Calculation of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>α</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>corrections to parapositronium decay

Czarnecki, Andrzej; Melnikov, Kirill; Yelkhovsky, Alexander

doi:10.1103/physreva.61.052502

Cited by 35 publications

(21 citation statements)

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“…(1), then the complete result for δ ann Γ (2) decreases and is in accord with the expectations advocated in Ref. [3].We recall, that in bound state calculations there are two different types of contributions. The hard corrections arise as contributions of virtual photons with momenta k ∼ m. These contributions renormalize local operators in the non-relativistic Hamiltonian.…”

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confidence: 73%

Virtual annihilation contribution to orthopositronium decay rate

1999

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Order α 2 contribution to the orthopositronium decay rate due to one-photon virtual annihilation is found to be δannΓ (2) = α π 2 π 2 ln α − 0.8622(9) ΓLO.PACS numbers: 36.10.Dr, 06.20.Jr, 12.20.Ds, 31.30.Jv Positronium, the bound state of an electron and positron, is an excellent laboratory to test our understanding of Quantum Electrodynamics of bound states. Although in the majority of cases the agreement between theory and experiment is very good, the case of orthopositronium (o-Ps) decay into three photons is outstanding, since the theoretical predictions differ by about 6 standard deviations from the most accurate experimental result [1] (see, however, an alternative result in [2]). Provided that the experiment [1] is correct, the theory can only be rescued if the second order correction to the o-Ps lifetime turns out to be ∼ 250(α/π) 2 Γ LO . It is however difficult to imagine how such a large number could appear in the perturbative calculations, even if the bound state is involved. This point of view is supported by a recent complete calculation of the O(α 2 ) correction to the parapositronium (p-Ps) decay rate into two photons [3]. It has shown that the "natural scale" of the gauge-invariant contributions is [several units]×(α/π) 2 Γ LO . For this reason, it was conjectured in [3] that the O(α 2 ) correction to the orthopositronium decay rate o-Ps → 3γ most likely is of the same order of magnitude.At first sight, the result of Ref.[4],for the gauge-invariant contribution to the o-Ps→ 3γ decay rate induced by the single-photon virtual annihilation, does not provide much support for this conjec- * e-mail: g adkins@acad.fandm.edu † e-mail: melnikov@particle.physik.uni-karlsruhe.de ‡ e-mail: yelkhovsky@inp.nsk.su ture. In fact, the value of the non-logarithmic constant in Eq. (1) is larger by approximately one order of magnitude than the values of coefficients in gauge-invariant contributions to p-Ps→ 2γ decay rate. In this note we would like to point out that the result for the second order correction to virtual annihilation contribution given in Eq. (1) is incomplete, in that closely related contributions should be included as well. It turns out that if the missing pieces are added to Eq.(1), then the complete result for δ ann Γ (2) decreases and is in accord with the expectations advocated in Ref. [3].We recall, that in bound state calculations there are two different types of contributions. The hard corrections arise as contributions of virtual photons with momenta k ∼ m. These contributions renormalize local operators in the non-relativistic Hamiltonian. For this reason they can be computed without any reference to the bound state.On the contrary, the soft scale contributions come from a typical momenta scale k ∼ mα in virtual loops, and for this reason are sensitive to the bound state dynamics. For δ ann Γ (2) , it is easy to see that the soft scale contribution reads:whereis the reduced Green function of the Schrödinger equation in the Coulomb field.Let us write the expansion of the Green function ...

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confidence: 73%

Virtual annihilation contribution to orthopositronium decay rate

1999

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“…When this paper was in preparation we learned that the same result was just obtained in the NRQED framework by Czarnecki and Melnikov [9]. Numerically, the correction in Eq.…”

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confidence: 62%

Radiative-recoil corrections of orderα(Zα)5(m/M)mto the Lamb shift revisited

2001

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The results and main steps of an analytic calculation of radiative-recoil corrections of order α(Zα) 5 (m/M )m to the Lamb shift in hydrogen are presented. The calculations are performed in the infrared safe Yennie gauge. The discrepancy between two previous numerical calculations of these corrections existing in the literature is resolved. Our new result eliminates the largest source of the theoretical uncertainty in the magnitude of the deuterium-hydrogen isotope shift.

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“…The two-photon decay takes place when an electron-positron pair is in the singlet state (the statistical weight of which is w = 1/4), while the three-photon decay occurs in the triplet state (w = 3/4). The expressions for 2γ and 3γ in the positronium atom, including several leading radiative corrections, are known [56][57][58]. In this work, however, we must limit ourselves with the corrections proportional to .…”

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confidence: 99%

Ground-state energy and relativistic corrections for positronium hydride

Bubin

Varga

2011

Phys. Rev. A

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Variational calculations of the ground state of positronium hydride (HPs) are reported, including various expectation values, electron-positron annihilation rates, and leading relativistic corrections to the total and dissociation energies. The calculations have been performed using a basis set of 4000 thoroughly optimized explicitly correlated Gaussian basis functions. The relative accuracy of the variational energy upper bound is estimated to be of the order of 2×10 −10 , which is a significant improvement over previous nonrelativistic results.

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Calculation ofα2corrections to parapositronium decay

Cited by 35 publications

References 28 publications

Virtual annihilation contribution to orthopositronium decay rate

Virtual annihilation contribution to orthopositronium decay rate

Radiative-recoil corrections of orderα(Zα)5(m/M)mto the Lamb shift revisited

Ground-state energy and relativistic corrections for positronium hydride

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