Parapositronium Decay Research Articles

Application of quantum entanglement induced polarization for dual-positron and prompt gamma imaging.

The intrinsic resolution of Positron Emission Tomography (PET) imaging is bound by positron range effects, wherein the radioactive decay of the imaging tracer occurs at a disjoint location from positron annihilation. Compounding this issue are the variable ranges positrons achieve, depending on tracer species (the energy they are emitted with) and the medium they travel in (bone vs soft tissue, for example) - causing the range to span more than an order of magnitude across various study scenarios (~0.19 mm to ~6.4 mm). Radioisotopes, such as Zr-89, exhibit dual emissions of positron and prompt gammas, offering an opportunity for accurate tracer positioning as prompt gammas originate from the tracer location. These multi-emission radiotracers have historically suffered from increased noise corresponding to the third gamma interfering in annihilation gamma coincidence pairing. Recent advancements, however, have brought to light the unique property of annihilation gammas having scattering kinematics distinct from random gamma pairs. These properties are born from the singular quantum entanglement state available to the gamma pair following para-positronium decay which prescribes linearly orthogonal polarization. Such coherent polarization is not shared by prompt gamma emissions, offering an opportunity for their discrimination. We present an investigation into this technique, comparing the distribution of relevant scattering kinematics of entangled annihilation gammas and corresponding prompt gammas via a Monte Carlo simulation.

Two-loop master integrals for pseudo-scalar quarkonium and leptonium production and decay

We compute the master integrals relevant for the two-loop corrections to pseudo-scalar quarkonium and leptonium production and decay. We present both analytic and high-precision numerical results. The analytic expressions are given in terms of multiple polylogarithms (MPLs), elliptic multiple polylogarithms (eMPLs) and iterated integrals of Eisenstein series. As an application of our results, we obtain for the first time an analytic expression for the two-loop amplitude for para-positronium decay to two photons at two loops.

Two-loop diagrams in nonrelativistic QCD with elliptics

We consider two-loop two-, three-, and four-point diagrams with elliptic subgraphs involving two different masses, m and M. Such diagrams generally arise in matching procedures within nonrelativistic QCD and QED and are relevant, e.g., for top-quark pair production at threshold and parapositronium decay. We present the obtained results in several different representations: series solution with binomial coefficients, integral representation, and representation in terms of generalized hypergeometric functions. The results are valid up to terms of O(ε) in d=4−2ε space-time dimensions. In the limit of equal masses, m=M, the obtained results are written in terms of elliptic constants with explicit series representations.

Parapositronium can decay into three photons

We calculate the decay rate and spectrum for the decay of parapositronium into three photons. This process violates charge conjugation symmetry. It is forbidden within quantum electrodynamics but proceeds through the weak interaction. The branching ratio we find is fifty orders of magnitude smaller than the previous estimate.

Positronium energy levels at ordermα7: Light-by-light scattering in the two-photon-annihilation channel

Recent and ongoing experimental work on the positronium spectrum motivates new efforts to calculate positronium energies at the level of $O({\ensuremath{\alpha}}^{3})$ corrections to the lowest-order result. 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 $1.58377\phantom{\rule{0.16em}{0ex}}(8)m{\ensuremath{\alpha}}^{7}/{\ensuremath{\pi}}^{3}$ for the $n=1$ singlet state, correcting the ground-state hyperfine splitting by $\ensuremath{-}6.95$ 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.

Two-photon decays of hadronic molecules

In many calculations of the two-photon decay of hadronic molecules, the decay matrix element is estimated using the wave function at the origin prescription, in analogy to the two-photon decay of parapositronium. We question the applicability of this procedure to the two-photon decay of hadronic molecules for it introduces an uncontrolled model dependence into the calculation. As an alternative approach, we propose an explicit evaluation of the hadron loop. For shallow bound states, this can be done as an expansion in powers of the range of the molecule binding force $1/\ensuremath{\beta}$. In the leading order one gets the well-known pointlike limit answer. We estimate, in a self-consistent and gauge-invariant way, the leading range corrections for the two-photon decay width of weakly bound hadronic molecules emerging from kaon loops. We find them to be small, of order $\mathcal{O}(m\ensuremath{\epsilon}/{\ensuremath{\beta}}^{2})$, where $m$ and $\ensuremath{\epsilon}$ denote the mass of the constituents and the binding energy, respectively. The role of possible short-ranged operators and of the width of the scalars remains to be investigated.

Spin dependence of heavy quarkonium production and annihilation rates: complete next-to-next-to-leading logarithmic result

The ratio of the photon mediated production or annihilation rates of spin triplet and spin singlet heavy quarkonium states is computed to the next-to-next-to-leading logarithmic accuracy within the nonrelativistic renormalization group approach. The result is presented in analytical form and applied to the phenomenology of t t ¯ , b b ¯ and c c ¯ systems. The use of the nonrelativistic renormalization group considerably improves the behaviour of the perturbative expansion and is crucial for accurate theoretical analysis. For bottomonium decays we predict Γ ( η b ( 1 S ) → γ γ ) = 0.659 ± 0.089 ( th. ) − 0.018 + 0.019 ( δ α s ) ± 0.015 ( exp. ) keV . Our results question the accuracy of the existing extractions of the strong coupling constant from the bottomonium annihilation. As a by-product we obtain a novel result for the ratio of the ortho- and parapositronium decay rates: the corrections of order α 4 ln 2 α and α 5 ln 3 α .

Positron scattering by molecules

Molecules are fascinating targets for the scattering of incident positrons in that they represent an increased level of complexity over that for atomic targets. Some of the measurements made in our laboratory for total, differential quasielastic, and positronium formation cross-sections for positrons (and electrons) scattered from various molecular targets are discussed. Comparisons between positron and electron scattering by molecules have revealed some intriguing similarities and differences. The more symmetric molecules are found in certain cases to have quite similar behavior to atomic targets, while the behavior for less symmetric molecules is quite different. Ratios of signals originating from the 3 gamma decay of ortho-positronium to that from 2 gamma decay of para-positronium and ortho-Ps conversion appears to provide information about the threshold behavior of positronium formation.

Order alpha(3) ln(1/alpha) corrections to positronium decays

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 uncertainty in the theoretical prediction for the parapositronium decay width is reduced to 10(-2) &mgr;s(-1).

Calculation ofα2corrections to parapositronium decay

We present details of our recent calculation of ${\ensuremath{\alpha}}^{2}$ corrections to the parapositronium decay into two photons. These corrections are rather small and our final result for the parapositronium lifetime agrees well with the most recent measurement. Implications for orthopositronium decays are briefly discussed.

Positronium in the undergraduate laboratory

Positronium is an exotic atom formed by an electron and its antiparticle, the positron. Orthopositronium, which is the state with total spin 1, has a decay constant of about 7.05 μs−1 and decays primarily into three gamma rays. A relatively simple experiment is described which will allow students to detect and measure the lifetime of orthopositronium in gases using apparatus often found at undergraduate institutions. Other effects, such as parapositronium decay, pick-off, and thermalization, can also be demonstrated.

Order-α radiative correction to the rate for parapositronium decay to four photons

We have calculated the $O(\ensuremath{\alpha})$ radiative correction affecting the decay rate of parapositronium to four photons. Our result for the rate is $\ensuremath{\Gamma}(4\ensuremath{\gamma})={\ensuremath{\Gamma}}_{\mathrm{LO}}(4\ensuremath{\gamma})[1\ensuremath{-}14.5(6)\ensuremath{\alpha}/\ensuremath{\pi}+O({\ensuremath{\alpha}}^{2})],$ where ${\ensuremath{\Gamma}}_{\mathrm{LO}}(4\ensuremath{\gamma})$ is the lowest order four-photon decay rate. Our prediction for the four-photon to two-photon branching ratio, including all $O(\ensuremath{\alpha})$ corrections, is $R=1.4388(21)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}.$ We also have a higher precision result for the lowest-order rate: ${\ensuremath{\Gamma}}_{\mathrm{LO}}(4\ensuremath{\gamma})=0.0138957(4)m{\ensuremath{\alpha}}^{7}.$

Search for very weakly interacting, short-lived, C-odd bosons and the orthopositronium decay rate problem

The discrepancy between theory and experiment for the orthopositronium (o-Ps) decay rate could be resolved by an exotic decay branch o-Ps\ensuremath{\rightarrow}${\mathrm{X}}^{0}$\ensuremath{\gamma}\ensuremath{\gamma}, where ${\mathrm{X}}^{0}$ is a low-mass C-odd boson. An experimental search for ${\mathrm{X}}^{0}$ is reported in which Compton-like interactions with electrons or decay \ensuremath{\gamma} rays (${\mathrm{X}}^{0}$\ensuremath{\rightarrow}3\ensuremath{\gamma}) could be detected. None are observed and sensitive, but model-dependent limits are set (for two specific models). One model, testable by this method, allows the good agreement between theory and experiment for the parapositronium decay rate to be reconciled with the disagreement for the o-Ps decay rate.

Four-photon decay of orthopositronium: A test of charge-conjugation invariance.

Charge-conjugation ({ital C}) invariance demands that ortho- and parapositronium decay into an odd number and an even number of photons, respectively. For the test of the {ital C} invariance, we searched for a {ital C}-violating process, i.e., four-photon decay from orthopositronium, using a multi-{gamma}-ray spectrometer. No {ital C}-violating process was observed leading to the upper limit as 2.6{times}10{sup {minus}6} at 90{percent} confidence level for the branching ratio of four- to three-photon decays from orthopositronium. {copyright} {ital 1996 The American Physical Society.}

Two-loop corrections to the orthopositronium and parapositronium decay rates due to vacuum polarization.

We have calculated all O(${\mathrm{\ensuremath{\alpha}}}^{2}$) corrections to the orthopositronium and parapositronium decay rates due to vacuum polarization graphs. These contributions are independent of gauge and bound state formalism. Our results are +0.964 960(4) (\ensuremath{\alpha}/\ensuremath{\pi}${)}^{2}$ for orthopositronium and +0.447 343 0(6) (\ensuremath{\alpha}/\ensuremath{\pi}${)}^{2}$ for parapositronium relative to the lowest order rates. We also have an improved result for the one-loop one-photon-annihilation orthopositronium decay graph of -0.814 057 4(10) (\ensuremath{\alpha}/\ensuremath{\pi}) times the lowest order rate.

Further measurements of positron annihilation lifetimes in neutron irradiated quartz

Crystalline quartz samples, irradiated with fast neutrons, have been studied using positron annihilation techniques. An improved setup was used, allowing much better accuracy than in previous measurements. The positron annihilation lifetime characteristics were measured for the doses: 1.67, 5.7, 9.9, 21, 47 × 1018 n/cm2. A mean lifetime analysis was done as well as two three-component analyses: one for a lifetime feed at 120 ps and one without any fixed lifetime. The analysis shows the presence of free parapositronium decay as anticipated, but previously masked by the contributions of the sample holder. It comfirms the existence of a long lifetime of about 1000 ps for which the intensity increases with dose. Contrary to the previous results, a distinct increase of the length of the long lifetime is not found in the studied dose range, which is in agreement with X-ray studies.

Radiative corrections to positronium decay

In this work a method for calculating radiative corrections to positronium decay is presented that is direct, and allows for a systematic extension applicable to the calculation of corrections beyond the first [ o( α)] correction. An expression for the decay amplitude in terms of the Bethe-Salpeter wavefunction is employed. The Bethe-Salpeter wavefunction is evaluated perturbatively in a scheme having a lowest-order bound state equation that is exactly soluble. The decay amplitude is evaluated in Coulomb gauge, without the introduction of a photon mass. One-loop renormalization in Coulomb gauge is shown to be consistent. Using this method the known analytic result for the o( α) correction to the parapositronium decay rate is obtained. The same method is applied to orthopositronium, and the existing theoretical discrepancy in the value of the o( α) correction to the decay rate is resolved. This o( α) correction is obtained with an error which corresponds to an uncertainty in the total rate much smaller than α 2 Γ LO (where Γ LO is the lowest-order rate). Also, the o( α) correction to the differential decay rate is computed for the first time.

The temperature dependence of the two positronium bubble states in liquid SF 6

Positron lifetime measurements have been performed on liquid SF 6 in the temperature range from −45°C to 71°C ( T c = 45.65°C). The positron lifetime spectra were resolved into four lifetime components. In the order of increasing lifetimes the four lifetime components are associated with the decay of para-positronium ( p-Ps), free positrons, ortho-positronium ( o-Ps) from a small bubble state, and o-Ps from a large bubble state. The lifetime of o-Ps annihilating from the large bubble state τ 4 increases from 5.7 ns at −45°C to 19.5 ns at 53°C. The lifetime of o-Ps annihilating from the small bubble state τ 3 was found to be 2–2.5 ns in the main part of the temperature range studied. Apparently, this is the first observation of two different o-Ps states in a liquid. The intensity I 4 ( I 3) increases (decreases) from 16.9% (16%) at −45°C to 47.2% (6.4%) at the critical point while above I 3 and I 4 are essentially temperature independent. The large Ps bubble state seems to be similar to the Ps bubble state found in most liquids.

Radiative corrections to parapositronium decay

Radiative corrections to the two-gamma decay of parapositronium are examined. Special care is taken in the handling of the so-called binding diagram; in particular, the limiting procedure related to the infrared divergence is considered carefully. The general covariant gauges and the Fried-Yennie gauge are used in the computation to see that gauge invariance is accounted for. The order α correction of Harris and Brown is confirmed. In addition, from a sharp peak of the matrix element at low momentum and the low-momentum correction to the wave function, an α 2 ln α −1 correction is derived.

Positron lifetime study of the transition from glassy to normal liquid state for two phenyl ethers

Positron lifetime measurements are reported as a function of temperature for bis[m-(m-phenoxyphenoxy)phenyl] ether and m-phenoxyphenyl-m-(m-phenoxyphenoxy)phenyl ether. The decay curves were analysed in terms of three lifetime components; two short lifetimes of typically 200 and 500 ps associated with the decay of para-positronium(p-Ps) and positrons and a longer component attributed to decay of the ortho-positronium (o-Ps). The o-Ps lifetime is nearly independent of temperature in the region from 213 to 233 K, above this it becomes strongly temperature dependent. The change in the temperature dependence at ≈ 233 K is associated with the glass transition for these liquids. A further change in the temperature dependence of the o-Ps lifetime was observed above 313 K where it becomes once more only weakly temperature dependent. Below the glass transition (Tg) Ps is probably trapped in pre-existing holes, which may be slightly enlarged due to the presence of Ps. Above 313 K Ps is apparently localized in a thermal equilibrated bubble. The size of the bubble is probably independent of the size of the pre-existing holes, as described by the “bubble model”. The transition between those two cases occurs between Tg and 313 K, reflecting the changes in the free volume and the thermal motion of the molecules as the temperature is increased. The results are correlated to viscosity data and a molecular interpretation is presented.