Few-Body Bound States and Resonances in Finite Volume

König, Sebastian

doi:10.1007/s00601-020-01550-8

Title: Few-Body Bound States and Resonances in Finite Volume

Journal Article · Mon Jun 29 00:00:00 EDT 2020 · Few-Body Systems

DOI:https://doi.org/10.1007/s00601-020-01550-8· OSTI ID:1768231

^[1]

Technische Univ. Darmstadt (Germany); GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt (Germany); North Carolina State Univ., Raleigh, NC (United States)

Since the pioneering work of Lüscher in the 1980s it is well known that considering quantum systems in finite volume, specifically, finite periodic boxes, can be used as a powerful computational tool to extract physical observables. While this formalism has been worked out in great detail in the two-body sector, much effort is currently being invested into deriving analogous relations for systems with more constituents. This work is relevant not only for nuclear physics, where lattice methods are now able to calculate few- and many-nucleon states, but also for other fields such as simulations of cold atoms. This article discusses recent progress regarding the extraction of few-body bound-state and resonance properties from finite-volume calculations of systems with an arbitrary number of constituents.

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

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP); ERC; STRONGINT and the Deutsche Forschungsgesellschaft (DFG)

Grant/Contract Number:: SC0013617; 307986; SFB 1245

OSTI ID:: 1768231

Journal Information:: Few-Body Systems, Vol. 61, Issue 3; ISSN 0177-7963

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

References (69)

Three-particle quantization condition in a finite volume: 1. The role of the three-particle force Hammer, Hans-Werner; Pang, Jin-Yi; Rusetsky, Akaki Journal of High Energy Physics, Vol. 2017, Issue 9, 23 p. https://doi.org/10.1007/JHEP09(2017)109	journal	September 2017
Ab Initio Calculation of the Spectrum and Structure of ${}^{16}O$ Epelbaum, Evgeny; Krebs, Hermann; Lähde, Timo A. Physical Review Letters, Vol. 112, Issue 10 https://doi.org/10.1103/PhysRevLett.112.102501	journal	March 2014
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
Energy shift of the three-particle system in a finite volume Pang, Jin-Yi; Wu, Jia-Jun; Hammer, Hans-Werner Physical Review D, Vol. 99, Issue 7 https://doi.org/10.1103/PhysRevD.99.074513	journal	April 2019
Non-relativistic bound states in a finite volume König, Sebastian; Lee, Dean; Hammer, H. -W. Annals of Physics, Vol. 327, Issue 6 https://doi.org/10.1016/j.aop.2011.12.015	journal	June 2012
Identification of resonance parameters from the finite volume energy spectrum Wiese, U. -J. Nuclear Physics B - Proceedings Supplements, Vol. 9 https://doi.org/10.1016/0920-5632(89)90171-0	journal	June 1989
Topological phases for bound states moving in a finite volume Bour, Shahin; König, Sebastian; Lee, Dean Physical Review D, Vol. 84, Issue 9 https://doi.org/10.1103/PhysRevD.84.091503	journal	November 2011
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
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
Medium-heavy nuclei from nucleon-nucleon interactions in lattice QCD Inoue, Takashi; Aoki, Sinya; Charron, Bruno Physical Review C, Vol. 91, Issue 1 https://doi.org/10.1103/PhysRevC.91.011001	journal	January 2015
Extracting scattering phase shifts in higher partial waves from lattice QCD calculations Luu, Thomas; Savage, Martin J. Physical Review D, Vol. 83, Issue 11 https://doi.org/10.1103/PhysRevD.83.114508	journal	June 2011
Combining ab initio calculations and low-energy effective field theory for halo nuclear systems: The case of ${}^{7}{Be} + p \to {}^{8}B + γ$ Zhang, Xilin; Nollett, Kenneth M.; Phillips, D. R. Physical Review C, Vol. 89, Issue 5 https://doi.org/10.1103/PhysRevC.89.051602	journal	May 2014
Exponential reduction of finite volume effects with twisted boundary conditions Cherman, Aleksey; Sen, Srimoyee; Wagman, Michael L. Physical Review D, Vol. 95, Issue 7 https://doi.org/10.1103/PhysRevD.95.074512	journal	April 2017
Improving the volume dependence of two-body binding energies calculated with lattice QCD Davoudi, Zohreh; Savage, Martin J. Physical Review D, Vol. 84, Issue 11 https://doi.org/10.1103/PhysRevD.84.114502	journal	December 2011
Overall Normalization of the Astrophysical $S$ Factor and the Nuclear Vertex Constant for ${}^{7}{Be} {(p, γ)}^{8} B$ Reactions Xu, H. M.; Gagliardi, C. A.; Tribble, R. E. Physical Review Letters, Vol. 73, Issue 15 https://doi.org/10.1103/PhysRevLett.73.2027	journal	October 1994
Proton-Proton Fusion and Tritium $β$ Decay from Lattice Quantum Chromodynamics Savage, Martin J.; Shanahan, Phiala E.; Tiburzi, Brian C. Physical Review Letters, Vol. 119, Issue 6 https://doi.org/10.1103/PhysRevLett.119.062002	journal	August 2017
Three-particle quantization condition in a finite volume: 2. General formalism and the analysis of data Hammer, Hans-Werner; Pang, Jin-Yi; Rusetsky, Akaki Journal of High Energy Physics, Vol. 2017, Issue 10, 31 p. https://doi.org/10.1007/JHEP10(2017)115	journal	October 2017
Numerical exploration of three relativistic particles in a finite volume including two-particle resonances and bound states Romero-López, Fernando; Sharpe, Stephen R.; Blanton, Tyler D. Journal of High Energy Physics, Vol. 2019, Issue 10 https://doi.org/10.1007/JHEP10(2019)007	journal	October 2019
Possibility of generating a 4-neutron resonance with a $T = 3 / 2$ isospin 3-neutron force Hiyama, E.; Lazauskas, R.; Carbonell, J. Physical Review C, Vol. 93, Issue 4 https://doi.org/10.1103/PhysRevC.93.044004	journal	April 2016
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
Two-particle elastic scattering in a finite volume including QED Beane, Silas R.; Savage, Martin J. Physical Review D, Vol. 90, Issue 7 https://doi.org/10.1103/PhysRevD.90.074511	journal	October 2014
Three particles in a finite volume Polejaeva, K.; Rusetsky, A. The European Physical Journal A, Vol. 48, Issue 5 https://doi.org/10.1140/epja/i2012-12067-8	journal	May 2012
Three-particle scattering amplitudes from a finite volume formalism Briceño, Raúl A.; Davoudi, Zohreh Physical Review D, Vol. 87, Issue 9 https://doi.org/10.1103/PhysRevD.87.094507	journal	May 2013
Magnetic structure of light nuclei from lattice QCD Chang, Emmanuel; Detmold, William; Orginos, Kostas Physical Review D, Vol. 92, Issue 11 https://doi.org/10.1103/PhysRevD.92.114502	journal	December 2015
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
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
Time-dependent density functional theory with twist-averaged boundary conditions Schuetrumpf, B.; Nazarewicz, W.; Reinhard, P. -G. Physical Review C, Vol. 93, Issue 5 https://doi.org/10.1103/PhysRevC.93.054304	journal	May 2016
Two-particle multichannel systems in a finite volume with arbitrary spin Briceño, Raúl A. Physical Review D, Vol. 89, Issue 7 https://doi.org/10.1103/PhysRevD.89.074507	journal	April 2014
Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude Hansen, Maxwell T.; Sharpe, Stephen R. Physical Review D, Vol. 92, Issue 11 https://doi.org/10.1103/PhysRevD.92.114509	journal	December 2015
Two-baryon systems with twisted boundary conditions Briceño, Raúl A.; Davoudi, Zohreh; Luu, Thomas C. Physical Review D, Vol. 89, Issue 7 https://doi.org/10.1103/PhysRevD.89.074509	journal	April 2014
Unitarity of the infinite-volume three-particle scattering amplitude arising from a finite-volume formalism Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R. Physical Review D, Vol. 100, Issue 5 https://doi.org/10.1103/PhysRevD.100.054508	journal	September 2019
Using Gaussian elimination for computation of the central difference equation coefficients Cynar, Sandra J. ACM SIGNUM Newsletter, Vol. 22, Issue 2 https://doi.org/10.1145/24936.24939	journal	April 1987
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
Three particles in a finite volume: The breakdown of spherical symmetry Kreuzer, S.; Grießhammer, H. W. The European Physical Journal A, Vol. 48, Issue 7 https://doi.org/10.1140/epja/i2012-12093-6	journal	July 2012
Causality and the effective range expansion Hammer, H. -W.; Lee, Dean Annals of Physics, Vol. 325, Issue 10 https://doi.org/10.1016/j.aop.2010.06.006	journal	October 2010
Study of quark mass dependence of binding energy for light nuclei in $2 + 1$ flavor lattice QCD Yamazaki, Takeshi; Ishikawa, Ken-ichi; Kuramashi, Yoshinobu Physical Review D, Vol. 92, Issue 1 https://doi.org/10.1103/PhysRevD.92.014501	journal	July 2015
Three-Body Physics in a Finite Volume Kreuzer, Simon; Hammer, H. -W. Few-Body Systems, Vol. 54, Issue 1-4 https://doi.org/10.1007/s00601-012-0365-7	journal	March 2012
Twisted boundary conditions in lattice simulations Sachrajda, C. T.; Villadoro, G. Physics Letters B, Vol. 609, Issue 1-2 https://doi.org/10.1016/j.physletb.2005.01.033	journal	March 2005
Three-body unitarity in the finite volume Mai, M.; Döring, M. The European Physical Journal A, Vol. 53, Issue 12 https://doi.org/10.1140/epja/i2017-12440-1	journal	December 2017
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
Ab initio alpha–alpha scattering Elhatisari, Serdar; Lee, Dean; Rupak, Gautam Nature, Vol. 528, Issue 7580 https://doi.org/10.1038/nature16067	journal	December 2015
Angular momentum on a lattice Johnson, R. C. Physics Letters B, Vol. 114, Issue 2-3 https://doi.org/10.1016/0370-2693(82)90134-4	journal	July 1982
Nuclear Binding Near a Quantum Phase Transition Elhatisari, Serdar; Li, Ning; Rokash, Alexander Physical Review Letters, Vol. 117, Issue 13 https://doi.org/10.1103/PhysRevLett.117.132501	journal	September 2016
Candidate Resonant Tetraneutron State Populated by the ${}^{4}{He} ({}^{8}{He}, {}^{8}{Be})$ 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
Effective field theory description of halo nuclei Hammer, H-W; Ji, C.; Phillips, D. R. Journal of Physics G: Nuclear and Particle Physics, Vol. 44, Issue 10 https://doi.org/10.1088/1361-6471/aa83db	journal	September 2017
Spin-2 NΩ dibaryon from lattice QCD Etminan, Faisal; Nemura, Hidekatsu; Aoki, Sinya Nuclear Physics A, Vol. 928 https://doi.org/10.1016/j.nuclphysa.2014.05.014	journal	August 2014
Calculation of three-body resonances using slow-variable discretization coupled with a complex absorbing potential Blandon, Juan; Kokoouline, Viatcheslav; Masnou-Seeuws, Françoise Physical Review A, Vol. 75, Issue 4 https://doi.org/10.1103/PhysRevA.75.042508	journal	April 2007
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
Tetraneutron resonance in the presence of a dineutron Deltuva, A.; Lazauskas, R. Physical Review C, Vol. 100, Issue 4 https://doi.org/10.1103/PhysRevC.100.044002	journal	October 2019
Two-nucleon higher partial-wave scattering from lattice QCD Berkowitz, Evan; Kurth, Thorsten; Nicholson, Amy Physics Letters B, Vol. 765 https://doi.org/10.1016/j.physletb.2016.12.024	journal	February 2017
The ratio method: A new tool to study one-neutron halo nuclei Capel, P.; Johnson, R. C.; Nunes, F. M. Physical Review C, Vol. 88, Issue 4 https://doi.org/10.1103/PhysRevC.88.044602	journal	October 2013
Two-nucleon scattering in multiple partial waves Nicholson, Amy Proceedings of The 33rd International Symposium on Lattice Field Theory — PoS(LATTICE 2015) https://doi.org/10.22323/1.251.0083	conference	July 2016
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
Lattice simulations for few- and many-body systems Lee, Dean Progress in Particle and Nuclear Physics, Vol. 63, Issue 1 https://doi.org/10.1016/j.ppnp.2008.12.001	journal	July 2009
The triton in a finite volume Kreuzer, Simon; Hammer, H. -W. Physics Letters B, Vol. 694, Issue 4-5 https://doi.org/10.1016/j.physletb.2010.10.003	journal	January 2011
Light nuclei and nucleon form factors in $N_f=2+1$ lattice QCD Yamazaki, Takeshi Proceedings of The 33rd International Symposium on Lattice Field Theory — PoS(LATTICE 2015) https://doi.org/10.22323/1.251.0081	conference	July 2016
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
Three-body spectrum in a finite volume: The role of cubic symmetry Döring, M.; Hammer, H. -W.; Mai, M. Physical Review D, Vol. 97, Issue 11 https://doi.org/10.1103/PhysRevD.97.114508	journal	June 2018
Applying twisted boundary conditions for few-body nuclear systems Körber, Christopher; Luu, Thomas Physical Review C, Vol. 93, Issue 5 https://doi.org/10.1103/PhysRevC.93.054002	journal	May 2016
Solution of few-body problems with the stochastic variational method I. Central forces with zero orbital momentum Varga, K.; Suzuki, Y. Computer Physics Communications, Vol. 106, Issue 1-2 https://doi.org/10.1016/S0010-4655(97)00059-3	journal	October 1997
Pion-less effective field theory for atomic nuclei and lattice nuclei Bansal, A.; Binder, S.; Ekström, A. Physical Review C, Vol. 98, Issue 5 https://doi.org/10.1103/PhysRevC.98.054301	journal	November 2018
Finite-volume effects for two-hadron states in moving frames Kim, C. H.; Sachrajda, C. T.; Sharpe, Stephen R. Nuclear Physics B, Vol. 727, Issue 1-2 https://doi.org/10.1016/j.nuclphysb.2005.08.029	journal	October 2005
Is a physically observable tetraneutron resonance compatible with realistic nuclear interactions? Lazauskas, Rimantas; Carbonell, Jaume Physical Review C, Vol. 72, Issue 3 https://doi.org/10.1103/PhysRevC.72.034003	journal	September 2005
Finite volume effects in low-energy neutron–deuteron scattering Rokash, A.; Epelbaum, E.; Krebs, H. Journal of Physics G: Nuclear and Particle Physics, Vol. 41, Issue 1 https://doi.org/10.1088/0954-3899/41/1/015105	journal	December 2013
Volume dependence of N -body bound states König, Sebastian; Lee, Dean Physics Letters B, Vol. 779 https://doi.org/10.1016/j.physletb.2018.01.060	journal	April 2018
Effective field theory in the harmonic oscillator basis Binder, S.; Ekström, A.; Hagen, G. Physical Review C, Vol. 93, Issue 4 https://doi.org/10.1103/PhysRevC.93.044332	journal	April 2016
Complex Scaling of the Hyper-Spheric Coordinates and Faddeev Equations Fedorov, D. V.; Garrido, E.; Jensen, A. S. Few-Body Systems, Vol. 33, Issue 2-3 https://doi.org/10.1007/s00601-003-0012-4	journal	October 2003
Magnetic Moments of Light Nuclei from Lattice Quantum Chromodynamics Beane, S. R.; Chang, E.; Cohen, S. Physical Review Letters, Vol. 113, Issue 25 https://doi.org/10.1103/PhysRevLett.113.252001	journal	December 2014
Can Tetraneutron be a Narrow Resonance? Fossez, K.; Rotureau, J.; Michel, N. Physical Review Letters, Vol. 119, Issue 3 https://doi.org/10.1103/PhysRevLett.119.032501	journal	July 2017

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