Building light nuclei from neutrons, protons, and pions

Phillips, Daniel R.

doi:10.1007/s10582-002-0079-z

Cited by 43 publications

(100 citation statements)

References 74 publications

(151 reference statements)

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“…[49,50] for reviews and Ref. [51] for a pedagogical introduction. Its organizational scheme ("power counting") is based on two basic scales: the breakdown scale Q high estimated as m π and an unnaturally small scale ℵ related to the inverse of the two-nucleon scattering lengths 1,3 a NN in the singlet/triplet channels.…”

Section: Pionless Effective Field Theorymentioning

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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Section: Pionless Effective Field Theorymentioning

confidence: 99%

Spectra and scattering of light lattice nuclei from effective field theory

et al. 2015

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“…O(1) when measured in units of Λ. 3 Consequently we begin by encoding the fact that the LECs a 0 , . .…”

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confidence: 99%

Bayesian methods for parameter estimation in effective field theories

Schindler

Phillips

2009

Annals of Physics

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We demonstrate and explicate Bayesian methods for fitting the parameters that encode the impact of short-distance physics on observables in effective field theories (EFTs). We use Bayes' theorem together with the principle of maximum entropy to account for the prior information that these parameters should be natural, i.e. O(1) in appropriate units. Marginalization can then be employed to integrate the resulting probability density function (pdf) over the EFT parameters that are not of specific interest in the fit. We also explore marginalization over the order of the EFT calculation, M , and over the variable, R, that encodes the inherent ambiguity in the notion that these parameters are O(1). This results in a very general formula for the pdf of the EFT parameters of interest given a data set, D. We use this formula and the simpler "augmented χ 2 " in a toy problem for which we generate pseudo-data. These Bayesian methods, when used in combination with the "naturalness prior", facilitate reliable extractions of EFT parameters in cases where χ 2 methods are ambiguous at best. We also examine the problem of extracting the nucleon mass in the chiral limit, M 0 , and the nucleon sigma term, from pseudo-data on the nucleon mass as a function of the pion mass. We find that Bayesian techniques can provide reliable information on M 0 , even if some of the data points used for the extraction lie outside the region of applicability of the EFT.

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“…In the chiral expansion, the different contributions to the potential can be divided in short range (with range on QCD scales r ∼ 1/Λ QCD ) and long distance (with range on the pion scale r ∼ 1/m π ) [9,10,11]. They generate ESC suppressed by factors of, respectively, e −Λ QCD L and e −mπ L .…”

Section: S 0 Nucleon-nucleon Scatteringmentioning

confidence: 99%

Fitting two nucleons inside a box: Exponentially suppressed corrections to Lüscher’s formula

Sato

Bedaque

2007

Phys. Rev. D

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Scattering observables can be computed in lattice field theory by measuring the volume dependence of energy levels of two particle states. The dominant volume dependence, proportional to inverse powers of the volume, is determined by the phase shifts. This universal relation (Lüscher's formula) between energy levels and phase shifts is distorted by corrections which, in the large volume limit, are exponentially suppressed. They may be sizable, however, for the volumes used in practice and they set a limit on how small the lattice can be in these studies. We estimate these corrections, mostly in the case of two nucleons.Qualitatively, we find that the exponentially suppressed corrections are proportional to the square of the potential (or to terms suppressed in the chiral expansion) and the effect due to pions going "around the world" vanishes. Quantitatively, the size of the lattice should be greater than ≈ (5 fm) 3 in order to keep finite volume corrections to the phase less than 1 • for realistic pion mass.

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Building light nuclei from neutrons, protons, and pions

Cited by 43 publications

References 74 publications

Spectra and scattering of light lattice nuclei from effective field theory

Spectra and scattering of light lattice nuclei from effective field theory

Bayesian methods for parameter estimation in effective field theories

Fitting two nucleons inside a box: Exponentially suppressed corrections to Lüscher’s formula

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