B. A. Kniehl, A. V. Kotikov, O. L. Veretin
We establish irrational constants, that contribute to the positronium lifetime at $O(α)$ and $O(α^2)$ order. In particular we show, that a new type of constants appear, which are not related to Euler--Zagier sums or multiple $ζ$ values.
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Corrections $\sim α^2 $ to the positronium decay rate, induced by one--loop vacuum polarization diagram, are calculated. Their relative values are $0.4468(3)(α/π)^2$ for para- and $0.960(3)(α/π)^2$ for orthopositronium.
Relativistic corrections to the positronium decay rate are calculated. They are close to $40(α/π)^2$ and $46(α/π)^2$ for singlet and triplet states respectively.
Positronium, the electron-positron bound state, is described to a good approximation by pure QED. The states of positronium have definite values of C and P. Consequently, positronium is an attractive system for the investigation of possible violations of the discrete symmetries in the leptonic sector. We discuss signals for CP and CPT violation in the decay of spin-polarized orthopositronium and show where such correlations might arise in the context of the Standard-Model Extension.
Self-energy corrections of order O(alpha^2) to the parapositronium and orthopositronium decay rates are calculated. Numerical values of the corresponding coefficients are B_p=-3.74, B_o=2.02.
We briefly review the theoretical and experimental results concerning decays of positronium. Possible solutions of the "orthopositronium lifetime puzzle" are discussed. Positronium annihilation into neutrinos is examined and disagreement is found with previously published results.
We investigate the invisible decay of positronium to probe the fermionic light dark matter mediated by the dark $Z$ boson. Too tiny is the invisible decay rate of positronium through weak interaction in the standard model to be detected in the experiment. We show that it can be enhanced to be observed in the future if the dark matter is lighter than the electron in the dark $Z$ model. We also compute the relic abundance of such light dark matter and discuss the Big Bang Nucleosynthesis constraint with an alternative thermal history scenario.
Two-photon decay of para-positronium within a composite approach
本文在复合量子场论框架下研究仲正电子素双光子衰变，通过考虑电子-正电子 dressing、Weinberg 复合性条件及三角形图，揭示了顶点函数选择对衰变率的影响，并展望了其他衰变通道。
Whether in the Standard Model or beyond it, neutrinos contribute to the invisible decay mode of orthopositronium but practically not at all to that of parapositronium. Although this remark does not resolve the orthopositronium decay puzzle, it allows for upper bounds to be set on neutrino magnetic moments.
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 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.
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…
The weak decay constant of positronium
本研究针对正电子素弱相互作用部分被抑制的问题，扩展复合QFT框架并引入仲正电子素弱衰变常数，量化其与弱轴流的耦合，通过数值计算及与夸克偶素的比较确定了连接正电子素与自身组分的顶点函数。
A QFT scalar toy model analogous to positronium and pion decays
本文在标量QFT中通过三角形图研究大质量态衰变为两个无质量粒子，类比π介子和正电子素衰变，探讨相对论与非相对论束缚态的异同。
The present status of theoretical and experimental investigations of the decay rate of a positronium is considered. The increasing interest to this problem has been caused by the disagreement of the calculated value of $Γ_3 (o-Ps)$ and the recent series of precise experiments. The necessity of new calculations on the basis of the quantum field methods in bound state theory is pointed out with taking into account the dependence of the interaction kernel on relative energies.
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 rederive here in a simple and transparent way the master formula for the dominant part of large relativistic corrections to the positronium decay rate.
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…
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 logarithmically enhanced alpha^3 ln(1/alpha) corrections to the para- and orthopositronium decay widths are calculated in the framework of dimensionally regularized nonrelativistic quantum electrodynamics.In the case of parapositronium, the correction is negative, approximately doubles the effect of the leading logarithmic alpha^3 ln^2(1/alpha) one, and is comparable to the nonlogarithmic O(alpha^2) one. As for orthopositronium, the correction is positive and almost cancels the alpha^3 ln^2(1/alpha) one. The uncertainties in the theoretical predictions for the decay widths are reduced.
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.
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 …
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 …
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.
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.
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.
We discuss positronium decays with emphasis on tests of fundamental symmetries and the constraints from measurements of other precision observables involving electrons and photons.
Despite its very short lifetime positronium provides us with a number of accurate tests of the bound state QED. In this note a brief overview of QED theory and precision experiments on the spectrum and annihilation decay of the positronium atom is presented. Special attention is paid to the accuracy of theoretical predictions.
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 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…
A first result related to a CPT test in the decay of ortho-positronium based on data collected by means of the J-PET detector is already available, and a new test of CP symmetry is under investigation. Both results are based on the determination of angular correlations between momenta of gamma rays and other vector properties of the investigated system. Here, arguments for the possible usage of data collected by the J-PET group to test CPT symmetry within the Standard-Model Extension framework are shortly presented.
Following recent theoretical results, it is suggested that positronium (Ps) might undergo spontaneous oscillations between two 4D spacetime 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 non accelerator experiments this new invisible decay mode.
Positronium hydride decay into proton, electron, and one or zero photons
本文确定了氢化正电子素PsH在两个稀有衰变通道中的衰变率，纠正了先前研究分别高估约2倍和700倍的问题，并利用变分法确认了其多项静态性质。
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…
Unparticles as suggested recently by Georgi have surprising phenomenological implications, distinctive from any other new physics that we know of. But they must interact very feebly with ordinary matter to have avoided detection thus far. We determine how feebly they can interact with the electron, using the precisely measured quantities in QED: the electron g-2 and the bounds on invisible and exotic positronium decays. The most stringent bound comes from invisible ortho-positronium decays: the effective energy scale entering the vector unparticle-electron interaction must exceed 4 x 10^5 TeV …
Ortho-Positronium Three-Photon Decays: Physics Constraints and a Closed-Form Energy Method for Annihilation Vertex Reconstruction
本文研究正正电子对三光子衰变的物理基础，探讨能量动量守恒对物理解空间的约束，并提出一种基于能量的顶点重建算法。
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 …
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 calculate the lifetime of both the o-Ps and the p-Ps positronium annihilation decay $ Ps\toγγ$ in the strong circular polarized laser field. We take a strategy of the factorization to separate the effects caused by the Coulomb interaction and the strong laser field interaction. It is factorized in the time direction but not in the space direction. Our results show that in the laser with long wavelength and high intensity, the lifetimes of those Ps states are dramatically increased. For $\rm CO_2$ laser with $10\, μm$ wavelength and $10^{13} W/cm^2$ intensity, lifetime of the spin-single pos…
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 Physics and Biomedical Applications
本文综述正电子素在QED检验、新物理搜寻及生物医学成像中的双重价值，并重点提出利用PET中高达40%的正电子经正电子素湮灭这一事实，将正电子素发展为组织病理与氧化程度的临床生物标志物。
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 $M_B$…
Weak decay of the positronium ion
研究正电子素离子通过弱相互作用衰变为电子和中微子对的稀有过程，计算衰变率并与正电子素弱衰变比较。
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 …
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.
The order - αradiative corrections to the differential decay rate of polarized orthopositronium are obtained. Their influences on the three photons coincidence rate as a function of positronium polarization is considered.
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.
A kind of asymptotic expansion for calculation of the (para)positronium decay rate is formulated. The method is completely relativistic and gauge invariant. The expansion goes over the inverse square of relative momentum $k$ of two photons in Euclidean region and the actual width is determined at $k^2=-m^2$, $m$ being the electron mass.
Discrete symmetries tested at 10$^{-4}$ precision using linear polarization of photons from positronium annihilations
本研究利用J-PET中康普顿散射逐事件测定正—正电子素湮灭光子的偏振，在无需外磁场控制自旋的情况下，以10$^{-4}$精度检验P、T和CP对称性，结果与QED预期一致。
Positronium decay into a muon-antimuon pair by virtue of the interaction with a superintense laser field of linear polarization is considered. The minimum laser intensity required amounts to a few 10^22 W/cm^2 in the near-infrared frequency range. Within the framework of laser-dressed quantum electrodynamics, the total reaction rate is calculated and related to the cross section for field-free electron-positron annihilation into muons. The muons are created with ultrarelativistic energies and emitted under narrow angles along the laser propagation direction. The dynamical properties of the muo…
Positronium decay rates are computed at the one-loop level, using convolution-type factorized amplitudes. The dynamics of this factorization is probed with dispersion relations, showing that unallowed approximations are usually made, and some ordre alpha^2 corrections missed. Further, we discuss the relevance of the Schrodinger wavefunction as the basis for perturbative calculations. Finally, we apply our formalism to the parapositronium two-photon decay.
Comments on the publication "Discrete symmetries tested at 10e-4 precision using linear polarization of photons from positronium annihilations" by P. Moskal et al
本文针对Moskal等人声称的高精度正电子素衰变分立对称性检验，从理论关联、方法依据、装置表征等多方面指出其研究存在的问题，否定了该关联测量的物理有效性。
Quantum electrodynamics is the first successful and still the most successful quantum field theory. Simple atoms, being essentially QED systems, allow highly accurate theoretical predictions. Because of their simple spectra, such atoms have been also efficiently studied experimentally frequently offering the most precisely measured quantities. Our review is devoted to comparison of theory and experiment in the field of precision physics of light simple atoms. In particular, we consider the Lamb shift in the hydrogen atom, the hyperfine structure in hydrogen, deuterium, helium-3 ion, muonium an…
Recent results on second order quantum corrections to semileptonic decays of b quarks and positronium spectroscopy are reviewed. Similarities between calculations in these seemingly different problems are demonstrated. Technical aspects of solving systems of recurrence relations, and application of dimensional regularization to bound states are explained.
$(τ^+τ^-)_b$ is an atom of simple hydrogenlike structure similar to positronium $(e^+e^-)_b$ and $(μ^+μ^-)_b$. In this paper energy levels and decay widths of different decay channels of $(τ^+τ^-)_b$ are given. Cross section of production of this atomic system in $e^+e^-$ annihilation taking into account radiative corrections is calculated. According to our estimates 886 $(τ^+τ^-)_b$ atoms may be produced at BEPCII and 29 $(τ^+τ^-)_b$ atoms are produced at VEPP-4M under the present experimental conditions.
Recently, much work has been devoted to the calculation of order $α$ corrections to the decay rate of pionium, the $π^+ π^-$ bound state. In previous calculations, nonrelativistic QED corrections were neglected since they start at order $α^2$ in hydrogen and positronium. In this note, we point out that there is one correction which is actually of order $α$ times a function of the ratio $μ_r α/ m_e$, where $μ_r$ is the reduced mass of the system. When $μ_r α\ll m_e$, this function can be Taylor expanded and leads to higher order corrections. When $μ_r α\approx m_e$, as is the case in pionium, t…
We present a theory with axion flux monodromies coupled to gravity, that reduces to the local vacuum energy sequester below the axion mass scales. If the axion potentials include a term generated by nonperturbative couplings to gauge sectors, with a decay constant incommensurate with monodromy periods, the low energy potential germinates a landscape of irrational axion vacua, with arbitrarily small cosmological constants. The sensitivity of the values of cosmological constants to unknown UV physics can be greatly reduced. The variation of the cosmological constant in each vacuum, from one orde…
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