Spectra and scattering of light lattice nuclei from effective field theory

Kirscher, Johannes; Barnea, Nir; Gazit, Doron; Pederiva, Francesco; Kolck, U. van

doi:10.1103/physrevc.92.054002

Cited by 56 publications

(66 citation statements)

References 100 publications

(209 reference statements)

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“…Related discussions in the context of pionless EFTs for multi-nucleon systems can be found in Ref. [72,73] and implicitly in the presentation of the effective range expansion above.…”

Section: Observations About Nucleon-nucleon Effective Field Theormentioning

confidence: 99%

Two nucleon systems atmπ∼450 MeVfrom lattice QCD

Orginos¹,

Parreño²,

Savage³

et al. 2015

Phys. Rev. D

128

137

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Nucleon-nucleon systems are studied with lattice quantum chromodynamics at a pion mass of mπ ∼ 450 MeV in three spatial volumes using n f = 2 + 1 flavors of light quarks. At the quark masses employed in this work, the deuteron binding energy is calculated to be B d = 14.4 +3.2 −2.6 MeV, while the dineutron is bound by Bnn = 12.5 +3.0 −5.0 MeV. Over the range of energies that are studied, the S-wave scattering phase shifts calculated in the 1 S0 and 3 S1-3 D1 channels are found to be similar to those in nature, and indicate repulsive short-range components of the interactions, consistent with phenomenological nucleon-nucleon interactions. In both channels, the phase shifts are determined at three energies that lie within the radius of convergence of the effective range expansion, allowing for constraints to be placed on the inverse scattering lengths and effective ranges. The extracted phase shifts allow for matching to nuclear effective field theories, from which low energy counterterms are extracted and issues of convergence are investigated. As part of the analysis, a detailed investigation of the single hadron sector is performed, enabling a precise determination of the violation of the Gell-Mann-Okubo mass relation.

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“…Related discussions in the context of pionless EFTs for multi-nucleon systems can be found in Ref. [72,73] and implicitly in the presentation of the effective range expansion above.…”

Section: Observations About Nucleon-nucleon Effective Field Theormentioning

confidence: 99%

Two nucleon systems atmπ∼450 MeVfrom lattice QCD

Orginos¹,

Parreño²,

Savage³

et al. 2015

Phys. Rev. D

128

137

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“…In this case, the value of all SW coefficients except for c 5 are consistent with zero, a manifestation of the SUð16Þ spin-flavor symmetry in the LO SUð3Þ interactions, i.e., the a ≫ b=3 hierarchy in the SUð6Þ spin-flavor symmetric interactions. With these results, and the binding energies of light hypernuclei [20], ongoing ab initio many-body calculations using the LQCD input at this value of the quark masses [59][60][61][62] can be extended to systems containing hyperons. Appendix B is devoted to summarizing the constraints obtained for the LO scattering amplitudes in flavor space.…”

Section: Leading Suð3þ Interactions In Effective Field Theorymentioning

confidence: 99%

Baryon-baryon interactions and spin-flavor symmetry from lattice quantum chromodynamics

et al. 2017

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Lattice quantum chromodynamics is used to constrain the interactions of two octet baryons at the SUð3Þ flavor-symmetric point, with quark masses that are heavier than those in nature (equal to that of the physical strange quark mass and corresponding to a pion mass of ≈806 MeV). Specifically, the S-wave scattering phase shifts of two-baryon systems at low energies are obtained with the application of Lüscher's formalism, mapping the energy eigenvalues of two interacting baryons in a finite volume to the two-particle scattering amplitudes below the relevant inelastic thresholds. The leading-order low-energy scattering parameters in the two-nucleon systems that were previously obtained at these quark masses are determined with a refined analysis, and the scattering parameters in two other channels containing the Σ and Ξ baryons are constrained for the first time. It is found that the values of these parameters are consistent with an approximate SUð6Þ spin-flavor symmetry in the nuclear and hypernuclear forces that is predicted in the large-N c limit of QCD. The two distinct SUð6Þ-invariant interactions between two baryons are constrained for the first time at this value of the quark masses, and their values indicate an approximate accidental SUð16Þ symmetry. The SUð3Þ irreps containing the NNð 1 S 0 Þ, NNð 3 S 1 Þ and 1 ffiffi 2 p ðΞ 0 n þ Ξ − pÞð 3 S 1 Þ channels unambiguously exhibit a single bound state, while the irrep containing the Σ þ pð 3 S 1 Þ channel exhibits a state that is consistent with either a bound state or a scattering state close to threshold. These results are in agreement with the previous conclusions of the NPLQCD collaboration regarding the existence of twonucleon bound states at this value of the quark masses.

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“…The absence of an essential four-body parameter has also been verified in the context of potential models with a short range [38][39][40][41] and of renormalization-group analyses [42][43][44]. As a consequence, the 3N LO strength parameter Λ ⋆ , together with the LO two-body interactions, determines the spectrum and scattering for systems with more particles [10,[25][26][27][28][29][30][31][32][33][34]45,46]. This single relevant 3N parameter generates correlations among few-body observables such as the Phillips [47] and Tjon [48] lines.…”

mentioning

confidence: 99%

“…Derivative corrections to this 3N interaction start at next-to-next-toleading order (N 2 LO) [19,[21][22][23][24]. Little is known about the orders at which higher-body interactions appear, except that they are not LO [10,[25][26][27][28][29][30][31][32][33][34]. Based on a zero-range model, Refs.…”

mentioning

confidence: 99%

Nuclear Physics Around the Unitarity Limit

et al. 2017

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We argue that many features of the structure of nuclei emerge from a strictly perturbative expansion around the unitarity limit, where the two-nucleon S waves have bound states at zero energy. In this limit, the gross features of states in the nuclear chart are correlated to only one dimensionful parameter, which is related to the breaking of scale invariance to a discrete scaling symmetry and set by the triton binding energy. Observables are moved to their physical values by small perturbative corrections, much like in descriptions of the fine structure of atomic spectra. We provide evidence in favor of the conjecture that light, and possibly heavier, nuclei are bound weakly enough to be insensitive to the details of the interactions but strongly enough to be insensitive to the exact size of the two-nucleon system. DOI: 10.1103/PhysRevLett.118.202501 For the purposes of nuclear physics, QCD, the theory of strong interactions, has essentially two independent parameters, namely the up and down quark masses. Their average controls the pion mass and consequently, the range of the nuclear force R ∼ M −1 π ≃ 1.4 fm. Their difference, plus electromagnetism, generates small differences in masses and interactions between neutrons and protons. At the physical point, the two-nucleon (NN) scattering length in the 3 S 1 channel is a t ≃ 5.4 fm, with the deuteron as a shallow bound state (B D ≃ 2.224 MeV); in the 1 S 0 channel, a s ≃ −23.7 fm, and a shallow virtual bound state exists at B NN Ã ≃ 0.068 MeV. With relatively small changes in quark masses, these states become, respectively, unbound and bound [1][2][3][4]. In the physics of cold atoms near Feshbach resonances, external magnetic fields play a role similar to the quark masses and allow the scattering length to be tuned arbitrarily [5].Approximate correlations B D;NN Ã ≈ 1=ðM N a 2 t;s Þ, with M N ≃ 940 MeV the nucleon mass, hold because the size of all these scales is unnatural compared to the typical interaction range R. The NN system therefore appears close to the unitarity (or unitary) limit, where both states cross zero energy, the scattering lengths become infinite (1=a t;s ¼ 0), and cross sections saturate the unitarity bound. It has indeed been suggested that this happens not far from the physical point [6]. While this presumed proximity has been discussed qualitatively for a long time, it has traditionally not played any special role in constructing nuclear forces, and it is neither assessed nor exploited in order to simplify the description of nuclei. As an exception, Refs. [7,8] use potential models to map out correlations between observables in three-and fournucleon systems as the limit is approached at fixed a t =a s .Here, we argue that the typical particle binding momentum Q A of the A-nucleon system satisfies 1=a s;t < Q A < 1=R so that a combined expansion in Q A R and 1=ðQ A a s;t Þ converges quickly and quantitatively reproduces the physical systems. With this, the gross features of states in the nuclear chart are determined by a very simple le...

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Spectra and scattering of light lattice nuclei from effective field theory

Cited by 56 publications

References 100 publications

Two nucleon systems atmπ∼450 MeVfrom lattice QCD

Two nucleon systems atmπ∼450 MeVfrom lattice QCD

Baryon-baryon interactions and spin-flavor symmetry from lattice quantum chromodynamics

Nuclear Physics Around the Unitarity Limit

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