrino pair go undetected, this appears as a single photon decay of positronium. These decay channel are mediated through the exchange of the massive $W$ and $Z$ vector bosons of the electroweak interaction. After summing over the various neutrino channels, the standard model calculation yields the rate for such a single photon decay process of $Γ_{Ps \rightarrow γ}$ = 1.72 $\times 10^{-19}$ s$^{-1}$.
We investigate the double parton distributions (DPDs) for a positronium-like bound state using light-front QED. We incorporate the higher Fock three particle component of the state, that includes a photon. We obtain the overlap representation of the DPDs in terms of the three-particle light-front wave functions (LFWFs). Our calculation explores the correlations between the momentum fractions of the particles probed and the transverse distance between them, without any assumption of factorization between them. We also investigate the behavior of the DPDs near the kinematical boundary when the s…
We consider hard three-loop nonlogarithmic corrections of order $mα^7$ 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 $ΔE=-1.2917(1)mα^7/π^3=-5.672$ kHz.
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 wavefunction are removed. Non-factorizable amplitudes are naturally introduced. Their dynamics is described, especially regarding the enforcement of gauge invariance and analyticity through delicate interferences. The important question of the completeness …
We consider the production of ultrarelativistic positronium (Ps) in $γA \to Ps + A$ and $e A \to Ps + e A$ processes where $A$ is an atom or a nucleus with charge $Ze$. For the photoproduction of para- and ortho-Ps and the electroproduction of para-Ps we obtain the most complete description compared with previous works. It includes high order $Z α$ corrections and polarization effects. The accuracy of the obtained cross sections is determined by omitted terms of the order of the inverse Ps Lorentz factor squared. The studied high order multi-photon electroproduction of ortho-Ps dominates for t…
We calculate hard spin-independent three-loop radiative corrections to energy levels in muonium and positronium which are due to radiative insertions in two-photon exchange diagrams. These corrections could be relevant for the new generation of precise $1S-2S$ and $2S-2P$ measurements in muonium and positronium.
The decay of ortho-positronium into three photons produces a physical realization of a pure state with three-party entanglement. Its quantum correlations are analyzed using recent results on quantum information theory, looking for the final state which has the maximal amount of GHZ-like correlations. This state allows for a statistical dismissal of local realism stronger than the one obtained using any entangled state of two spin one-half particles.
We present a precise theoretical prediction for the decay width of the bound state of two electrons and a positron (a negative positronium ion), Gamma(Ps^-) = 2.087 085(12)/ns. We include O(alpha^2) effects of hard virtual photons as well as soft corrections to the wave function and the decay amplitude. An outcome of a large-scale variational calculation, this is the first result for second-order corrections to a decay of a three-particle bound state. It will be tested experimentally in the new positronium-ion facility in Garching in Germany.
The electron and the positron treated as point particles in the Two Body Dirac equations of constraint dynamics for QED possess a new and as yet undiscovered peculiar ${}^1S_0$ bound-state which has a very large binding energy of about 300 keV, in addition to the usual ${}^1S_0$ positronium state with a binding energy of 6.8 eV. The production and detection of the peculiar ${}^1S_0$ state provide a test of the electron point-charge property. As the peculiar ${}^1S_0$ state lies lower than the usual ${}^1S_0$ state, the peculiar ${}^1S_0$ state can be produced by a two-photon decay of the usual…
Two-Body Dirac equations of constraint dynamics provide a covariant framework to investigate the problem of highly relativistic quarks in meson bound states. This formalism eliminates automatically the problems of relative time and energy, leading to a covariant three dimensional formalism with the same number of degrees of freedom as appears in the corresponding nonrelativistic problem. It provides bound state wave equations with the simplicity of the nonrelativistic Schroedinger equation. Unlike other three-dimensional truncations of the Bethe-Salpeter equation, this covariant formalism has …
Decay rates of the positronium molecule $\text{Ps}_{2}$ into two photons and into an electron-positron pair are determined. Previous studies find that these rates are very different, \[ Γ\left(\text{Ps}_{2}\to e^{+}e^{-}\right)/Γ\left(\text{Ps}_{2}\toγγ\right)\simeq250\text{ (previous studies)}. \] This is puzzling since both processes have two body final states and are of the same order in the fine structure constant. We propose a simple calculational method and test it with the well-established decay of the positronium ion into an electron and a photon. We then employ it to correct predictio…
Two-Body Dirac equations of constraint dynamics provide a covariant framework to investigate the problem of highly relativistic quarks in meson bound states. This formalism eliminates automatically the problems of relative time and energy, leading to a covariant three dimensional formalism with the same number of degrees of freedom as appears in the corresponding nonrelativistic problem. It provides bound state wave equations with the simplicity of the nonrelativistic Schroedinger equation. Here we begin important tests of the relativistic sixteen component wave function solutions obtained in …
We present a calculation of the mass spectrum of positronium within the framework of the recently developed Basis Light-Front Quantization approach to non-perturbative quantum field theory. In this calculation, we employ a two-body effective interaction for the photon exchange, neglecting self-energy effects. We demonstrate the cancellation of Light-Front small-{\it x} divergences within our non-perturbative approach. The resulting spectrum is compared to both non-relativistic quantum mechanics and previous work in Discretized Light-Cone Quantization.
We discuss in detail potential NRQED (pNRQED), a previously proposed effective field theory for ultrasoft photons. The pNRQED lagrangian for the equal mass case is presented and it is shown that it correctly reproduces the positronium spectrum at order $mα^5$. The pNRQED lagrangian for the unequal mass case is also presented at the same order. Dimensional regularization is used throughout.
The photon spectrum in orthopositronium to 3 gamma decay is computed using effective field theory methods. For energetic photons, the spectrum agrees with the Ore-Powell result, but deviates from it when the photon energy is comparable to the positronium binding energy. The decay spectrum in this region depends on a positronium structure function, which is computed in this paper. At still lower energies the photon spectrum is dominated by the parapositronium resonance contribution. Our results are compatible with Low's theorem on soft photon emission.
We calculate the mass spectrum and the structure of the positronium system at a strong coupling in a basis light-front approach. We start from the light-front QED Hamiltonian and retain one dynamical photon in our basis. We perform the fermion mass renormalization associated with the nonperturbative fermion self-energy correction. We present the resulting mass spectrum and wave functions for the selected low-lying states. Next, we apply this approach to QCD and calculate the heavy meson system with one dynamical gluon retained. We illustrate the obtained mass spectrum and wave functions for th…
In this work, the non-relativistic asymptotic behavior of the transition $q\overline{q}\rightarrow2g\rightarrow q\overline{q}$ in the $^1S_0$ channel is discussed. Different with the usual calculation which expands the physical amplitude around the quark anti-quark threshold, we take the quark anti-quark pairs as off shell and only expand the expression on the three-dimensional momenta of the quarks and anti-quarks. We calculate the results to order 6. The imagine part of the results after applying the on shell conditions can reproduce the non-relativistic QCD (NRQCD) results in leading order …
