Effective field theory of the deuteron with dibaryon fields

Abstract

Pionless effective field theory with dibaryon fields is reexamined for observables involving the deuteron. The electromagnetic form factors of the deuteron and the total cross section of radiative neutron capture on the proton, n p → d γ, are calculated. The low energy constants of vector(photon)-dibaryon-dibaryon vertices in the effective lagrangian are fixed primarily by the one-body vector(photon)-nucleon-nucleon interactions. This scheme for fixing the values of the low energy constants satisfactorily reproduces the results of the effective range theory. We also show that, by including higher order corrections, one can obtain results that are close to those of Argonne v18 potential model. PACS: 25.10.+s, 25.30.Bf, 25.40 IntroductionEffective field theory (EFT) has proven to provide a useful tool for describing a wide class of meson-meson, meson-nucleon, and nucleon-nucleon (NN) processes with and without external probes in the low energy regime [1]. However, special care for the NN processes is required to deal with the 1 S 0 channel for its long scattering length (or existence of a quasi bound state) and the 3 S 1 − 3 D 1 channel for existence of the deuteron. In general, EFT is based on the perturbative expansion of physical observables in terms of small external momenta, but a non-perturbative treatment would be required for positions of the singularity at the small energy scales, which associated with the long scattering length and the small binding energy, compared to the chiral symmetry breaking scale, pion mass m π .3 To deal with the problem, Weinberg has suggested counting rules that allow one to handle this non-perturbative problem and derive the NN potential systematically [3]. With the potential calculated to a given order, the S-matrix is calculated from a wave function obtained by solving the Schrödinger equation. This scheme has shown good accuracy and convergence with only a few leading terms [4,5,6,7]. Kaplan, Savage, and Wise (KSW) suggested new counting rules, in which pions are treated perturbatively and do not appear in leading order (LO). They also employed the power divergence subtraction scheme for regularization [8]. Only a LO contact two-nucleon interaction is treated nonperturbatively and thus physical observables can be directly calculated from Feynman diagrams expanded order by order. Over the last decade both the Weinberg and KSW schemes have been used extensively in studying few-nucleon systems.4 For reviews, see, e.g., Refs.[10] and [11].Convergence of deuteron observables becomes slow near the deuteron pole due to a large expansion parameter γ ρ d ≃ 0.4, where γ ≃ 45.7 MeV and ρ d ≃ 1.764 fm in the KSW scheme. This would be a typical expansion parameter of the deuteron channel both in pionless effective field theory (pionless EFT) [12,13], where the pions are regarded as heavy degrees of freedom in study of very low energy reactions and integrated out from effective lagrangian, and in theories that treat pions perturbatively. It was suggested, however, that adjusting the de...

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“…The ANC of deuteron is accurately determined by two effective range parameters: the deuteron binding momentum and effective range [17,18], which are accurately fixed from the deuteron binding energy and elastic NN scattering at low energies. On the other hand, to deduce ANCs for nuclear reactions relevant in nuclear-astrophysics is not so simple: the Coulomb interaction between heavier nuclei plays a negative role by preventing ones from obtaining elastic scattering data at very low energies, which makes the deduction of ANCs in terms of effective range expansion difficult [19,20].…”

Proton–proton fusion in pionless effective theory

“…More detailed discussion about the separation of LO and NLO contact interaction with external probe in the di-baryon formalism can be found in Ref. [19].…”

“…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.…”

“…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.…”

Effective Range Corrections from Effective Field Theory with Dibaryon Fields and Perturbative Pions

“…We adopt the limit of the nontrivial fixed point as the "fine-tuned" ground state of the two nucleon system, utilize dibaryon fields [15,16,17,18], which have the same quantum numbers of two-nucleon 1 S 0 and 3 S 1 states and the infinite scattering length or the zero binding energy, as a zeroth order two-nucleon core, and incorporate pion clouds perturbatively (one-pion-exchange contribution in this work as the first chiral correction 4 ) around the non-trivial fixed point being represented by the di-baryon fields.…”