Three-body resonances in pionless effective field theory

Dietz, Sebastian; Hammer, Hans -Werner; König, S.; Schwenk, A.

doi:10.1103/physrevc.105.064002

Three-body resonances in pionless effective field theory

Journal Article · Mon Jun 13 00:00:00 EDT 2022 · Physical Review. C

DOI:https://doi.org/10.1103/physrevc.105.064002· OSTI ID:1957500

^[1]; ^[2]; ^[3]; ^[4]

Technische Univ. Darmstadt (Germany); North Carolina State University
Technische Univ. Darmstadt (Germany); GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt (Germany)
North Carolina State Univ., Raleigh, NC (United States); Technische Univ. Darmstadt (Germany)
Technische Univ. Darmstadt (Germany); GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt (Germany); Max-Planck-Inst. für Kernphysik, Heidelberg (Germany)

We investigate the appearance of resonances in three-body systems using pionless effective field theory at leading order with two complementary methods. The Faddeev equation is analytically continued to the unphysical sheet adjacent to the positive real energy axis using a contour rotation. We consider both the three-boson system and the three-neutron system. For the former, we calculate the trajectory of Borromean three-body Efimov states turning into resonances as they cross the three-body threshold. For the latter, we find no sign of three-body resonances or virtual states at leading order. Furthermore, this result is validated by exploring the level structure of three-body states in a finite volume approach.

View Accepted Manuscript (DOE)

Research Organization:: Michigan State Univ., East Lansing, MI (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: SC0013617

OSTI ID:: 1957500

Journal Information:: Physical Review. C, Journal Name: Physical Review. C Journal Issue: 6 Vol. 105; ISSN 2469-9985

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (86)

Nucleon-nucleon interaction and isospin violation van Kolck, U. Chiral Dynamics: Theory and Experiment https://doi.org/10.1007/bfb0104898	book	January 1998
On the use of resonant states in eigenfunction expansions of scattering and reaction amplitudes Berggren, Tore Nuclear Physics A, Vol. 109, Issue 2 https://doi.org/10.1016/0375-9474(68)90593-9	journal	February 1968
Indications for a bound tetraneutron Faestermann, Thomas; Bergmaier, Andreas; Gernhäuser, Roman Physics Letters B, Vol. 824 https://doi.org/10.1016/j.physletb.2021.136799	journal	January 2022
Recent development of complex scaling method for many-body resonances and continua in light nuclei Myo, Takayuki; Kikuchi, Yuma; Masui, Hiroshi Progress in Particle and Nuclear Physics, Vol. 79 https://doi.org/10.1016/j.ppnp.2014.08.001	journal	November 2014
Resonances in Few-body Systems Afnan, Ir Australian Journal of Physics, Vol. 44, Issue 3 https://doi.org/10.1071/ph910201	journal	January 1991
Complex scaling: Physics of unbound light nuclei and perspective Myo, Takayuki; Katō, Kiyoshi Progress of Theoretical and Experimental Physics, Vol. 2020, Issue 12 https://doi.org/10.1093/ptep/ptaa101	journal	December 2020
Energies and widths of Efimov states in the three-boson continuum Deltuva, A. Physical Review C, Vol. 102, Issue 3 https://doi.org/10.1103/physrevc.102.034003	journal	September 2020
Searching for three-nucleon resonances Csótó, A.; Oberhummer, H.; Pichler, R. Physical Review C, Vol. 53, Issue 4 https://doi.org/10.1103/physrevc.53.1589	journal	April 1996
Three-neutron resonance trajectories for realistic interaction models Lazauskas, Rimantas; Carbonell, Jaume Physical Review C, Vol. 71, Issue 4 https://doi.org/10.1103/physrevc.71.044004	journal	April 2005
Few-Body Bound States and Resonances in Finite Volume König, Sebastian GSI Helmholtzzentrum fuer Schwerionenforschung, GSI, Darmstadt https://doi.org/10.15120/gsi-2021-00633	text	January 2020
Ab initio calculations of the isotopic dependence of nuclear clustering Elhatisari, Serdar; Epelbaum, Evgeny; Krebs, Hermann arXiv https://doi.org/10.48550/arxiv.1702.05177	text	January 2017
Three-neutron resonance study using transition operators Deltuva, A. arXiv https://doi.org/10.48550/arxiv.1801.02919	text	January 2018
Comment on "Is a Trineutron Resonance Lower in Energy than a Tetraneutron Resonance?" [arXiv:1612.01502] Deltuva, A.; Lazauskas, R. arXiv https://doi.org/10.48550/arxiv.1904.00925	text	January 2019
Application of the complex scaling method in quantum scattering theory Lazauskas, Rimantas arXiv https://doi.org/10.48550/arxiv.1904.04675	preprint	January 2019
Gaussian characterization of the unitary window for $N=3$: bound, scattering and virtual states Kievsky, A. Deltuva. A.; Gattobigio, M.; Viviani, M. arXiv https://doi.org/10.48550/arxiv.2011.06828	preprint	January 2020
Two- and three-nucleon contact interactions and ground-state energies of light- and medium-mass nuclei Schiavilla, R.; Girlanda, L.; Gnech, A. arXiv https://doi.org/10.48550/arxiv.2102.02327	text	January 2021
Triatomic continuum resonances for large negative scattering lengths Bringas, F.; Yamashita, M. T.; Frederico, T. arXiv https://doi.org/10.48550/arxiv.cond-mat/0312291	text	January 2003
On the correlation between the binding energies of the triton and the alpha-particle Platter, L.; Hammer, H. -W.; Meißner, U. -G. arXiv https://doi.org/10.48550/arxiv.nucl-th/0409040	text	January 2004
Resonant Fermi gases with a large effective range Schwenk, A.; Pethick, C. J. arXiv https://doi.org/10.48550/arxiv.nucl-th/0506042	text	January 2005
Volume dependence of the energy spectrum in massive quantum field theories: II. Scattering states Lüscher, M. Communications in Mathematical Physics, Vol. 105, Issue 2 https://doi.org/10.1007/BF01211097	journal	June 1986
Volume dependence of the energy spectrum in massive quantum field theories: I. Stable particle states Lüscher, M. Communications in Mathematical Physics, Vol. 104, Issue 2 https://doi.org/10.1007/BF01211589	journal	June 1986
A class of analytic perturbations for one-body Schrödinger Hamiltonians Aguilar, J.; Combes, J. M. Communications in Mathematical Physics, Vol. 22, Issue 4 https://doi.org/10.1007/BF01877510	journal	December 1971
Spectral properties of many-body Schrödinger operators with dilatation-analytic interactions Balslev, E.; Combes, J. M. Communications in Mathematical Physics, Vol. 22, Issue 4 https://doi.org/10.1007/BF01877511	journal	December 1971
Few-Body Bound States and Resonances in Finite Volume König, Sebastian Few-Body Systems, Vol. 61, Issue 3 https://doi.org/10.1007/s00601-020-01550-8	journal	June 2020
Energy levels arising from resonant two-body forces in a three-body system Efimov, V. Physics Letters B, Vol. 33, Issue 8 https://doi.org/10.1016/0370-2693(70)90349-7	journal	December 1970
Is there a three-neutron resonance? Offermann, R.; Glöckle, W. Nuclear Physics A, Vol. 318, Issue 1-2 https://doi.org/10.1016/0375-9474(79)90475-5	journal	April 1979
Upper limits for bound states and resonance behavior in the trineutron system Miller, J. P.; Bistirlich, J. A.; Crowe, K. M. Nuclear Physics A, Vol. 343 https://doi.org/10.1016/0375-9474(80)90657-0	journal	July 1980
Pion double charge exchange on 3He and 4He Stetz, A.; Swenson, L. W.; Davis, J. Nuclear Physics A, Vol. 457, Issue 3-4 https://doi.org/10.1016/0375-9474(86)90474-4	journal	September 1986
Energy levels of light nuclei A = 3 Tilley, D. R.; Weller, H. R.; Hasan, H. H. Nuclear Physics A, Vol. 474, Issue 1 https://doi.org/10.1016/0375-9474(87)90193-X	journal	November 1987
Two-particle states on a torus and their relation to the scattering matrix Lüscher, Martin Nuclear Physics B, Vol. 354, Issue 2-3 https://doi.org/10.1016/0550-3213(91)90366-6	journal	May 1991
Signatures of unstable particles in finite volume Lüscher, Martin Nuclear Physics B, Vol. 364, Issue 1 https://doi.org/10.1016/0550-3213(91)90584-K	journal	October 1991
Resonance scattering phase shifts on a non-rest-frame lattice Rummukainen, K.; Gottlieb, Steven Nuclear Physics B, Vol. 450, Issue 1-2 https://doi.org/10.1016/0550-3213(95)00313-H	journal	September 1995
A new expansion for nucleon-nucleon interactions Kaplan, David B.; Savage, Martin J.; Wise, Mark B. Physics Letters B, Vol. 424, Issue 3-4 https://doi.org/10.1016/S0370-2693(98)00210-X	journal	April 1998
Nucleon-deuteron scattering from an effective field theory Bedaque, P. F.; van Kolck, U. Physics Letters B, Vol. 428, Issue 3-4 https://doi.org/10.1016/S0370-2693(98)00430-4	journal	June 1998
A renormalized equation for the three-body system with short-range interactions Hammer, H. -W.; Mehen, Thomas Nuclear Physics A, Vol. 690, Issue 4 https://doi.org/10.1016/S0375-9474(00)00710-7	journal	July 2001
Effective field theory of short-range forces van Kolck, U. Nuclear Physics A, Vol. 645, Issue 2 https://doi.org/10.1016/S0375-9474(98)00612-5	journal	January 1999
The three-boson system with short-range interactions Bedaque, P. F.; Hammer, H. -W.; van Kolck, U. Nuclear Physics A, Vol. 646, Issue 4 https://doi.org/10.1016/S0375-9474(98)00650-2	journal	February 1999
Two-nucleon systems from effective field theory Kaplan, David B.; Savage, Martin J.; Wise, Mark B. Nuclear Physics B, Vol. 534, Issue 1-2 https://doi.org/10.1016/S0550-3213(98)00440-4	journal	November 1998
Three-boson recombination at ultralow temperatures Yamashita, M. T.; Frederico, T.; Tomio, Lauro Physics Letters A, Vol. 363, Issue 5-6 https://doi.org/10.1016/j.physleta.2006.11.040	journal	April 2007
On the correlation between the binding energies of the triton and the α-particle Platter, L.; Hammer, H. -W.; Meißner, Ulf-G. Physics Letters B, Vol. 607, Issue 3-4 https://doi.org/10.1016/j.physletb.2004.12.068	journal	February 2005
Universality in few-body systems with large scattering length Braaten, Eric; Hammer, H. -W. Physics Reports, Vol. 428, Issue 5-6 https://doi.org/10.1016/j.physrep.2006.03.001	journal	June 2006
Resonances in Few-body Systems Afnan, Ir Australian Journal of Physics, Vol. 44, Issue 3 https://doi.org/10.1071/PH910201	journal	January 1991
Unnuclear physics: Conformal symmetry in nuclear reactions Hammer, Hans-Werner; Son, Dam Thanh Proceedings of the National Academy of Sciences, Vol. 118, Issue 35 https://doi.org/10.1073/pnas.2108716118	journal	August 2021
Subthreshold resonances in few-neutron systems Sofianos, S. A.; Rakityansky, S. A.; Vermaak, G. P. Journal of Physics G: Nuclear and Particle Physics, Vol. 23, Issue 11 https://doi.org/10.1088/0954-3899/23/11/010	journal	November 1997
Extracting the neutron–neutron scattering length—recent developments Gårdestig, Anders Journal of Physics G: Nuclear and Particle Physics, Vol. 36, Issue 5 https://doi.org/10.1088/0954-3899/36/5/053001	journal	April 2009
Efimov physics: a review Naidon, Pascal; Endo, Shimpei Reports on Progress in Physics, Vol. 80, Issue 5 https://doi.org/10.1088/1361-6633/aa50e8	journal	March 2017
Triatomic continuum resonances for large negative scattering lengths Bringas, F.; Yamashita, M. T.; Frederico, T. Physical Review A, Vol. 69, Issue 4 https://doi.org/10.1103/PhysRevA.69.040702	journal	April 2004
Four-boson system with short-range interactions Platter, L.; Hammer, H. -W.; Meißner, Ulf-G. Physical Review A, Vol. 70, Issue 5 https://doi.org/10.1103/PhysRevA.70.052101	journal	November 2004
Ab initio no-core Gamow shell-model calculations of multineutron systems Li, J. G.; Michel, N.; Hu, B. S. Physical Review C, Vol. 100, Issue 5 https://doi.org/10.1103/PhysRevC.100.054313	journal	November 2019
Three-neutron bound and continuum states Ishikawa, Souichi Physical Review C, Vol. 102, Issue 3 https://doi.org/10.1103/PhysRevC.102.034002	journal	September 2020
Energies and widths of Efimov states in the three-boson continuum Deltuva, A. Physical Review C, Vol. 102, Issue 3 https://doi.org/10.1103/PhysRevC.102.034003	journal	September 2020
Gaussian characterization of the unitary window for N = 3 : Bound, scattering, and virtual states Deltuva, A.; Gattobigio, M.; Kievsky, A. Physical Review C, Vol. 102, Issue 6 https://doi.org/10.1103/PhysRevC.102.064001	journal	December 2020
Comprehensive study of the three- and four-neutron systems at low energies Higgins, Michael D.; Greene, Chris H.; Kievsky, A. Physical Review C, Vol. 103, Issue 2 https://doi.org/10.1103/PhysRevC.103.024004	journal	February 2021
Two- and three-nucleon contact interactions and ground-state energies of light- and medium-mass nuclei Schiavilla, R.; Girlanda, L.; Gnech, A. Physical Review C, Vol. 103, Issue 5 https://doi.org/10.1103/PhysRevC.103.054003	journal	May 2021
S-matrix pole trajectory in a three-neutron model Glöckle, W. Physical Review C, Vol. 18, Issue 1 https://doi.org/10.1103/PhysRevC.18.564	journal	July 1978
Resonance poles in three-body systems Pearce, B. C.; Afnan, I. R. Physical Review C, Vol. 30, Issue 6 https://doi.org/10.1103/PhysRevC.30.2022	journal	December 1984
Faddeev equations with three-nucleon force in momentum space Stadler, A.; Glöckle, W.; Sauer, P. U. Physical Review C, Vol. 44, Issue 6 https://doi.org/10.1103/PhysRevC.44.2319	journal	December 1991
Resonances in Λ d scattering and the Σ hypertriton Afnan, I. R.; Gibson, B. F. Physical Review C, Vol. 47, Issue 3 https://doi.org/10.1103/PhysRevC.47.1000	journal	March 1993
Resonant state expansion of the resolvent Berggren, Tore; Lind, Patric Physical Review C, Vol. 47, Issue 2 https://doi.org/10.1103/PhysRevC.47.768	journal	February 1993
Searching for three-nucleon resonances Csótó, A.; Oberhummer, H.; Pichler, R. Physical Review C, Vol. 53, Issue 4 https://doi.org/10.1103/PhysRevC.53.1589	journal	April 1996
Pion double charge exchange and inelastic scattering on3He Yuly, M.; Fong, W.; Kinney, E. R. Physical Review C, Vol. 55, Issue 4 https://doi.org/10.1103/PhysRevC.55.1848	journal	April 1997
Effective theory for neutron-deuteron scattering: Energy dependence Bedaque, P. F.; Hammer, H. -W.; van Kolck, U. Physical Review C, Vol. 58, Issue 2 https://doi.org/10.1103/PhysRevC.58.R641	journal	August 1998
Resonances in the three-neutron system Witała, H.; Glöckle, W. Physical Review C, Vol. 60, Issue 2 https://doi.org/10.1103/PhysRevC.60.024002	journal	June 1999
Indications for the nonexistence of three-neutron resonances near the physical region Hemmdan, A.; Glöckle, W.; Kamada, H. Physical Review C, Vol. 66, Issue 5 https://doi.org/10.1103/PhysRevC.66.054001	journal	November 2002
Three-neutron resonance trajectories for realistic interaction models Lazauskas, Rimantas; Carbonell, Jaume Physical Review C, Vol. 71, Issue 4 https://doi.org/10.1103/PhysRevC.71.044004	journal	April 2005
Use of the discrete variable representation basis in nuclear physics Bulgac, Aurel; Forbes, Michael McNeil Physical Review C, Vol. 87, Issue 5 https://doi.org/10.1103/PhysRevC.87.051301	journal	May 2013
Universal physics of three bosons with isospin Hyodo, Tetsuo; Hatsuda, Tetsuo; Nishida, Yusuke Physical Review C, Vol. 89, Issue 3 https://doi.org/10.1103/PhysRevC.89.032201	journal	March 2014
Resonances in the Λ n n system Afnan, Iraj R.; Gibson, Benjamin F. Physical Review C, Vol. 92, Issue 5 https://doi.org/10.1103/PhysRevC.92.054608	journal	November 2015
Quantum Monte Carlo calculations of two neutrons in finite volume Klos, P.; Lynn, J. E.; Tews, I. Physical Review C, Vol. 94, Issue 5 https://doi.org/10.1103/PhysRevC.94.054005	journal	November 2016
Three-neutron resonance study using transition operators Deltuva, A. Physical Review C, Vol. 97, Issue 3 https://doi.org/10.1103/PhysRevC.97.034001	journal	March 2018
Signatures of few-body resonances in finite volume Klos, P.; König, S.; Hammer, H. -W. Physical Review C, Vol. 98, Issue 3 https://doi.org/10.1103/PhysRevC.98.034004	journal	September 2018
Candidate Resonant Tetraneutron State Populated by the He 4 ( He 8 , Be 8 ) Reaction Kisamori, K.; Shimoura, S.; Miya, H. Physical Review Letters, Vol. 116, Issue 5 https://doi.org/10.1103/PhysRevLett.116.052501	journal	February 2016
Is a Trineutron Resonance Lower in Energy than a Tetraneutron Resonance? Gandolfi, S.; Hammer, H. -W.; Klos, P. Physical Review Letters, Vol. 118, Issue 23 https://doi.org/10.1103/PhysRevLett.118.232501	journal	June 2017
Ab initio Calculations of the Isotopic Dependence of Nuclear Clustering Elhatisari, Serdar; Epelbaum, Evgeny; Krebs, Hermann Physical Review Letters, Vol. 119, Issue 22 https://doi.org/10.1103/PhysRevLett.119.222505	journal	December 2017
Comment on “Is a Trineutron Resonance Lower in Energy than a Tetraneutron Resonance?” Deltuva, A.; Lazauskas, R. Physical Review Letters, Vol. 123, Issue 6 https://doi.org/10.1103/PhysRevLett.123.069201	journal	August 2019
Gandolfi et al. Reply: Gandolfi, S.; Hammer, H. -W.; Klos, P. Physical Review Letters, Vol. 123, Issue 6 https://doi.org/10.1103/PhysRevLett.123.069202	journal	August 2019
Nonresonant Density of States Enhancement at Low Energies for Three or Four Neutrons Higgins, Michael D.; Greene, Chris H.; Kievsky, A. Physical Review Letters, Vol. 125, Issue 5 https://doi.org/10.1103/PhysRevLett.125.052501	journal	July 2020
Renormalization of the Three-Body System with Short-Range Interactions Bedaque, P. F.; Hammer, H. -W.; van Kolck, U. Physical Review Letters, Vol. 82, Issue 3 https://doi.org/10.1103/PhysRevLett.82.463	journal	January 1999
Resonant Fermi Gases with a Large Effective Range Schwenk, A.; Pethick, C. J. Physical Review Letters, Vol. 95, Issue 16 https://doi.org/10.1103/PhysRevLett.95.160401	journal	October 2005
Modern theory of nuclear forces Epelbaum, E.; Hammer, H. -W.; Meißner, Ulf-G. Reviews of Modern Physics, Vol. 81, Issue 4 https://doi.org/10.1103/RevModPhys.81.1773	journal	December 2009
Feshbach resonances in ultracold gases Chin, Cheng; Grimm, Rudolf; Julienne, Paul Reviews of Modern Physics, Vol. 82, Issue 2 https://doi.org/10.1103/RevModPhys.82.1225	journal	April 2010
Scattering processes and resonances from lattice QCD Briceño, Raúl A.; Dudek, Jozef J.; Young, Ross D. Reviews of Modern Physics, Vol. 90, Issue 2 https://doi.org/10.1103/RevModPhys.90.025001	journal	April 2018
Nuclear effective field theory: Status and perspectives Hammer, H. -W.; König, Sebastian; van Kolck, U. Reviews of Modern Physics, Vol. 92, Issue 2 https://doi.org/10.1103/RevModPhys.92.025004	journal	June 2020
The quest for light multineutron systems Marqués, F. Miguel; Carbonell, Jaume The European Physical Journal A, Vol. 57, Issue 3 https://doi.org/10.1140/epja/s10050-021-00417-8	journal	March 2021
E FFECTIVE F IELD T HEORY FOR F EW -N UCLEON S YSTEMS Bedaque, Paulo F.; van Kolck, Ubirajara Annual Review of Nuclear and Particle Science, Vol. 52, Issue 1 https://doi.org/10.1146/annurev.nucl.52.050102.090637	journal	December 2002
Efimov states for systems with negative scattering lengths Jonsell, S. Europhysics Letters (EPL), Vol. 76, Issue 1 https://doi.org/10.1209/epl/i2006-10235-1	journal	October 2006

Similar Records

Method for resonances and virtual states: Efimov virtual states

Journal Article · Thu Jul 01 00:00:00 EDT 1982 · Phys. Rev. C; (United States) · OSTI ID:5013030

Separable expansions for virtual states and resonances

Journal Article · Thu Mar 31 23:00:00 EST 1983 · Phys. Rev. C; (United States) · OSTI ID:5906449

Production of three-body Efimov molecules in an optical lattice

Journal Article · Mon Aug 15 00:00:00 EDT 2005 · Physical Review. A · OSTI ID:20718134

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
Cold atoms & matter waves
Effective field theory
Efimov states
Few-body systems
Lifetimes & widths
Nucleon-nucleon interactions

Three-body resonances in pionless effective field theory

Citation Formats

References (86)

Similar Records

Related Subjects