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Title: Neutron-proton scattering at next-to-next-to-leading order in Nuclear Lattice Effective Field Theory

Abstract

Here, we present a systematic study of neutron-proton scattering in Nuclear Lattice Effective Field Theory (NLEFT), in terms of the computationally efficient radial Hamiltonian method. Our leading-order (LO) interaction consists of smeared, local contact terms and static one-pion exchange. We show results for a fully non-perturbative analysis up to next-to-next-to-leading order (NNLO), followed by a perturbative treatment of contributions beyond LO. The latter analysis anticipates practical Monte Carlo simulations of heavier nuclei. We explore how our results depend on the lattice spacing a, and estimate sources of uncertainty in the determination of the low-energy constants of the next-to-leading-order (NLO) two-nucleon force. We give results for lattice spacings ranging from a = 1.97 fm down to a = 0.98 fm, and discuss the effects of lattice artifacts on the scattering observables. At a = 0.98 fm, lattice artifacts appear small, and our NNLO results agree well with the Nijmegen partial-wave analysis for S-wave and P-wave channels. We expect the peripheral partial waves to be equally well described once the lattice momenta in the pion-nucleon coupling are taken to coincide with the continuum dispersion relation, and higher-order (N 3LO) contributions are included. Finally, we stress that for center-of-mass momenta below 100 MeV,more » the physics of the two-nucleon system is independent of the lattice spacing.« less

Authors:
 [1];  [2];  [3];  [2];  [4];  [2];  [2];  [2];  [5]
  1. Univ. of Bonn (Germany). Helmholtz-Inst. fur Strahlen- und Kernphysik and Bethe Center for Theoretical Physics; Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
  2. Forschungszentrum Julich (Germany). Inst. for Advanced Simulation, Inst. fur Kernphysik, and Julich Center for Hadron Physics
  3. Univ. of Bonn (Germany). Helmholtz-Inst. fur Strahlen- und Kernphysik and Bethe Center for Theoretical Physics
  4. North Carolina State Univ., Raleigh, NC (United States). Dept. of Physics
  5. Univ. of Bonn (Germany). Helmholtz-Inst. fur Strahlen- und Kernphysik and Bethe Center for Theoretical Physics; Forschungszentrum Julich (Germany). Inst. for Advanced Simulation, Inst. fur Kernphysik, and Julich Center for Hadron Physics; Forschungszentrum Julich (Germany). High Performance Computing (JARA-HPC)
Publication Date:
Research Org.:
Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)
OSTI Identifier:
1360957
Report Number(s):
JLAB-THY-17-2426; DOE/OR/-23177-4081
Journal ID: ISSN 1434-6001; PII: 827
Grant/Contract Number:
AC05-06OR23177
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
European Physical Journal. A
Additional Journal Information:
Journal Volume: 53; Journal Issue: 5; Journal ID: ISSN 1434-6001
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats

Alarcón, Jose Manuel, Du, Dechuan, Klein, Nico, Lähde, Timo A., Lee, Dean, Li, Ning, Lu, Bing-Nan, Luu, Thomas, and Meißner, Ulf-G. Neutron-proton scattering at next-to-next-to-leading order in Nuclear Lattice Effective Field Theory. United States: N. p., 2017. Web. doi:10.1140/epja/i2017-12273-x.
Alarcón, Jose Manuel, Du, Dechuan, Klein, Nico, Lähde, Timo A., Lee, Dean, Li, Ning, Lu, Bing-Nan, Luu, Thomas, & Meißner, Ulf-G. Neutron-proton scattering at next-to-next-to-leading order in Nuclear Lattice Effective Field Theory. United States. doi:10.1140/epja/i2017-12273-x.
Alarcón, Jose Manuel, Du, Dechuan, Klein, Nico, Lähde, Timo A., Lee, Dean, Li, Ning, Lu, Bing-Nan, Luu, Thomas, and Meißner, Ulf-G. 2017. "Neutron-proton scattering at next-to-next-to-leading order in Nuclear Lattice Effective Field Theory". United States. doi:10.1140/epja/i2017-12273-x.
@article{osti_1360957,
title = {Neutron-proton scattering at next-to-next-to-leading order in Nuclear Lattice Effective Field Theory},
author = {Alarcón, Jose Manuel and Du, Dechuan and Klein, Nico and Lähde, Timo A. and Lee, Dean and Li, Ning and Lu, Bing-Nan and Luu, Thomas and Meißner, Ulf-G.},
abstractNote = {Here, we present a systematic study of neutron-proton scattering in Nuclear Lattice Effective Field Theory (NLEFT), in terms of the computationally efficient radial Hamiltonian method. Our leading-order (LO) interaction consists of smeared, local contact terms and static one-pion exchange. We show results for a fully non-perturbative analysis up to next-to-next-to-leading order (NNLO), followed by a perturbative treatment of contributions beyond LO. The latter analysis anticipates practical Monte Carlo simulations of heavier nuclei. We explore how our results depend on the lattice spacing a, and estimate sources of uncertainty in the determination of the low-energy constants of the next-to-leading-order (NLO) two-nucleon force. We give results for lattice spacings ranging from a = 1.97 fm down to a = 0.98 fm, and discuss the effects of lattice artifacts on the scattering observables. At a = 0.98 fm, lattice artifacts appear small, and our NNLO results agree well with the Nijmegen partial-wave analysis for S-wave and P-wave channels. We expect the peripheral partial waves to be equally well described once the lattice momenta in the pion-nucleon coupling are taken to coincide with the continuum dispersion relation, and higher-order (N3LO) contributions are included. Finally, we stress that for center-of-mass momenta below 100 MeV, the physics of the two-nucleon system is independent of the lattice spacing.},
doi = {10.1140/epja/i2017-12273-x},
journal = {European Physical Journal. A},
number = 5,
volume = 53,
place = {United States},
year = 2017,
month = 5
}

Journal Article:
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  • We use effective field theory (EFT) to calculate the nucleon-nucleon scattering amplitude up to next-to-next-to-leading order (NNLO), where we include instantaneous pion exchange but ignore retardation effects. The scattering amplitude in the {sup 1}S{sub 0} channel is calculated using the Kaplan-Savage-Wise power counting scheme. An expansion of the amplitude about the pole at low (imaginary) momentum is used to derive matching conditions for the EFT couplings. After imposing constraints from a renormalization group flow analysis, there are no new free parameters in the amplitude at NNLO. We apply the calculation to a toy model in which there is only instantaneousmore » pion exchange by construction, namely, the two-Yukawa model. We find that, through next-to-next-to-leading order, each successive term in the low energy expansion does systematically improve the approximation to the full amplitude. {copyright} {ital 1999} {ital The American Physical Society}« less
  • The next-to-next-to-leading order spin1-spin2 potential for an inspiralling binary, that is essential for accuracy to fourth post-Newtonian order, if both components in the binary are spinning rapidly, has been recently derived independently via the ADM Hamiltonian and the Effective Field Theory approaches, using different gauges and variables. Here we show the complete physical equivalence of the two results, thereby we first prove the equivalence of the ADM Hamiltonian and the Effective Field Theory approaches at next-to-next-to-leading order with the inclusion of spins. The main difficulty in the spinning sectors, which also prescribes the manner in which the comparison of themore » two results is tackled here, is the existence of redundant unphysical spin degrees of freedom, associated with the spin gauge choice of a point within the extended spinning object for its representative worldline. After gauge fixing and eliminating the unphysical degrees of freedom of the spin and its conjugate at the level of the action, we arrive at curved spacetime generalizations of the Newton-Wigner variables in closed form, which can also be used to obtain further Hamiltonians, based on an Effective Field Theory formulation and computation. Finally, we make use of our validated result to provide gauge invariant relations among the binding energy, angular momentum, and orbital frequency of an inspiralling binary with generic compact spinning components to fourth post-Newtonian order, including all known sectors up to date.« less
  • The next-to-next-to-leading order spin-squared interaction potential for generic compact binaries is derived for the first time via the effective field theory for gravitating spinning objects in the post-Newtonian scheme. The spin-squared sector is an intricate one, as it requires the consideration of the point particle action beyond minimal coupling, and mainly involves the spin-squared worldline couplings, which are quite complex, compared to the worldline couplings from the minimal coupling part of the action. This sector also involves the linear in spin couplings, as we go up in the nonlinearity of the interaction, and in the loop order. Hence, there ismore » an excessive increase in the number of Feynman diagrams, of which more are higher loop ones. We provide all the Feynman diagrams and their values. The beneficial ''nonrelativistic gravitational'' fields are employed in the computation. This spin-squared correction, which enters at the fourth post-Newtonian order for rapidly rotating compact objects, completes the conservative sector up to the fourth post-Newtonian accuracy. The robustness of the effective field theory for gravitating spinning objects is shown here once again, as demonstrated in a recent series of papers by the authors, which obtained all spin dependent sectors, required up to the fourth post-Newtonian accuracy. The effective field theory of spinning objects allows to directly obtain the equations of motion, and the Hamiltonians, and these will be derived for the potential obtained here in a forthcoming paper.« less