<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi mathvariant="normal">He</mml:mi><mml:mprescripts /><mml:none /><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:mmultiscripts></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>p</mml:mi><mml:mi>d</mml:mi></mml:mrow></mml:math>scattering to next-to-leading order in pionless effective field theory

Vanasse, Jared; Egolf, David A.; Kerin, John F.; König, S.; Springer, Roxanne P.

doi:10.1103/physrevc.89.064003

Cited by 42 publications

(104 citation statements)

References 49 publications

(100 reference statements)

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“…[22,26,27]; for an expression with the angular integration carried out explicitly, see Ref. [28]. In contrast to earlier work [20,22], we do not approximate the bubble loop integral as a constant in this calculation but keep the full dynamical expression.…”

Section: Coulomb Diagramsmentioning

confidence: 96%

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Precision calculation of the quartet-channelp−dscattering length

König

Hammer

2014

Phys. Rev. C

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We present a fully perturbative calculation of the quartet-channel proton-deuteron scattering length up to next-to-next-to-leading order in pionless effective field theory. We use a framework that consistently extracts the Coulomb-modified effective range function for a screened Coulomb potential in momentum space and allows for a clear linear extrapolation back to the physical limit without screening. Our result of 4 a p-d = (10.9 ± 0.4) fm agrees with older experimental determinations of this quantity but deviates from potential-model calculations and a more recent result from Black et al., which find larger values around 14 fm. As a possible resolution to this discrepancy, we discuss the scheme dependence of Coulomb subtractions in a three-body system.

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Section: Coulomb Diagramsmentioning

confidence: 96%

“…[26][27][28]. According to the original counting of Rupak and Kong, this diagram formally scales like an NLO-correction.…”

Section: Coulomb Diagramsmentioning

confidence: 99%

Precision calculation of the quartet-channelp−dscattering length

König

Hammer

2014

Phys. Rev. C

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“…Indeed, the rate of convergence in observables provides ample evidence that Q 3 R is much smaller than its a priori estimate, see, e.g., Refs. [12,21,23,[58][59][60][61], and is suggestive that Q 4 R is smaller, too [29,32,46]. There is also circumstantial evidence that this may hold for A > 4 [10].…”

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confidence: 90%

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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“…For example, S-wave nD scattering in the quartet channel can be very accurately postdicted [16][17][18][19][20] once the two-nucleon LECs have been fixed in the two-nucleon system. In the doublet channel, in contrast, RG invariance requires that the three-body force with no derivatives appear already at LO, with isospin-symmetric corrections starting beyond NLO [19,[21][22][23][24][25][26][27][28]. Current evidence from the RG in the four-body system suggests that there is no fourbody force up to NLO [29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

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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He3andpdscattering to next-to-leading order in pionless effective field theory

Cited by 42 publications

References 49 publications

Precision calculation of the quartet-channelp−dscattering length

Precision calculation of the quartet-channelp−dscattering length

Nuclear Physics Around the Unitarity Limit

Spectra and scattering of light lattice nuclei from effective field theory

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