Rearranging pionless effective field theory

Beane, Silas R.; Savage, Martin J.

doi:10.1016/s0375-9474(01)01088-0

Cited by 177 publications

(277 citation statements)

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“…QED contributions to two-particle interactions in a FV will be considered in the context of the pionless EFT [46][47][48][49][50][51][52][53]. The effective range expansion (ERE), which describes the low-energy strong interactions between two hadrons, emerges naturally from the pionless EFT, and it was shown by Bethe [54] how the ERE is modified in the presence of Coulomb interactions.…”

Section: Coulomb Scatteringmentioning

confidence: 99%

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Two-particle elastic scattering in a finite volume including QED

2014

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The presence of long-range interactions violates a condition necessary to relate the energy of two particles in a finite volume to their S-matrix elements in the manner of Lüscher. While in infinite volume, QED contributions to low-energy charged particle scattering must be resummed to all orders in perturbation theory (the Coulomb ladder diagrams), in a finite volume the momentum operator is gapped, allowing for a perturbative treatment. The leading QED corrections to the two-particle finite-volume energy quantization condition below the inelastic threshold, as well as approximate formulas for energy eigenvalues, are obtained. In particular, we focus on two spinless hadrons in the A + 1 irreducible representation of the cubic group, and truncate the strong interactions to the s-wave. These results are necessary for the analysis of Lattice QCD+QED calculations of charged-hadron interactions, and can be straightforwardly generalized to other representations of the cubic group, to hadrons with spin, and to include higher partial waves.

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Section: Coulomb Scatteringmentioning

confidence: 99%

“…built out of a field ψ, it is straightforward to show, using equations of motion and integrating by parts, that [52,56] …”

Section: Coulomb Scatteringmentioning

confidence: 99%

Two-particle elastic scattering in a finite volume including QED

2014

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“…We will calculate the twobody hadronic current J µ from the pionless effective Lagrangian with di-baryon fields up to NLO. We adopt the standard counting rules of pionless EFT with di-baryon fields [18]. Introducing an expansion scale Q < Λ(≃ m π ), we count the magnitude of spatial part of the external and loop momenta, | p| and | l|, as Q, and their time components, p 0 and l 0 , as Q 2 .…”

Section: Pionless Effective Lagrangian With Di-baryon Fieldsmentioning

confidence: 99%

“…In this work, we employ a pionless EFT with di-baryon fields [18,19,20]. 3 The amplitude for the pp fusion process at the zero proton momentum is calculated up to NLO.…”

Section: Introductionmentioning

confidence: 99%

“…Thanks to the perturbative scheme in EFT, the accuracy of the N 4 LO calculation would, in principle, be (Q/Λ) 4 ∼ (1/3) 4 ≃ 1%, where Q/Λ ∼ 1/3 is a typical expansion parameter in the pionless theory. However, because of lack of the experimental data to fix an unknown LEC L 1A which appears in the two-nucleon-axial-current contact interaction in the pionless effective Lagrangian, an uncertainty estimated in the pionless EFT for the pp fusion process is still significantly larger than what is expected from the counting rules of the theory.In this work, we employ a pionless EFT with di-baryon fields [18,19,20]. 3 The amplitude for the pp fusion process at the zero proton momentum is calculated up to NLO.…”

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Proton–proton fusion in pionless effective theory

et al. 2008

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The proton-proton fusion reaction, pp → de + ν, is studied in pionless effective field theory (EFT) with di-baryon fields up to next-to leading order. With the aid of the di-baryon fields, the effective range corrections are naturally resummed up to the infinite order and thus the calculation is greatly simplified. Furthermore, the low-energy constant which appears in the axial-current-di-baryon-di-baryon contact vertex is fixed through the ratio of two-and one-body matrix elements which reproduces the tritium lifetime very precisely. As a result we can perform a parameter free calculation for the process. We compare our numerical result with those from the accurate potential model and previous pionless EFT calculations, and find a good agreement within the accuracy better than 1%. PACS IntroductionThe proton-proton fusion process, pp → de + ν e , is a fundamental reaction for the nuclear astrophysics, especially important for the understanding of the star evolutions [1] and solar neutrinos [2,3,4]. However, the process has never been studied experimentally because the event is extremely unlikely to take place in the laboratory at the proton energies in the sun. The calculation of the transition rate and its uncertainty has naturally become a challenge to nuclear theory. The first calculation of the process was carried out by Bethe and Critchfield [5] in 1938. This estimation was improved by Salpeter [6] 2 in 1952. Later, small corrections, such as the electromagnetic radiative corrections, were considered by Bahcall and his collaborators [8,9] in the framework of effective range theory. Recently, accurate phenomenological potential models were employed to study the process [10,11]. Furthermore, in Ref.[12] the two-nucleon current operators were calculated from heavybaryon chiral perturbation theory (HBχPT) up to next-to-next-to-next-to leading order (N 3 LO), and Park et al. obtained quite an accurate estimation (∼ 0.3% uncertaity) for the process by fixing an unknown parameter, so-called low energy constant (LEC), which appears in the two-nucleon-axial-current contact interaction in terms of the tritium lifetime [13,14].The kinetic energy relevant to the pp fusion process at the core of the sun is quite low, kT c ≃ 1.18 keV, where T c is the core temperature of the sun, T c ≃ 13.7 × 10 6 K, and k is the Boltzmann constant. The proton momentum at the core, p c ≃ 2m p kT c ≃ 1.5 MeV, where m p is the proton mass, is still significantly small compared to the pion mass, m π ≃ 140 MeV. Therefore, we may regard the pion as a heavy degree of freedom for the pp fusion process. It may be convenient and suitable to employ a pionless effective field theory (EFT) [15], in which the pions are integrated out of the effective Lagrangian for the process in question. The pp fusion process in the pionless theory has been studied by Kong and Ravndal [16] up to next-to leading order (NLO) and by Butler and Chen [17] up to fifth order (N 4 LO). Thanks to the perturbative scheme in EFT, the accuracy of the N 4 LO calculation w...

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Elastic $$\alpha $$-$$^{12}$$C Scattering at Low Energies with the Bound States of $$^{16}$$O in EFT

Ando

2020

Recent Progress in Few-Body Physics

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The elastic α-12 C scattering for l = 0, 1, 2, 3 channels at low energies is studied, including the energies of excited bound states of 16 O, in effective field theory. We introduce a new renormalization method due to the large suppression factor produced by the Coulomb interaction when fitting the effective range parameters to the phase sift data. After fitting the parameters, we calculate asymptotic normalization constants of the 0 + 2 , 1 − 1 , 2 + 1 , 3 − 1 states of 16 O. We also discuss the uncertainties of the present study when the amplitudes are interpolated to the stellar energy region of the 12 C(α,γ) 16 O reaction.

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Rearranging pionless effective field theory

Cited by 177 publications

References 35 publications

Two-particle elastic scattering in a finite volume including QED

Two-particle elastic scattering in a finite volume including QED

Proton–proton fusion in pionless effective theory

Elastic $$\alpha $$-$$^{12}$$C Scattering at Low Energies with the Bound States of $$^{16}$$O in EFT

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