Statistical uncertainties of a chiral interaction at next-to-next-to leading order

Ekström, Andreas; Carlsson, Boris; Wendt, Kyle; Forssén, Christian; Jensen, M Hjorth; Machleidt, R.; Wild, Stefan M.

doi:10.1088/0954-3899/42/3/034003

Cited by 38 publications

(42 citation statements)

References 35 publications

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“…For a = v = p = 0 and s = m q we obtain the nuclear potential 19) where H 0 is the free nucleon Hamiltonian. The individual contributions to V have a form similar to those obtained in TOPT and are given by a sequence of vertices and the corresponding energy denominators.…”

Section: Unitary Transformations Involving External Sourcesmentioning

confidence: 99%

“…Expanding the result in 1/m we obtain, in addition to the expressions for diagrams of Fig. 6, the contribution 19) which is already accounted for in Eq. (4.18).…”

Section: Fig 4: Tree-level and Tadpole Diagrams Yielding Non-vanishimentioning

confidence: 99%

“…A systematic investigation of the role of the many-body forces is an important frontier in low-energy nuclear physics [18]. With all these developments, coupled with on-going efforts towards a reliable quantification of various sources of theoretical uncertainties [19][20][21][22][23][24], nuclear chiral EFT is now entering the precision era [25].…”

Section: Introductionmentioning

confidence: 99%

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Nuclear axial current operators to fourth order in chiral effective field theory

2017

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We present the complete derivation of the nuclear axial charge and current operators as well as the pseudoscalar operators to fourth order in the chiral expansion relative to the dominant onebody contribution using the method of unitary transformation. We demonstrate that the unitary ambiguity in the resulting operators can be eliminated by the requirement of renormalizability and by matching of the pion-pole contributions to the nuclear forces. We give expressions for the renormalized single-, two-and three-nucleon contributions to the charge and current operators and pseudoscalar operators including the relevant relativistic corrections. We also verify explicitly the validity of the continuity equation.

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Section: Unitary Transformations Involving External Sourcesmentioning

confidence: 99%

“…Expanding the result in 1/m we obtain, in addition to the expressions for diagrams of Fig. 6, the contribution 19) which is already accounted for in Eq. (4.18).…”

Section: Fig 4: Tree-level and Tadpole Diagrams Yielding Non-vanishimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nuclear axial current operators to fourth order in chiral effective field theory

2017

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“…Therefore, uncertainties in the input Hamiltonian, such as truncations in the chiral EFT expansion or uncertainties in the low-energy couplings, likely remain the dominant source of uncertainty. Note that recently, first studies of the statistical uncertainties from numerically optimized chiral forces [23,24] and to quantify correlations between chiral EFT couplings [25,26] have been performed.In this work we investigate all sd-shell nuclei based on chiral two-nucleon (NN) and 3N interactions with realistic saturation properties. We derive microscopic valence-space Hamiltonians, which we diagonalize to obtain ground-state energies, two-neutron and two-proton separation energies, and first excited 2…”

mentioning

confidence: 99%

mentioning

confidence: 99%

Exploringsd-shell nuclei from two- and three-nucleon interactions with realistic saturation properties

et al. 2016

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We study ground-and excited-state properties of all sd-shell nuclei with neutron and proton numbers 8 N, Z 20, based on a set of low-resolution two-and three-nucleon interactions that predict realistic saturation properties of nuclear matter. We focus on estimating the theoretical uncertainties due to variation of the resolution scale, the low-energy couplings, as well as from the many-body method. The experimental two-neutron and two-proton separation energies are reasonably well reproduced, with an uncertainty range of ∼ 5 MeV. The first excited 2 + energies also show overall agreement, with a more narrow uncertainty range of ∼ 500 keV. In most cases, this range is dominated by the uncertainties in the Hamiltonian. Introduction. Recent advances in nuclear theory have established the importance of three-nucleon (3N) forces in understanding the structure of medium-mass nuclei, for the evolution to the neutron and proton driplines [1][2][3][4][5] and the formation of shell structure [6][7][8][9][10][11][12][13]. Threenucleon forces are also key for realistic saturation properties of nuclear matter [14][15][16][17][18], which in turn are obtained from global analyses of all nuclei. To date, ab initio studies of medium-mass nuclei have largely focused on closedshell nuclei or isotopic chains, generally in the vicinity of semi-magic nuclei, and no comprehensive study exists to explore nuclear forces over a full range of the nuclear chart, such as the sd shell.An additional challenge is the quantification of theoretical uncertainties [19]. Calculations in oxygen and calcium isotopes based on nuclear forces derived from chiral effective field theory (EFT) [20,21] suggest that the uncertainties from the many-body methods are well controlled [4,5,11,13,22]. Therefore, uncertainties in the input Hamiltonian, such as truncations in the chiral EFT expansion or uncertainties in the low-energy couplings, likely remain the dominant source of uncertainty. Note that recently, first studies of the statistical uncertainties from numerically optimized chiral forces [23,24] and to quantify correlations between chiral EFT couplings [25,26] have been performed.In this work we investigate all sd-shell nuclei based on chiral two-nucleon (NN) and 3N interactions with realistic saturation properties. We derive microscopic valence-space Hamiltonians, which we diagonalize to obtain ground-state energies, two-neutron and two-proton separation energies, and first excited 2

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Recent Progress in Few-Body Physics

Davoudi

2020

Springer Proceedings in Physics

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One of the key challenges in ab initio nuclear theory is to understand the emergence of nuclear structure from quantum chromodynamics. I will address this challenge and focus on the statistical aspects of uncertainty quantification and parameter estimation in chiral effective field theory. It is well-known that quantum chromodynamics (QCD) is non-perturbative in the low-energy region where atomic nuclei exist. This feature prevents us from direct application of perturbation theory. To make progress, two complementary approaches are presently employed; lattice QCD (LQCD) [1] and chiral effective field theory (χ EFT) [2]. The former amounts to numerical evaluation of the QCD path integral on a space-time lattice, while the latter is aimed at exploiting the decoupling principles of the renormalization group (RG) to systematically formulate a potential description of the nuclear interaction rooted in QCD. LQCD is a computationally expensive approach that requires at least exascale resources for a realistic analysis of multinucleon systems, and will most likely not be the most economical choice for analyzing nuclear systems. Nevertheless, in cases where numerically converged results can be obtained, LQCD offers a unique computational laboratory for theoretical studies of QCD in a low-energy setting [3]. The derivation of a nuclear potential in χ EFT proceeds via the construction of an effective Lagrangian consisting of pions, nucleons, sometimes also the Δ isobar, endowed with all possible interactions compatible with the symmetries of low-energy QCD. The details can be found in extensive reviews [4-6]. All short-distance physics, normally associated with quarks and gluons, reside beyond a hard momentum scale Λ b ∼ 1 GeV, that remains unresolved in χ EFT. Such high-momentum dynamics is instead encoded in a set of low-energy constants (LECs) that must be determined from experimental data, or in a future scenario hopefully computed directly from LQCD. χ EFT is the theoretical framework to calculate observables in an expan

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Statistical uncertainties of a chiral interaction at next-to-next-to leading order

Cited by 38 publications

References 35 publications

Nuclear axial current operators to fourth order in chiral effective field theory

Nuclear axial current operators to fourth order in chiral effective field theory

Exploringsd-shell nuclei from two- and three-nucleon interactions with realistic saturation properties

Recent Progress in Few-Body Physics

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