How to Classify Three-Body Forces – And Why

Grießhammer, Harald W.

doi:10.1007/s00601-005-0139-6

Cited by 11 publications

(9 citation statements)

References 9 publications

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“…[50], the leading volume-dependent corrections to the energy of more than two unitary fermions with many two-body s-wave operators tuned is expected to be of order L −3 , coming from an untuned two-derivative two-body p-wave operator. Subleading corrections are expected to be of order L −4.33 , due to the lowest dimension three-body operator, which has = 0 and scaling dimension 4.67 [65][66][67][68]. Performing a fit to the data using the functional form c 0 + c 1 /L 3 yields an infinite volume extrapolation result of E/E F ree = 0.3735 +0.0014 −0.0007 , and is consistent with the exact infinite volume result of Pricoupenko and Castin [63] within 0.3% uncertainties.…”

Section: Few-body Resultsmentioning

confidence: 99%

Lattice Monte Carlo calculations for unitary fermions in a finite box

Endres

Kaplan²,

Lee

et al. 2013

Phys. Rev. A

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We perform lattice Monte Carlo simulations for up to 66 unitary fermions in a finite box using a highly improved lattice action for nonrelativistic spin 1/2 fermions. We obtain a value of 0.366 +0.016 −0.011 for the Bertsch parameter, defined as the energy of the unitary Fermi gas measured in units of the free gas energy in the thermodynamic limit. In addition, for up to four unitary fermions, we compute the spectrum of the lattice theory by exact diagonalization of the transfer matrix projected onto irreducible representations of the octahedral group for small to moderate size lattices, providing an independent check of our few-body simulation results. We compare our exact numerical and simulation results for the spectrum to benchmark studies of other research groups, as well as perform an extended analysis of our lattice action improvement scheme, including an analysis of the errors associated with higher partial waves and finite temporal discretization.

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Section: Few-body Resultsmentioning

confidence: 99%

Lattice Monte Carlo calculations for unitary fermions in a finite box

Endres

Kaplan²,

Lee

et al. 2013

Phys. Rev. A

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“…as is the kernel K. It has been demonstrated before [13,14,22] that the solutions to the resulting integral equations in the UV limit are linear combinations of with the asymptotic exponents s l (λ) of the amplitudes at large half-offshell momenta p, q ≫ √ ME, k, γ s/t given for the lowest angular momenta in Table 1. For the spin-quartet channels, the spin-isospin parameter is λ = − 1 2 .…”

Section: Parity-conserving Partmentioning

confidence: 94%

“…With the two configurations d t N and d s N, it is convenient to follow Ref. [13,14,App. A.1] in representing operators O by a 2 × 2-matrix in the so-called cluster-decomposition space:…”

Section: Parity-conserving Partmentioning

confidence: 99%

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On parity-violating three-nucleon interactions and the predictive power of few-nucleon EFT at very low energies

Grießhammer

Schindler

2010

Eur. Phys. J. A

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We address the typical strengths of hadronic parity-violating three-nucleon interactions in "pion-less" Effective Field Theory in the nucleon-deuteron (iso-doublet) system. By analysing the superficial degree of divergence of loop diagrams, we conclude that no such interactions are needed at leading order, O(ǫQ −1 ). The only two distinct parity-violating three-nucleon structures with one derivative mix 2 S 1 2 and 2 P 1 2 waves with iso-spin transitions ∆I = 0 or 1. Due to their structure, they cannot absorb any divergence ostensibly appearing at next-to-leading order, O(ǫQ 0 ). This observation is based on the approximate realisation of Wigner's combined SU (4) spin-isospin symmetry in the two-nucleon system, even when effective-range corrections are included. Parity-violating three-nucleon interactions thus only appear beyond next-to-leading order. This guarantees renormalisability of the theory to that order without introducing new, unknown coupling constants and allows the direct extraction of parity-violating two-nucleon interactions from three-nucleon experiments.

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“…Measuring highly accurate three-nucleon scattering lengths, as undertaken in this thesis, provides therefore stringent constraints and crucial input for nuclear theory. For example, three-nucleon forces are introduced for conceptual reasons in P πEFT already at leading order to ensure that physical observables do not depend on the details of the short-distance physics chosen for the theoretical calculation [Gri06,Gri08]. Thereby, the strengths of the three-body forces have to be fixed by experimentally welldetermined input parameters.…”

Section: Three-nucleon Forcesmentioning

confidence: 99%