Three-Body Halo States in Effective Field Theory: Renormalization and Three-Body Interactions in the Helium-6 System

Ryberg, Emil; Forssén, Christian; Platter, Lucas

doi:10.1007/s00601-017-1307-1

Cited by 16 publications

(15 citation statements)

References 27 publications

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“…(2) or (4) and leading to the appearance of shallow bound, virtual or resonance states. While such resonant systems have already been extensively studied using EFT formulations with auxiliary dimer fields [30,39,[44][45][46][47][48][49], see Ref. [53] for a review article, we have employed here the effective Lagrangian written solely in terms of contact interactions.…”

Section: Discussionmentioning

confidence: 99%

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Effective Field Theory for Shallow P-Wave States

et al. 2021

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We discuss the formulation of a non-relativistic effective field theory for two-body P-wave scattering in the presence of shallow states and critically address various approaches to renormalization proposed in the literature. It is demonstrated that the consistent renormalization involving only a finite number of parameters in the well-established formalism with auxiliary dimer fields corresponds to the inclusion of an infinite number of counterterms in the formulation with contact interactions only. We also discuss the implications from the Wilsonian renormalization group analysis of P-wave scattering.

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Section: Discussionmentioning

confidence: 99%

“…Refs. [44][45][46][47][48][49]. Notice that the UV divergences in the dimeron self-energy at leading order are cancelled by the counterterms generated by the bare particle-dimeron coupling constant g 1 and the residual dimeron mass 1 , see Refs.…”

Section: Halo Eft With a Dimer Field Versus The Lcrg-invariant Approachmentioning

confidence: 99%

Effective Field Theory for Shallow P-Wave States

et al. 2021

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“…A similar subtraction scheme based on expanding the unphysical pole in the momentum variable k * was previously considered in Refs. [17,34]. It should, however, be demonstrated that the change in the amplitude, which results by replacing the deep pole by its Taylor expansion, can be indeed accounted for by adjusting the effective couplings.…”

Section: Methodsmentioning

confidence: 99%

An alternative scheme for effective range corrections in pionless EFT

2021

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We discuss an alternative scheme for including effective range corrections in pionless effective field theory. The standard approach treats range terms as perturbative insertions in the T-matrix. In a finite volume this scheme can lead to singular behavior close to the unperturbed energies. We consider an alternative scheme that resums the effective range but expands the spurious pole of the T-matrix created by this resummation. We test this alternative expansion for several model potentials and observe good convergence.

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“…It should be noted that the ∇ 2 A 0 terms in Eq. (19) were considered to be of higher order in Ref. [21].…”

Section: The Charge Radius Formulamentioning

confidence: 99%

“…HEFT power counting is a generalization of the power counting for Pionless EFT allowing for dominant interactions in waves with non-vanishing angular momentum and for a breakdown scale k hi estimated from the first excitation of the core and/or its size. In the first cases considered, 5,6 He [11,12,[17][18][19], there is an alpha-particle core, and the neutron-alpha (n-α) interaction is mostly of P-wave nature, generating a near-threshold 5 He resonance. The α-α interaction, in turn, is obtained [13] from α-α scattering and the lowest 8 Be state.…”

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confidence: 99%

Finite-size effects in heavy halo nuclei from effective field theory

et al. 2020

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Halo/Cluster Effective Field Theory describes halo/cluster nuclei in an expansion in the small ratio of the size of the core(s) to the size of the system. Even in the point-particle limit, neutron halo nuclei have a finite charge radius, because their center of mass does not coincide with their center of charge. This point-particle contribution decreases as 1/Ac, where Ac is the mass number of the core, and diminishes in importance compared to other effects, e.g., the size of the core to which the neutrons are bound. Here we propose that for heavy cores the EFT expansion should account for the small factors of 1/Ac. As a specific example, we discuss the implications of this organizational scheme for the inclusion of finite-size effects in expressions for the charge radii of halo nuclei. We show in particular that a short-range operator could be the dominant effect in the charge radius of one-neutron halos bound by a P-wave interaction. The point-particle contribution remains the leading piece of the charge radius for one-proton halos, and so Halo EFT has more predictive power in that case. I. INTRODUCTIONTheoretical models of many-body systems usually treat the constituent particles as having no internal structure. This point-particle approximation is also used in cluster models, e.g., for the description of halo systems [1-3], even though one might encounter situations for which the core is rather large. Finite-size effects are included a posteriori, but can become significant for certain observables. As an example, the total charge radius is usually calculated by simply adding in quadrature [4] the charge radii of the constituents and the calculated point-particle radius, see e.g. the calculation of charge radii for neutron-rich helium isotopes in the Gamow Shell Model [5]. Instead, it would be useful to construct a framework in which finite-size effects can be included systematically.Constituent-size effects can be accounted for in effective field theories (EFTs), where they appear through derivative interactions. For example, the nucleon charge radius (and, more generally, nucleon form factors) can be calculated [6] in Chiral Perturbation Theory (ChPT) in an expansion in powers of k π /M QCD , where k π ∼ 150 MeV is a momentum scale associated with the lightest carrier of the nuclear force, the pion, and M QCD ∼ 1 GeV is the characteristic mass scale of QCD. The relevant pion parameters are its mass and decay constant. Chiral EFT [7] is a generalization of ChPT to a typical nucleus, for which the binding energy per nucleon is B/A ∼ k 2 π /M QCD and the radius R ∼ A 1/3 /k π . The nuclear charge radius includes the sum of the nucleons' radii plus many-body effects generated by internucleon interactions and currents [8]. We would like to have a similar framework for clusterized systems.Clusterized systems, with much smaller energies and larger radii, are additionally characterized by scales beyond the pion scales. These nuclei can be viewed as a collection of valence nucleons orbiting around either no core (few...

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Three-Body Halo States in Effective Field Theory: Renormalization and Three-Body Interactions in the Helium-6 System

Cited by 16 publications

References 27 publications

Effective Field Theory for Shallow P-Wave States

Effective Field Theory for Shallow P-Wave States

An alternative scheme for effective range corrections in pionless EFT

Finite-size effects in heavy halo nuclei from effective field theory

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