<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mi>−</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>atom in chiral perturbation theory

Ivanov, Mikhail A.; Lyubovitskij, Valery E.; Lipartia, E. Z.; Rusetsky, Akaki

doi:10.1103/physrevd.58.094024

Cited by 29 publications

(15 citation statements)

References 30 publications

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“…[12], while our result has no term involving ln α and contains the scattering parameters that include the effect of electromagnetic interaction. As Ivanov et al [15] have pointed out, these differences come from the same source: the treatment of Coulomb photons. In our method the Coulomb potential is included in the RSEs (1), which are solved exactly.…”

Section: From Pionium Data To Hadronic Pion-pion Scattering Lengthsmentioning

confidence: 99%

New light on electromagnetic corrections to the scattering parameters obtained from experiments on pionium

et al. 2002

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We calculate the electromagnetic corrections needed to obtain isospin invariant hadronic pion-pion s-wave scattering lengths a 0 , a 2 from the elements a cc , a 0c of the s-wave scattering matrix for the (π + π − , π 0 π 0 ) system at the π + π − threshold. The latter can be extracted from experiments on the π + π − atom (pionium). Our calculation uses energy independent hadronic pion-pion potentials V 0 , V 2 that satisfactorily reproduce the low-energy phase shifts given by two-loop chiral perturbation theory, with the hadronic mass of the pion taken first as the charged pion mass and then as the neutral pion mass. We also take into account an important relativistic effect whose inclusion influences the corrections considerably. PACS: 13.75. Gx,25.80.Dj

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Section: From Pionium Data To Hadronic Pion-pion Scattering Lengthsmentioning

confidence: 99%

New light on electromagnetic corrections to the scattering parameters obtained from experiments on pionium

et al. 2002

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“…2 In this respect it is worth noting that the pole term of Eq. ͑7͒ is separable with respect to initial and final state variables, thus for a two-body system ⌽ ( P)ϵ⌽ ( P,p) is a function of the initial relative momentum p while ⌽( P)ϵ⌽( P,pЈ) is a function of the final relative momentum pЈ.…”

Section: A Basic Equationsmentioning

confidence: 99%

Perturbation theory for bound states and resonances where potentials and propagators have arbitrary energy dependence

Kvinikhidze

Blankleider

2003

Phys. Rev. D

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Standard derivations of ''time-independent perturbation theory'' of quantum mechanics cannot be applied to the general case where potentials are energy dependent or where the inverse free Green function is a nonlinear function of energy. Such derivations cannot be used, for example, in the context of relativistic quantum field theory. Here we solve this problem by providing a new, general formulation of perturbation theory for calculating the changes in the energy spectrum and wave function of bound states and resonances induced by perturbations to the Hamiltonian. Although our derivation is valid for energy-dependent potentials and is not restricted to inverse free Green functions that are linear in the energy, the expressions obtained for the energy and wave function corrections are compact, practical, and maximally similar to the ones of quantum mechanics. For the case of relativistic quantum field theory, our approach provides a direct covariant way of obtaining corrections to wave functions that are not in the center of mass frame.

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“…Such an evaluation was recently done by several authors. In the frameworks of quantum field the-ory and χP T , three different methods of evaluation have led to the same estimate, of the order of 6%, of these corrections [6][7][8][9]. The first method uses a three-dimensionally reduced form of the Bethe-Salpeter equation (constraint theory approach) and deals with an off-mass shell formalism [6,7].…”

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confidence: 99%

“…The first method uses a three-dimensionally reduced form of the Bethe-Salpeter equation (constraint theory approach) and deals with an off-mass shell formalism [6,7]. The second method uses the Bethe-Salpeter equation with the Coulomb gauge [8]. The third one uses the approach of nonrelativistic effective theory [9].…”

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Pionium lifetime and ππ scattering lengths in generalized chiral perturbation theory

Sazdjian

2000

Nuclear Physics B - Proceedings Supplements

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The relationship between the pionium lifetime and the ππ scattering lengths is established, including the sizable electromagnetic corrections. The bound state formalism that is used is that of constraint theory which provides a covariant three-dimensional reduction of the Bethe-Salpeter equation. The framework of generalized chiral perturbation theory allows then an analysis of the lifetime value as a function of the ππ scattering lengths, the latter being dependent on the quark condensate value.The possible measurement of the pionium (π + π − atom) lifetime with a 10% precision in the DIRAC experiment at CERN [1] is expected to allow a determination of the combination (a 0 0 − a 2 0 ) of the ππ scattering lengths with 5% accuracy; here, a I 0 is the strong interaction (dimensionless) S-wave scattering length in the isospin I channel. The strong interaction scattering lengths a 0 0 and a 2 0 have been evaluated in the literature in the framework of chiral perturbation theory (χP T ) to two-loop order of the chiral effective lagrangian [2][3][4]. Therefore, the pionium lifetime measurement provides a high precision experimental test of chiral perturbation theory predictions.The nonrelativistic formula of the pionium lifetime in lowest order of electromagnetic interactions was first evaluated by Deser et al. [5]. It reads:where ∆m π = m π + −m π 0 and ψ +− (0) is the wave function of the pionium at the origin (in x-space).A precise comparison of the theoretical values of the strong interaction scattering lengths with experimental data necessitates, however, an evaluation of the corrections of order O(α) (α being the fine structure constant) to the above formula. Such an evaluation was recently done by several authors. In the frameworks of quantum field the-ory and χP T , three different methods of evaluation have led to the same estimate, of the order of 6%, of these corrections [6][7][8][9]. The first method uses a three-dimensionally reduced form of the Bethe-Salpeter equation (constraint theory approach) and deals with an off-mass shell formalism [6,7]. The second method uses the Bethe-Salpeter equation with the Coulomb gauge [8]. The third one uses the approach of nonrelativistic effective theory [9].The pionium lifetime, with the sizable O(α) corrections included in, can be represented as:where Re M 00,+− is the real part of the onmass shell scattering amplitude of the process π + π − → π 0 π 0 , calculated at threshold, in the presence of electromagnetic interactions and from which singularities of the infra-red photons have been appropriately subtracted [10]; the factor γ represents contributions at second-order of perturbation theory with respect to the nonrelativistic zeroth-order Coulomb hamiltonian of the bound state formalism. The explicit expressions

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π+π−atom in chiral perturbation theory

Cited by 29 publications

References 30 publications

New light on electromagnetic corrections to the scattering parameters obtained from experiments on pionium

New light on electromagnetic corrections to the scattering parameters obtained from experiments on pionium

Perturbation theory for bound states and resonances where potentials and propagators have arbitrary energy dependence

Pionium lifetime and ππ scattering lengths in generalized chiral perturbation theory

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