Steven D. Bass
We discuss positronium decays with emphasis on tests of fundamental symmetries and the constraints from measurements of other precision observables involving electrons and photons.
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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.
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.
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.
Bound state problem in the relativistic QED is investigated by the functional integral methods. The ortho- para- positron mass difference is calculated. Contribution of the "nonphysical"$~$ time variable turned out to be important and leads to the nonanalytic dependence of the bound state mass of the order $α^{2\over3}$. It is shown that the relativistic and non-relativistic QED gives different results for this mass shift. In addition so-called abnormal states as "time excitations" arise. Sequential application of relativistic QED to bound state problem is in contradiction with real ortho- and…
Numerical results on the positronium spectrum in the front form of QED at large coupling constant are presented. Emphasis is put on the question whether one can derive an effective interaction at all, and whether this effective interaction is rotationally invariant. (Proceedings of Les Houches 1997)
To have an analytic understanding of the higher-twist structure functions, we calculate twist four longitudinal structure function for a positronium-like bound state in weak coupling light-front QED. We find that in the weakly coupled system, the fermionic part of $F_L$ is related to the kinetic energy of the fermions and not to the interaction. We verify a previously proposed sum rule in this limit, which in this case reduces to a relation connecting the kinetic and the potential energies to the binding energy of positronium. Using the analytic form of the wave function of positronium in this…
QED positronium and the exact renormalization group
本文在精确重整化群框架下结合维度正规化研究QED，通过引入实标量场描述正电子素束缚态，并用有效作用量拟设和低动量展开分析流方程。
A maximum value for the magnetic field is determined, which provides the full compensation of the positronium rest mass by the binding energy in the maximum symmetry state and disappearance of the energy gap separating the electron-positron system from the vacuum. The compensation becomes possible owing to the falling to the center phenomenon. The maximum magnetic field may be related to the vacuum and describe its structure.
An effective theory of the excited states of positronium is derived and some of its consequences are explored. At large physical separation, the binding of the electron and positron is assumed to be described completely by QED, whereas all short-ranged phenomena, including those within and beyond QED, can be accounted for with energy-dependent quantum defects. This theory has at least two practical applications. First, it provides an accurate and economical, yet largely QED-independent, means to fit the positronium spectrum in order to predict and compare the outcome of experiments. Second, ma…
We study the QED bound-state problem in a light-front hamiltonian approach. It is important to establish the equivalence (or not) of equal-time and light-front approaches in the well-understood arena of Quantum Electrodynamics. Along these lines, the singlet-triplet ground state spin splitting in positronium is calculated. The well-known result, $(7/6) α^2 Ryd$, is obtained analytically, which establishes the equivalence between the equal-time and light-front approaches (at least to this order). The true equivalence of the two approaches can only be established after higher-order calculations.…
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…
\\The Bethe-Salpeter equation in a strong magnetic field is studied for positronium atom in an ultra-relativistic regime, and a (hypercritical) value for the magnetic field is determined, which provides the full compensation of the positronium rest mass by the binding energy in the maximum symmetry state. The compensation becomes possible owing to the falling to the center phenomenon. The relativistic form in two-dimensional Minkowsky space is derived for the four-dimensional Bethe-Salpeter equation in the limit of an infinitely strong magnetic field, and used for finding the above hypercritic…
An "ultrafine" splitting in positronium between the $L=1$ spin-singlet state and the spin-average of the spin-triplet states is shown to arise only at order $α^6$. The QED prediction for $n=2$ states is $Δ_{2,P}=(683/172800)mα^6=73.7(1.2)$ kHz. This represents the smallest leading-order QED splitting known. Current experimental efforts could observe this splitting, and its observation can constrain new ultralight interactions, such as axions or $Z'$.
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。
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…
We study the QED bound-state problem in a light-front hamiltonian approach. Starting with a bare cutoff QED Hamiltonian, $H_{_{B}}$, with matrix elements between free states of drastically different energies removed, we perform a similarity transformation that removes the matrix elements between free states with energy differences between the bare cutoff, $Λ$, and effective cutoff, $\lam$ ($\lam < \Lam$). This generates effective interactions in the renormalized Hamiltonian, $H_{_{R}}$. These effective interactions are derived to order $α$ in this work, with $α\ll 1$. $H_{_{R}}$ is renormalize…
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, 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.
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.
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。
We review recent applications of the Two Body Dirac equations of constraint dynamics to meson spectroscopy and describe new extensions to three-body problems in their use in the study of baryon spectroscopy. We outline unique aspects of these equations for QED bound states that distinguish them among the various other approaches to the relativistic two body problem. Finally we discuss recent theorectial solutions of new peculiar bound states for positronium arising from the Two Body Dirac equations of constraint dynamics, assuming point particles for the electron and the positron.
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。
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 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 present a brief overview of precision tests of bound state QED and mainly pay our attention to laser spectroscopy as an appropriate tool for these tests. We particularly consider different precision tests of bound state QED theory based on the laser spectroscopy of optical transitions in hydrogen, muonium and positronium and related experiments.
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 …
We consider the most accurate tests of bound state QED, precision theory of simple atoms, related to the hyperfine splitting in light hydrogen-like atoms. We discuss the HFS interval of the 1s state in muonium and positronium and of the 2s state in hydrogen, deuterium and helium-3 ion. We summarize their QED theory and pay attention to involved effects of strong interactions. We also consider recent optical measurements of the 2s HFS interval in hydrogen and deuterium.
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 …
The soft photon theorem in U(1) gauge theories with only massless charged particles has recently been shown to be the Ward identity of an infinite-dimensional asymptotic symmetry group. This symmetry group is comprised of gauge transformations which approach angle-dependent constants at null infinity. In this paper, we extend the analysis to all U(1) theories, including those with massive charged particles such as QED.
The formulation of relativistic two-body bound state wave equations and the study of their relationship to quantum field theory began with work by Eddington and Gaunt in 1928. However, the large variety of approaches attempted in recent years shows that this problem still has no generally agreed-upon solution. We describe here a recent approach resulting from " Two-Body Dirac Equations" (emerging from Dirac's Relativistic Constraint Dynamics) that satisfies many of the requirements one would demand of a treatment of the relativistic two-body problem. We use its applications to QED bound states…
Recently, the contribution of positronium bound states to the electron anomalous magnetic moment was computed in Refs.[1,2]. It was argued there that this O(alpha^5) contribution is missed if electron g-2 is calculated within conventional perturbative QED and, as such, it must be added to the perturbative five-loop result. We show that this conclusion is flawed and that no additional contributions to g-2 are generated in QED beyond the perturbation theory.
We consider the scattering of massless particles coupled to an abelian gauge field in 2n-dimensional Minkowski spacetime. Weinberg's soft photon theorem is recast as Ward identities for infinitely many new nontrivial symmetries of the massless QED S-matrix, with one such identity arising for each propagation direction of the soft photon. These symmetries are identified as large gauge transformations with angle-dependent gauge parameters that are constant along the null generators of null infinity. Almost all of the symmetries are spontaneously broken in the standard vacuum and the soft photons…
Exclusive Leptonium Electroproduction
本研究在非相对论QED框架下计算ep碰撞中排他性矢量轻子偶素电产生的NLO QCD修正，指出Bethe–Heitler过程主导产生率，支持在EIC和JLab搜寻双μ子素，正电子素可用于精密QED研究。
We consider hyperfine splitting of 1s and, in part, of 2s levels in light hydrogen-like atoms: hydrogen, deuterium, tritium, helium-3 ion, muonium and positronium. We discuss present status of precision theory and experiment for the hfs intervals. We pay a special attention to a specific difference, D_{21} = 8 E_{hfs}(2s) - E_{hfs}(1s), which is known experimentally for hydrogen, deuterium and ^3He^+ ion. The difference is weakly affected by the effects of the nuclear structure and thus may be calculated with a high accuracy. We complete a calculation of the fourth order QED contributions to t…
In this paper we discuss the global symmetries and the renormalizibility of Lee-Wick scalar QED. In particular, in the "auxiliary-field" formalism we identify softly broken SO(1,1) global symmetries of the theory. We introduce SO(1,1) invariant gauge-fixing conditions that allow us to show in the two-field formalism directly that the number of superficially divergent amplitudes in a LW Abelian gauge theory is finite. To illustrate the renormalizability of the theory, we explicitly carry out the one-loop renormalization program in LW scalar QED and demonstrate how the counterterms required are …
An infinite number of physically nontrivial symmetries are found for abelian gauge theories with massless charged particles. They are generated by large $U(1)$ gauge transformations that asymptotically approach an arbitrary function $\varepsilon(z,\bar{z})$ on the conformal sphere at future null infinity ($\mathscr I^+$) but are independent of the retarded time. The value of $\varepsilon$ at past null infinity ($\mathscr I^-$) is determined from that on $\mathscr I^+$ by the condition that it take the same value at either end of any light ray crossing Minkowski space. The $\varepsilon\neq$ con…
It might be expected that only global symmetries are fundamental symmetries of Nature, whereas local symmetries and associated massless gauge fields could solely emerge due to spontaneous breaking of underlying spacetime symmetries involved, such as relativistic invariance and supersymmetry. This breaking, taken in the form of the nonlinear sigma-model type pattern for vector fields or superfields, puts essential restrictions on geometrical degrees of freedom of a physical field system that makes it to adjust itself in such a way that its global internal symmetry G turns into the local symmetr…
We identify infinitely many non-invertible generalized global symmetries in QED and QCD for the real world in the massless limit. In QED, while there is no conserved Noether current for the $U(1)_\text{A}$ axial symmetry because of the ABJ anomaly, for every rational angle $2πp/N$, we construct a conserved and gauge-invariant topological symmetry operator. Intuitively, it is a composition of the axial rotation and a fractional quantum Hall state coupled to the electromagnetic $U(1)$ gauge field. These conserved symmetry operators do not obey a group multiplication law, but a non-invertible fus…
We discuss the regularization and renormalization of QED with Lorentz and CPT violation, and argue that the coefficient of the Chern-Simons term is an independent parameter not determined by gauge invariance. We also study these issues in a model with spontaneous breaking of Lorentz and CPT symmetries and find an explicit relation with the ABJ anomaly. This explains the observed convergence of the induced Chern-Simons term.
Frohlich, Morchio and Strocchi long ago proved that Lorentz invariance is spontaneously broken in QED because of infrared effects. We develop a simple model where consequences of this breakdown can be explicitly and easily calculated. For this purpose, the superselected U(1) charge group of QED is extended to a superselected "Sky" group containing direction-dependent gauge transformations at infinity. It is the analog of the Spi group of gravity. As Lorentz transformations do not commute with Sky, they are spontaneously broken. These abelian considerations and model are extended to non-Abelian…
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