Constraining the neutron-neutron scattering length using the effective field theory without explicit pions

Kirscher, Johannes; Phillips, Daniel R.

doi:10.1103/physrevc.84.054004

Cited by 14 publications

(20 citation statements)

References 64 publications

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“…Refs. [47,48]). Since the theoretical error for B T and B α is large relative to the experimental one, the Phillips and Tjon lines at LO in π /EFT do not constrain observables further at physical m π .…”

Section: Resultsmentioning

confidence: 99%

“…This is analogous to the use of π /EFT correlations [47,48] to infer values of poorly measured observables in the real world. If and when scattering observables are determined directly on the lattice, our predictions will be a further test of the consistency between π EFT and LQCD, establishing the validity of a theory with only contact interactions over a range of m π from 140 MeV up to 805 MeV.…”

Section: Introductionmentioning

confidence: 99%

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Spectra and scattering of light lattice nuclei from effective field theory

et al. 2015

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An effective field theory is used to describe light nuclei, calculated from quantum chromodynamics on a lattice at unphysically large pion masses. The theory is calibrated at leading order to two available data sets on two-and three-body nuclei for two pion masses. At those pion masses we predict the quartet and doublet neutron-deuteron scattering lengths, and the alpha-particle binding energy. For mπ=510 MeV we obtain, respectively, 4 anD = 2.3 ± 1.3 fm, 2 anD = 2.2 ± 2.1 fm, and B α = 35 ± 22 MeV, while for mπ=805 MeV 4 anD = 1.6 ± 1.3 fm, 2 anD = 0.62 ± 1.0 fm, and B α = 94 ± 45 MeV are found. Phillips-and Tjon-like correlations to the triton binding energy are established. We find the theoretical uncertainty in the respective correlation bands to be independent of the pion mass. As a benchmark, we present results for the physical pion mass, using experimental two-body scattering lengths and the triton binding energy as input. Hints of subtle changes in the structure of the triton and alpha particle are discussed.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Spectra and scattering of light lattice nuclei from effective field theory

et al. 2015

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“…[25], this difference is accounted for here by an N 2 LO correction, and for definiteness the central value favored by the pionless analysis of Ref. [43], a t,nn −(22.9 ± 4.1) fm, is adopted here. The small isospin breaking in the effective ranges, r C − r t 0.06 fm is also included at N 2 LO.…”

Section: Power Counting Around the Unitarity Limitmentioning

confidence: 99%

“…It has become clear that if perturbative renormalization is to be maintained, including electromagnetic effects is not as simple as adding a Coulomb potential to the short-range terms, as it is typically done in calculations based on effective pionless potentials [41][42][43][44]. Based on studying the regulator (cutoff) dependence of the amplitude, it was realized that in the presence of nonperturbative Coulomb effects an isospin breaking three-nucleon force is required to ensure renormalization at next-to-leading order (NLO) [24,45].…”

Section: Introductionmentioning

confidence: 99%

Second-order perturbation theory for ${}^{3}\mathrm{He}$ andpdscattering in pionless EFT

König¹

2017

J. Phys. G: Nucl. Part. Phys.

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This work implements pionless effective field theory with the two-nucleon system expanded around the unitarity limit at second-order perturbation theory. The expansion is found to converge well. All Coulomb effects are treated in perturbation theory, including two-photon contributions at next-to-next-to-leading order. After fixing a three-nucleon force to the 3 He binding energy at this order, proton-deuteron scattering in the doublet S-wave channel is calculated for moderate center-of-mass momenta. * koenig.389@osu.edu 1 arXiv:1609.03163v2 [nucl-th]

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“…To obtain 2-body scattering wave functions, we alternated between three methods to minimize the possibility of a mistake in the numerical implementation of either method: a Numerov integration, a version [39] of the variable phase method, and a variational method with a Gaussian trial wave function. Three-body wave functions and matrix elements were calculated with the refined-resonating-group method (RGM, original formulation: [40,41]; refinement and triton/ 3 He implementation: [42,43]) [44]. The variational RGM, as applied here, is significantly less accurate than the Numerov integration and the variable-phase method.…”

Section: Toolboxmentioning

confidence: 99%

The Coulomb interaction in Helium-3: Interplay of strong short-range and weak long-range potentials

Kirscher

Gazit

2016

Physics Letters B

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Quantum chromodynamics and the electroweak theory at low energies are prominent instances of the combination of a short-range and a long-range interaction. For the description of light nuclei, the large nucleon-nucleon scattering lengths produced by the strong interaction, and the reduction of the weak interaction to the Coulomb potential, play a crucial role. Helium-3 is the first bound nucleus comprised of more than one proton in which this combination of forces can be studied.We demonstrate a proper renormalization of Helium-3 using the pionless effective field theory as the formal representation of the nuclear regime as strongly interacting fermions. The theory is found consistent at leading and next-to-leading order without isospin-symmetry-breaking 3nucleon interactions and a non-perturbative treatment of the Coulomb interaction. The conclusion highlights the significance of the regularization method since a comparison to previous work is contradictory if the difference in those methods is not considered.With a perturbative Coulomb interaction, as suggested by dimensional analysis, we find the Helium-3 system properly renormalized, too.For both treatments, renormalization-scheme independence of the effective field theory is demonstrated by regulating the potential and a variation of the associated cutoff.

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Constraining the neutron-neutron scattering length using the effective field theory without explicit pions

Cited by 14 publications

References 64 publications

Spectra and scattering of light lattice nuclei from effective field theory

Spectra and scattering of light lattice nuclei from effective field theory

Second-order perturbation theory for ${}^{3}\mathrm{He}$ andpdscattering in pionless EFT

The Coulomb interaction in Helium-3: Interplay of strong short-range and weak long-range potentials

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