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K. and others", collaboration = "Belle", title = "{Observation of a narrow charmonium-like state in exclusive $B^\pm \to K^\pm \pi^+ \pi^- J/\psi$ decays}", eprint = "hep-ex/0309032", archivePrefix = "arXiv", doi = "10.1103/PhysRevLett.91.262001", journal = "Phys. Rev. Lett.", volume = "91", pages = "262001", year = "2003" } @article{Hansen:2014eka, author = "Hansen, Maxwell T. and Sharpe, Stephen R.", title = "{Relativistic, model-independent, three-particle quantization condition}", doi = "10.1103/PhysRevD.90.116003", journal = "Phys. Rev. D", volume = "90", number = "11", pages = "116003", year = "2014" } @article{Hansen:2015zga, author = "Hansen, Maxwell T. and Sharpe, Stephen R.", title = "{Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude}", doi = "10.1103/PhysRevD.92.114509", journal = "Phys. Rev. D", volume = "92", number = "11", pages = "114509", year = "2015" } @article{Briceno:2017tce, author = "Brice\~no, Ra\'ul A. and Hansen, Maxwell T. and Sharpe, Stephen R.", title = "{Relating the finite-volume spectrum and the two-and-three-particle $S$ matrix for relativistic systems of identical scalar particles}", eprint = "1701.07465", archivePrefix = "arXiv", primaryClass = "hep-lat", reportNumber = "JLAB-THY-17-2400", doi = "10.1103/PhysRevD.95.074510", journal = "Phys. Rev. D", volume = "95", number = "7", pages = "074510", year = "2017" } @article{Briceno:2018aml, author = "Brice\~no, Ra\'ul A. and Hansen, Maxwell T. and Sharpe, Stephen R.", title = "{Three-particle systems with resonant subprocesses in a finite volume}", eprint = "1810.01429", archivePrefix = "arXiv", primaryClass = "hep-lat", reportNumber = "JLAB-THY-18-2819", doi = "10.1103/PhysRevD.99.014516", journal = "Phys. Rev. D", volume = "99", number = "1", pages = "014516", year = "2019" } @article{Blanton:2021mih, author = "Blanton, Tyler D. and Sharpe, Stephen R.", title = "{Three-particle finite-volume formalism for \ensuremath{\pi}+\ensuremath{\pi}+K+ and related systems}", eprint = "2105.12094", archivePrefix = "arXiv", primaryClass = "hep-lat", doi = "10.1103/PhysRevD.104.034509", journal = "Phys. Rev. D", volume = "104", number = "3", pages = "034509", year = "2021" } @article{RevModPhys.90.025001, title = {Scattering processes and resonances from lattice QCD}, author = {Brice\~no, Ra\'ul A. and Dudek, Jozef J. and Young, Ross D.}, journal = {Rev. Mod. Phys.}, volume = {90}, issue = {2}, pages = {025001}, numpages = {38}, year = {2018}, month = {Apr}, publisher = {American Physical Society}, doi = {10.1103/RevModPhys.90.025001}, url = {https://link.aps.org/doi/10.1103/RevModPhys.90.025001} } @article{doi:10.1146/annurev-nucl-101918-023723, author = {Hansen, Maxwell T. and Sharpe, Stephen R.}, title = {Lattice QCD and Three-Particle Decays of Resonances}, journal = {Annual Review of Nuclear and Particle Science}, volume = {69}, number = {1}, pages = {65-107}, year = {2019}, doi = {10.1146/annurev-nucl-101918-023723}, URL = { https://doi.org/10.1146/annurev-nucl-101918-023723 }, eprint = { https://doi.org/10.1146/annurev-nucl-101918-023723 } , abstract = { Most strong-interaction resonances have decay channels involving three or more particles, including many of the recently discovered X, Y, and Z resonances. In order to study such resonances from first principles using lattice QCD, one must understand finite-volume effects for three particles in the cubic box used in calculations. We review efforts to develop a three-particle quantization condition that relates finite-volume energies to infinite-volume scattering amplitudes. We describe in detail the three approaches that have been followed, and present new results on the relationship between the corresponding results. We show examples of the numerical implementation of all three approaches and point out the important issues that remain to be resolved. } } @article{PhysRevLett.123.042002, title = {Quark-Mass Dependence of Elastic $\ensuremath{\pi}K$ Scattering from QCD}, author = {Wilson, David J. and Brice\~no, Ra\'ul A. and Dudek, Jozef J. and Edwards, Robert G. and Thomas, Christopher E.}, collaboration = {for the Hadron Spectrum Collaboration}, journal = {Phys. Rev. Lett.}, volume = {123}, issue = {4}, pages = {042002}, numpages = {7}, year = {2019}, month = {Jul}, publisher = {American Physical Society}, doi = {10.1103/PhysRevLett.123.042002}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.123.042002} } @article{PhysRevD.100.114514, title = {Cross-channel study of pion scattering from lattice QCD}, author = {Mai, M. and Culver, C. and Alexandru, A. and D\"oring, M. and Lee, F. X.}, journal = {Phys. Rev. D}, volume = {100}, issue = {11}, pages = {114514}, numpages = {11}, year = {2019}, month = {Dec}, publisher = {American Physical Society}, doi = {10.1103/PhysRevD.100.114514}, url = {https://link.aps.org/doi/10.1103/PhysRevD.100.114514} } @article{Fischer:2020yvw, author = "Fischer, Matthias and Kostrzewa, Bartosz and Mai, Maxim and Petschlies, Marcus and Pittler, Ferenc and Ueding, Martin and Urbach, Carsten and Werner, Markus", collaboration = "Extended Twisted Mass, ETM", title = "{The $\rho$-resonance from $N_f$ = 2 lattice QCD including the physical pion mass}", eprint = "2006.13805", archivePrefix = "arXiv", primaryClass = "hep-lat", doi = "10.1016/j.physletb.2021.136449", journal = "Phys. Lett. B", volume = "819", pages = "136449", year = "2021" } @article{ExtendedTwistedMass:2019omo, author = "Werner, Markus and others", collaboration = "Extended Twisted Mass", title = "{Hadron-Hadron Interactions from $N_f=2+1+1$ Lattice QCD: The $\rho$-resonance}", eprint = "1907.01237", archivePrefix = "arXiv", primaryClass = "hep-lat", doi = "10.1140/epja/s10050-020-00057-4", journal = "Eur. Phys. J. A", volume = "56", number = "2", pages = "61", year = "2020" } @article{BRETT201829, title = {Determination of s- and p-wave I = 1/2 $K\pi$ scattering amplitudes in Nf = 2 + 1 lattice QCD}, journal = {Nuclear Physics B}, volume = {932}, pages = {29-51}, year = {2018}, issn = {0550-3213}, doi = {https://doi.org/10.1016/j.nuclphysb.2018.05.008}, url = {https://www.sciencedirect.com/science/article/pii/S0550321318301329}, author = {Ruairí Brett and John Bulava and Jacob Fallica and Andrew Hanlon and Ben Hörz and Colin Morningstar}, abstract = {The elastic I=1/2, s- and p-wave kaon-pion scattering amplitudes are calculated using a single ensemble of anisotropic lattice QCD gauge field configurations with Nf=2+1 flavors of dynamical Wilson-clover fermions at mπ=230 MeV. A large spatial extent of L=3.7 fm enables a good energy resolution while partial wave mixing due to the reduced symmetries of the finite volume is treated explicitly. The p-wave amplitude is well described by a Breit–Wigner shape with parameters mK⁎/mπ=3.808(18) and gK⁎KπBW=5.33(20) which are insensitive to the inclusion of d-wave mixing and variation of the s-wave parametrization. An effective range description of the near-threshold s-wave amplitude yields mπa0=−0.353(25).} } @article{Blanton:2019vdk, author = "Blanton, Tyler D. and Romero-L\'opez, Fernando and Sharpe, Stephen R.", title = "{$I=3$ Three-Pion Scattering Amplitude from Lattice QCD}", eprint = "1909.02973", archivePrefix = "arXiv", primaryClass = "hep-lat", doi = "10.1103/PhysRevLett.124.032001", journal = "Phys. Rev. Lett.", volume = "124", number = "3", pages = "032001", year = "2020" } @article{Mai:2019fba, author = {Mai, M. and D\"oring, M. and Culver, C. and Alexandru, A.}, title = "{Three-body unitarity versus finite-volume $\pi^+\pi^+\pi^+$ spectrum from lattice QCD}", doi = "10.1103/PhysRevD.101.054510", journal = "Phys. Rev. D", volume = "101", number = "5", pages = "054510", year = "2020" } @book{Schoenberg:1973, author = {Schoenberg, I. J.}, title = {Cardinal Spline Interpolation}, publisher = {Society for Industrial and Applied Mathematics}, year = {1973}, doi = {10.1137/1.9781611970555}, address = {}, edition = {}, URL = {https://epubs.siam.org/doi/abs/10.1137/1.9781611970555}, eprint = {https://epubs.siam.org/doi/pdf/10.1137/1.9781611970555} } @article{PhysRev.167.1505, title = {Off-Shell Solution of Scattering Equations}, author = {Brayshaw, D. D.}, journal = {Phys. Rev.}, volume = {167}, issue = {5}, pages = {1505--1516}, numpages = {0}, year = {1968}, month = {Mar}, publisher = {American Physical Society}, doi = {10.1103/PhysRev.167.1505}, url = {https://link.aps.org/doi/10.1103/PhysRev.167.1505} } @article{Huber:2022nzs, author = "Huber, Markus Q. and Kern, Wolfgang and Alkofer, Reinhard", title = "{On the analytic structure of three-point functions from contour deformations}", eprint = "2212.02515", archivePrefix = "arXiv", primaryClass = "hep-ph", month = "12", year = "2022" } @article{Hansen:2016ync, author = "Hansen, Maxwell T. and Sharpe, Stephen R.", title = "{Applying the relativistic quantization condition to a three-particle bound state in a periodic box}", eprint = "1609.04317", archivePrefix = "arXiv", primaryClass = "hep-lat", doi = "10.1103/PhysRevD.95.034501", journal = "Phys. Rev. D", volume = "95", number = "3", pages = "034501", year = "2017" } @article{Briceno:2018mlh, author = "Brice\~no, Ra\'ul A. and Hansen, Maxwell T. and Sharpe, Stephen R.", title = "{Numerical study of the relativistic three-body quantization condition in the isotropic approximation}", eprint = "1803.04169", archivePrefix = "arXiv", primaryClass = "hep-lat", reportNumber = "JLAB-THY-18-2657, CERN-TH-2018-046", doi = "10.1103/PhysRevD.98.014506", journal = "Phys. Rev. D", volume = "98", number = "1", pages = "014506", year = "2018" } @article{Bogaert:2014, author = {Bogaert, I.}, title = {Iteration-Free Computation of Gauss--Legendre Quadrature Nodes and Weights}, journal = {SIAM Journal on Scientific Computing}, volume = {36}, number = {3}, pages = {A1008-A1026}, year = {2014}, doi = {10.1137/140954969}, URL = { https://doi.org/10.1137/140954969 }, eprint = { https://doi.org/10.1137/140954969 } , abstract = { Gauss--Legendre quadrature rules are of considerable theoretical and practical interest because of their role in numerical integration and interpolation. In this paper, a series expansion for the zeros of the Legendre polynomials is constructed. In addition, a series expansion useful for the computation of the Gauss--Legendre weights is derived. Together, these two expansions provide a practical and fast iteration-free method to compute individual Gauss--Legendre node-weight pairs in \${\mathcal{O}}(1)\$ complexity and with double precision accuracy. An expansion for the barycentric interpolation weights for the Gauss--Legendre nodes is also derived. A C++ implementation is available online. } } @article{Horacek:1977pv, author = "Horacek, J. and Malina, L.", title = "{Cubic Splines and the Lippmann-Schwinger Equation}", doi = "10.1007/BF01587479", journal = "Czech. J. Phys. B", volume = "27", pages = "1--6", year = "1977" } @article{Sadasivan:2021emk, author = {Sadasivan, Daniel and Alexandru, Andrei and Akdag, Hakan and Amorim, Felipe and Brett, Ruair\'\i{} and Culver, Chris and D\"oring, Michael and Lee, Frank X. and Mai, Maxim}, title = "{Pole position of the a1(1260) resonance in a three-body unitary framework}", reportNumber = "JLAB-THY-21-3533", doi = "10.1103/PhysRevD.105.054020", journal = "Phys. Rev. D", volume = "105", number = "5", pages = "054020", year = "2022" } @article{Garofalo:2022pux, author = "Garofalo, Marco and Mai, Maxim and Romero-L\'opez, Fernando and Rusetsky, Akaki and Urbach, Carsten", title = "{Three-body resonances in the \ensuremath{\varphi}$^{4}$ theory}", eprint = "2211.05605", archivePrefix = "arXiv", primaryClass = "hep-lat", reportNumber = "MIT-CTP/5487", doi = "10.1007/JHEP02(2023)252", journal = "JHEP", volume = "02", pages = "252", year = "2023" } @article{Blanton:2021llb, author = {Blanton, Tyler D. and Hanlon, Andrew D. and H\"orz, Ben and Morningstar, Colin and Romero-L\'opez, Fernando and Sharpe, Stephen R.}, title = "{Interactions of two and three mesons including higher partial waves from lattice QCD}", eprint = "2106.05590", archivePrefix = "arXiv", primaryClass = "hep-lat", doi = "10.1007/JHEP10(2021)023", journal = "JHEP", volume = "10", pages = "023", year = "2021" } @article{Hansen:2020otl, author = "Hansen, Maxwell T. and Brice\~no, Raul A. and Edwards, Robert G. and Thomas, Christopher E. and Wilson, David J.", collaboration = "Hadron Spectrum", title = "{Energy-Dependent $\pi^+ \pi^+ \pi^+$ Scattering Amplitude from QCD}", reportNumber = "CERN-TH-2020-147, JLAB-THY-20-3242", doi = "10.1103/PhysRevLett.126.012001", journal = "Phys. Rev. Lett.", volume = "126", pages = "012001", year = "2021" } @article{Fischer:2020jzp, author = "Fischer, Matthias and Kostrzewa, Bartosz and Liu, Liuming and Romero-L\'opez, Fernando and Ueding, Martin and Urbach, Carsten", title = "{Scattering of two and three physical pions at maximal isospin from lattice QCD}", eprint = "2008.03035", archivePrefix = "arXiv", primaryClass = "hep-lat", doi = "10.1140/epjc/s10052-021-09206-5", journal = "Eur. Phys. J. C", volume = "81", number = "5", pages = "436", year = "2021" } @article{Horz:2019rrn, author = {H\"orz, Ben and Hanlon, Andrew}, title = "{Two- and three-pion finite-volume spectra at maximal isospin from lattice QCD}", eprint = "1905.04277", archivePrefix = "arXiv", primaryClass = "hep-lat", reportNumber = "MITP/19-033", doi = "10.1103/PhysRevLett.123.142002", journal = "Phys. Rev. Lett.", volume = "123", number = "14", pages = "142002", year = "2019" } @article{Blanton:2020gha, author = "Blanton, Tyler D. and Sharpe, Stephen R.", title = "{Alternative derivation of the relativistic three-particle quantization condition}", eprint = "2007.16188", archivePrefix = "arXiv", primaryClass = "hep-lat", doi = "10.1103/PhysRevD.102.054520", journal = "Phys. Rev. D", volume = "102", number = "5", pages = "054520", year = "2020" } @article{Muller:2021uur, author = {M\"uller, Fabian and Pang, Jin-Yi and Rusetsky, Akaki and Wu, Jia-Jun}, title = "{Relativistic-invariant formulation of the NREFT three-particle quantization condition}", eprint = "2110.09351", archivePrefix = "arXiv", primaryClass = "hep-lat", doi = "10.1007/JHEP02(2022)158", journal = "JHEP", volume = "02", pages = "158", year = "2022" } @article{Blanton:2020jnm, author = "Blanton, Tyler D. and Sharpe, Stephen R.", title = "{Equivalence of relativistic three-particle quantization conditions}", eprint = "2007.16190", archivePrefix = "arXiv", primaryClass = "hep-lat", doi = "10.1103/PhysRevD.102.054515", journal = "Phys. Rev. D", volume = "102", number = "5", pages = "054515", year = "2020" } @article{Jackura:2019bmu, author = "Jackura, A. W. and Dawid, S. M. and Fern\'andez-Ram\'\i{}rez, C. and Mathieu, V. and Mikhasenko, M. and Pilloni, A. and Sharpe, S. R. and Szczepaniak, A. P.", title = "{Equivalence of three-particle scattering formalisms}", eprint = "1905.12007", archivePrefix = "arXiv", primaryClass = "hep-ph", reportNumber = "JLAB-THY-19-2947", doi = "10.1103/PhysRevD.100.034508", journal = "Phys. Rev. D", volume = "100", number = "3", pages = "034508", year = "2019" } @article{Mai:2017bge, author = {Mai, M. and D\"oring, M.}, title = "{Three-body Unitarity in the Finite Volume}", reportNumber = "JLAB-THY-17-2554", doi = "10.1140/epja/i2017-12440-1", journal = "Eur. Phys. J. 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D}, volume = {97}, issue = {5}, pages = {054513}, numpages = {24}, year = {2018}, month = {Mar}, publisher = {American Physical Society}, doi = {10.1103/PhysRevD.97.054513}, url = {https://link.aps.org/doi/10.1103/PhysRevD.97.054513} } @article{PhysRevC.103.014003, title = {Two-nucleon $S$-wave interactions at the SU(3) flavor-symmetric point with ${m}_{ud}\ensuremath{\approx}{m}_{s}^{\text{phys}}$: A first lattice QCD calculation with the stochastic Laplacian Heaviside method}, author = {H\"orz, Ben and Howarth, Dean and Rinaldi, Enrico and Hanlon, Andrew and Chang, Chia Cheng and K\"orber, Christopher and Berkowitz, Evan and Bulava, John and Clark, M. A. and Lee, Wayne Tai and Morningstar, Colin and Nicholson, Amy and Vranas, Pavlos and Walker-Loud, Andr\'e}, journal = {Phys. Rev. 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The future holds more surprises for us, thanks to new-generation experiments. Understanding the signals and determining the properties of the states requires a parallel theoretical effort. To make full use of available and forthcoming data, a careful amplitude modeling is required, together with a sound treatment of the statistical uncertainties, and a systematic survey of the model dependencies. We review the contributions made by the Joint Physics Analysis Center to the field of hadron spectroscopy.} } @Article{Mai:2017vot, Title = {{Three-body Unitarity with Isobars Revisited}}, Author = {Mai, M. and Hu, B. and D\"oring, M. and Pilloni, A. and Szczepaniak, A.}, Journal = {Eur.Phys.J.}, Year = {2017}, Pages = {177}, Volume = {A53}, Doi = {10.1140/epja/i2017-12368-4}, Reportnumber = {JLAB-THY-17-2496}, Slaccitation = {%%CITATION = ARXIV:1706.06118;%%} } @Article{Grisaru:1966xyz, Title = {Three-Particle Contributions to Elastic Scattering}, Author = {Grisaru, M. 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D", volume = "100", number = "9", pages = "094001", year = "2019" } @article{Mikhasenko:2018bzm, author = "Mikhasenko, M. and Pilloni, A. and Albaladejo, M. and Fern\'andez-Ram\'\i{}rez, C. and Jackura, A. and Mathieu, V. and Nys, J. and Rodas, A. and Ketzer, B. and Szczepaniak, A.P.", collaboration = "JPAC", title = "{Pole position of the $a_1(1260)$ from $\tau$-decay}", eprint = "1810.00016", archivePrefix = "arXiv", primaryClass = "hep-ph", reportNumber = "JLAB-THY-18-2816", doi = "10.1103/PhysRevD.98.096021", journal = "Phys. Rev. D", volume = "98", number = "9", pages = "096021", year = "2018" } @article{LHCb:2015yax, author = "Aaij, Roel and others", collaboration = "LHCb", title = "{Observation of $J/\psi p$ Resonances Consistent with Pentaquark States in $\Lambda_b^0 \to J/\psi K^- p$ Decays}", eprint = "1507.03414", archivePrefix = "arXiv", primaryClass = "hep-ex", reportNumber = "CERN-PH-EP-2015-153, LHCB-PAPER-2015-029", doi = "10.1103/PhysRevLett.115.072001", journal = "Phys. Rev. Lett.", volume = "115", pages = "072001", year = "2015" } @article{Garzia:2018ctr, author = "Garzia, I.", collaboration = "BESIII", title = "{Recent results for the BESIII experiment}", doi = "10.1393/ncc/i2018-18102-0", journal = "Nuovo Cim. C", volume = "41", number = "3", pages = "102", year = "2018" } @article{Roper:1964, title = {Evidence for a ${P}_{11}$ Pion-Nucleon Resonance at 556 MeV}, author = {Roper, L. David}, journal = {Phys. Rev. Lett.}, volume = {12}, issue = {12}, pages = {340--342}, numpages = {0}, year = {1964}, month = {Mar}, publisher = {American Physical Society}, doi = {10.1103/PhysRevLett.12.340}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.12.340} } @article{E852:1998mbq, author = "Adams, G. S. and others", collaboration = "E852", title = "{Observation of a new J(PC) = 1-+ exotic state in the reaction pi- p --\ensuremath{>} pi+ pi- pi- p at 18-GeV/c}", doi = "10.1103/PhysRevLett.81.5760", journal = "Phys. Rev. Lett.", volume = "81", pages = "5760--5763", year = "1998" } @article{COMPASS:2018uzl, author = "Aghasyan, M. and others", collaboration = "COMPASS", title = "{Light isovector resonances in $\pi^- p \to \pi^-\pi^-\pi^+ p$ at 190 GeV/${\it c}$}", eprint = "1802.05913", archivePrefix = "arXiv", primaryClass = "hep-ex", reportNumber = "CERN-EP-2018-021", doi = "10.1103/PhysRevD.98.092003", journal = "Phys. Rev. D", volume = "98", number = "9", pages = "092003", year = "2018" } @article{LHCb:2020fvo, author = "Aaij, Roel and others", collaboration = "LHCb", title = "{Study of the $\psi_2(3823)$ and $\chi_{c1}(3872)$ states in $B^+ \rightarrow \left( J\psi\pi^+\pi^-\right)K^+$ decays}", eprint = "2005.13422", archivePrefix = "arXiv", primaryClass = "hep-ex", reportNumber = "CERN-EP-2020-071, LHCb-PAPER-2020-009", doi = "10.1007/JHEP08(2020)123", journal = "JHEP", volume = "08", pages = "123", year = "2020" } @article{E705:1993pry, author = "Antoniazzi, L. and others", collaboration = "E705", title = "{Search for hidden charm resonance states decaying into J / Psi or Psi-prime plus pions}", reportNumber = "FERMILAB-PUB-92-265-E", doi = "10.1103/PhysRevD.50.4258", journal = "Phys. Rev. D", volume = "50", pages = "4258--4264", year = "1994" } @article{Belle:2003nnu, author = "Choi, S. K. and others", collaboration = "Belle", title = "{Observation of a narrow charmonium-like state in exclusive $B^\pm \to K^\pm \pi^+ \pi^- J/\psi$ decays}", eprint = "hep-ex/0309032", archivePrefix = "arXiv", doi = "10.1103/PhysRevLett.91.262001", journal = "Phys. Rev. Lett.", volume = "91", pages = "262001", year = "2003" } @article{Briceno:2017tce, author = "Brice\~no, Ra\'ul A. and Hansen, Maxwell T. and Sharpe, Stephen R.", title = "{Relating the finite-volume spectrum and the two-and-three-particle $S$ matrix for relativistic systems of identical scalar particles}", eprint = "1701.07465", archivePrefix = "arXiv", primaryClass = "hep-lat", reportNumber = "JLAB-THY-17-2400", doi = "10.1103/PhysRevD.95.074510", journal = "Phys. Rev. D", volume = "95", number = "7", pages = "074510", year = "2017" } @article{Hansen:2020zhy, author = "Hansen, Maxwell T. and Romero-L\'opez, Fernando and Sharpe, Stephen R.", title = "{Generalizing the relativistic quantization condition to include all three-pion isospin channels}", eprint = "2003.10974", archivePrefix = "arXiv", primaryClass = "hep-lat", reportNumber = "CERN-TH-2020-045", doi = "10.1007/JHEP07(2020)047", journal = "JHEP", volume = "07", pages = "047", year = "2020", note = "[Erratum: JHEP 02, 014 (2021)]" } @article{Blanton:2021mih, author = "Blanton, Tyler D. and Sharpe, Stephen R.", title = "{Three-particle finite-volume formalism for \ensuremath{\pi}+\ensuremath{\pi}+K+ and related systems}", eprint = "2105.12094", archivePrefix = "arXiv", primaryClass = "hep-lat", doi = "10.1103/PhysRevD.104.034509", journal = "Phys. Rev. D", volume = "104", number = "3", pages = "034509", year = "2021" } @article{Luscher:1986pf, author = "Luscher, M.", title = "{Volume Dependence of the Energy Spectrum in Massive Quantum Field Theories. 2. Scattering States}", reportNumber = "DESY-86-034", doi = "10.1007/BF01211097", journal = "Commun. Math. Phys.", volume = "105", pages = "153--188", year = "1986" } @article{RevModPhys.90.025001, title = {Scattering processes and resonances from lattice QCD}, author = {Brice\~no, Ra\'ul A. and Dudek, Jozef J. and Young, Ross D.}, journal = {Rev. Mod. Phys.}, volume = {90}, issue = {2}, pages = {025001}, numpages = {38}, year = {2018}, month = {Apr}, publisher = {American Physical Society}, doi = {10.1103/RevModPhys.90.025001}, url = {https://link.aps.org/doi/10.1103/RevModPhys.90.025001} } @article{doi:10.1146/annurev-nucl-101918-023723, author = {Hansen, Maxwell T. and Sharpe, Stephen R.}, title = {Lattice QCD and Three-Particle Decays of Resonances}, journal = {Annual Review of Nuclear and Particle Science}, volume = {69}, number = {1}, pages = {65-107}, year = {2019}, doi = {10.1146/annurev-nucl-101918-023723}, URL = { https://doi.org/10.1146/annurev-nucl-101918-023723 }, eprint = { https://doi.org/10.1146/annurev-nucl-101918-023723 } , abstract = { Most strong-interaction resonances have decay channels involving three or more particles, including many of the recently discovered X, Y, and Z resonances. In order to study such resonances from first principles using lattice QCD, one must understand finite-volume effects for three particles in the cubic box used in calculations. We review efforts to develop a three-particle quantization condition that relates finite-volume energies to infinite-volume scattering amplitudes. We describe in detail the three approaches that have been followed, and present new results on the relationship between the corresponding results. We show examples of the numerical implementation of all three approaches and point out the important issues that remain to be resolved. } } @article{PhysRevLett.123.042002, title = {Quark-Mass Dependence of Elastic $\ensuremath{\pi}K$ Scattering from QCD}, author = {Wilson, David J. and Brice\~no, Ra\'ul A. and Dudek, Jozef J. and Edwards, Robert G. and Thomas, Christopher E.}, collaboration = {for the Hadron Spectrum Collaboration}, journal = {Phys. Rev. Lett.}, volume = {123}, issue = {4}, pages = {042002}, numpages = {7}, year = {2019}, month = {Jul}, publisher = {American Physical Society}, doi = {10.1103/PhysRevLett.123.042002}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.123.042002} } @article{PhysRevD.100.114514, title = {Cross-channel study of pion scattering from lattice QCD}, author = {Mai, M. and Culver, C. and Alexandru, A. and D\"oring, M. and Lee, F. X.}, journal = {Phys. Rev. D}, volume = {100}, issue = {11}, pages = {114514}, numpages = {11}, year = {2019}, month = {Dec}, publisher = {American Physical Society}, doi = {10.1103/PhysRevD.100.114514}, url = {https://link.aps.org/doi/10.1103/PhysRevD.100.114514} } @article{Fischer:2020yvw, author = "Fischer, Matthias and Kostrzewa, Bartosz and Mai, Maxim and Petschlies, Marcus and Pittler, Ferenc and Ueding, Martin and Urbach, Carsten and Werner, Markus", collaboration = "Extended Twisted Mass, ETM", title = "{The $\rho$-resonance from $N_f$ = 2 lattice QCD including the physical pion mass}", eprint = "2006.13805", archivePrefix = "arXiv", primaryClass = "hep-lat", doi = "10.1016/j.physletb.2021.136449", journal = "Phys. Lett. B", volume = "819", pages = "136449", year = "2021" } @article{ExtendedTwistedMass:2019omo, author = "Werner, Markus and others", collaboration = "Extended Twisted Mass", title = "{Hadron-Hadron Interactions from $N_f=2+1+1$ Lattice QCD: The $\rho$-resonance}", eprint = "1907.01237", archivePrefix = "arXiv", primaryClass = "hep-lat", doi = "10.1140/epja/s10050-020-00057-4", journal = "Eur. Phys. J. A", volume = "56", number = "2", pages = "61", year = "2020" } @article{BRETT201829, title = {Determination of s- and p-wave I = 1/2 $K\pi$ scattering amplitudes in Nf = 2 + 1 lattice QCD}, journal = {Nuclear Physics B}, volume = {932}, pages = {29-51}, year = {2018}, issn = {0550-3213}, doi = {https://doi.org/10.1016/j.nuclphysb.2018.05.008}, url = {https://www.sciencedirect.com/science/article/pii/S0550321318301329}, author = {Ruairí Brett and John Bulava and Jacob Fallica and Andrew Hanlon and Ben Hörz and Colin Morningstar}, abstract = {The elastic I=1/2, s- and p-wave kaon-pion scattering amplitudes are calculated using a single ensemble of anisotropic lattice QCD gauge field configurations with Nf=2+1 flavors of dynamical Wilson-clover fermions at mπ=230 MeV. A large spatial extent of L=3.7 fm enables a good energy resolution while partial wave mixing due to the reduced symmetries of the finite volume is treated explicitly. The p-wave amplitude is well described by a Breit–Wigner shape with parameters mK⁎/mπ=3.808(18) and gK⁎KπBW=5.33(20) which are insensitive to the inclusion of d-wave mixing and variation of the s-wave parametrization. An effective range description of the near-threshold s-wave amplitude yields mπa0=−0.353(25).} } @article{Dawid:2020uhn, author = "Dawid, Sebastian M. and Szczepaniak, Adam P.", title = "{Bound states in the B-matrix formalism for the three-body scattering}", reportNumber = "JLAB-THY-20-3274", doi = "10.1103/PhysRevD.103.014009", journal = "Phys. Rev. D", volume = "103", number = "1", pages = "014009", year = "2021" } @article{Hansen:2016ync, author = "Hansen, Maxwell T. and Sharpe, Stephen R.", title = "{Applying the relativistic quantization condition to a three-particle bound state in a periodic box}", doi = "10.1103/PhysRevD.95.034501", journal = "Phys. Rev. D", volume = "95", number = "3", pages = "034501", year = "2017" } @article{Briceno:2018mlh, author = "Brice\~no, Ra\'ul A. and Hansen, Maxwell T. and Sharpe, Stephen R.", title = "{Numerical study of the relativistic three-body quantization condition in the isotropic approximation}", reportNumber = "JLAB-THY-18-2657, CERN-TH-2018-046", doi = "10.1103/PhysRevD.98.014506", journal = "Phys. Rev. D", volume = "98", number = "1", pages = "014506", year = "2018" } @article{Muller:2021uur, author = {M\"uller, Fabian and Pang, Jin-Yi and Rusetsky, Akaki and Wu, Jia-Jun}, title = "{Relativistic-invariant formulation of the NREFT three-particle quantization condition}", eprint = "2110.09351", archivePrefix = "arXiv", primaryClass = "hep-lat", doi = "10.1007/JHEP02(2022)158", journal = "JHEP", volume = "02", pages = "158", year = "2022" } @article{Mai:2017wdv, author = "Mai, Maxim and Hu, Bin and Doring, Michael and Pilloni, Alessandro and Szczepaniak, Adam", title = "{Three-body scattering in isobar ansatz}", doi = "10.22323/1.310.0140", journal = "PoS", volume = "Hadron2017", pages = "140", year = "2018" } @article{Doring:2018xxx, author = {D\"oring, M. and Hammer, H. -W. and Mai, M. and Pang, J. -Y. and Rusetsky, \textsection{} A. and Wu, J.}, title = "{Three-body spectrum in a finite volume: the role of cubic symmetry}", eprint = "1802.03362", archivePrefix = "arXiv", primaryClass = "hep-lat", reportNumber = "JLAB-THY-18-2646", doi = "10.1103/PhysRevD.97.114508", journal = "Phys. Rev. D", volume = "97", number = "11", pages = "114508", year = "2018" } @article{Woss:2018irj, author = "Woss, Antoni and Thomas, Christopher E. and Dudek, Jozef J. and Edwards, Robert G. and Wilson, David J.", title = "{Dynamically-coupled partial-waves in $\rho\pi$ isospin-2 scattering from lattice QCD}", eprint = "1802.05580", archivePrefix = "arXiv", primaryClass = "hep-lat", reportNumber = "DAMTP-2018-6, JLAB-THY-18-2643", doi = "10.1007/JHEP07(2018)043", journal = "JHEP", volume = "07", pages = "043", year = "2018" } @article{PhysRevD.97.054513, title = {Isoscalar $\ensuremath{\pi}\ensuremath{\pi},\text{ }K\overline{K},\text{ }\ensuremath{\eta}\ensuremath{\eta}$ scattering and the $\ensuremath{\sigma},\text{ }{f}_{0},\text{ }{f}_{2}$ mesons from QCD}, author = {Brice\~no, Raul A. and Dudek, Jozef J. and Edwards, Robert G. and Wilson, David J.}, collaboration = {for the Hadron Spectrum Collaboration}, journal = {Phys. Rev. D}, volume = {97}, issue = {5}, pages = {054513}, numpages = {24}, year = {2018}, month = {Mar}, publisher = {American Physical Society}, doi = {10.1103/PhysRevD.97.054513}, url = {https://link.aps.org/doi/10.1103/PhysRevD.97.054513} } @article{PhysRevC.103.014003, title = {Two-nucleon $S$-wave interactions at the SU(3) flavor-symmetric point with ${m}_{ud}\ensuremath{\approx}{m}_{s}^{\text{phys}}$: A first lattice QCD calculation with the stochastic Laplacian Heaviside method}, author = {H\"orz, Ben and Howarth, Dean and Rinaldi, Enrico and Hanlon, Andrew and Chang, Chia Cheng and K\"orber, Christopher and Berkowitz, Evan and Bulava, John and Clark, M. A. and Lee, Wayne Tai and Morningstar, Colin and Nicholson, Amy and Vranas, Pavlos and Walker-Loud, Andr\'e}, journal = {Phys. Rev. C}, volume = {103}, issue = {1}, pages = {014003}, numpages = {18}, year = {2021}, month = {Jan}, publisher = {American Physical Society}, doi = {10.1103/PhysRevC.103.014003}, url = {https://link.aps.org/doi/10.1103/PhysRevC.103.014003} } @article{PhysRevD.102.114520, title = {$I=1/2$ $S$-wave and $P$-wave $K\ensuremath{\pi}$ scattering and the $\ensuremath{\kappa}$ and ${K}^{*}$ resonances from lattice QCD}, author = {Rendon, Gumaro and Leskovec, Luka and Meinel, Stefan and Negele, John and Paul, Srijit and Petschlies, Marcus and Pochinsky, Andrew and Silvi, Giorgio and Syritsyn, Sergey}, journal = {Phys. Rev. D}, volume = {102}, issue = {11}, pages = {114520}, numpages = {22}, year = {2020}, month = {Dec}, publisher = {American Physical Society}, doi = {10.1103/PhysRevD.102.114520}, url = {https://link.aps.org/doi/10.1103/PhysRevD.102.114520} } @article{Woss:2019hse, author = "Woss, Antoni J. and Thomas, Christopher E. and Dudek, Jozef J. and Edwards, Robert G. and Wilson, David J.", title = "{$b_1$ resonance in coupled $\pi\omega$, $\pi\phi$ scattering from lattice QCD}", eprint = "1904.04136", archivePrefix = "arXiv", primaryClass = "hep-lat", reportNumber = "DAMTP-2019-12, JLAB-THY-19-2910", doi = "10.1103/PhysRevD.100.054506", journal = "Phys. Rev. D", volume = "100", number = "5", pages = "054506", year = "2019" } @article{Gayer:2021xzv, author = "Gayer, Luke and Lang, Nicolas and Ryan, Sin\'ead M. and Tims, David and Thomas, Christopher E. and Wilson, David J.", collaboration = "Hadron Spectrum", title = "{Isospin-1/2 D\ensuremath{\pi} scattering and the lightest $ {D}_0^{\ast } $ resonance from lattice QCD}", eprint = "2102.04973", archivePrefix = "arXiv", primaryClass = "hep-lat", doi = "10.1007/JHEP07(2021)123", journal = "JHEP", volume = "07", pages = "123", year = "2021" } @article{PhysRevD.97.014506, title = {Elastic $I=3/2$ $p$-wave nucleon-pion scattering amplitude and the $\mathrm{\ensuremath{\Delta}}(1232)$ resonance from ${N}_{f}=2+1$ lattice QCD}, author = {Andersen, Christian Walther and Bulava, John and H\"orz, Ben and Morningstar, Colin}, journal = {Phys. Rev. D}, volume = {97}, issue = {1}, pages = {014506}, numpages = {7}, year = {2018}, month = {Jan}, publisher = {American Physical Society}, doi = {10.1103/PhysRevD.97.014506}, url = {https://link.aps.org/doi/10.1103/PhysRevD.97.014506} } @article{Luscher:1985dn, author = "Luscher, M.", title = "{Volume Dependence of the Energy Spectrum in Massive Quantum Field Theories. 1. Stable Particle States}", reportNumber = "DESY-85-144", doi = "10.1007/BF01211589", journal = "Commun. Math. Phys.", volume = "104", pages = "177", year = "1986" } @article{LUSCHER1991531, title = {Two-particle states on a torus and their relation to the scattering matrix}, journal = {Nuclear Physics B}, volume = {354}, number = {2}, pages = {531-578}, year = {1991}, issn = {0550-3213}, doi = {https://doi.org/10.1016/0550-3213(91)90366-6}, url = {https://www.sciencedirect.com/science/article/pii/0550321391903666}, author = {Martin Lüscher}, abstract = {The energy spectrum of a system of two particles enclosed in a box with periodic boundary conditions is characteristic for the forces between the particles. For box sizes greater than the interaction range, and for energies below the inelastic threshold, the spectrum is shown to be determined by the scattering phases at these energies. Simple exact formulae are derived which can be used to compute the energy levels given the scattering phases or, conversely, to calculate the scattering phases if the energy spectrum is known.} } @article{Bourjaily:2020wvq, author = "Bourjaily, Jacob L. and Hannesdottir, Holmfridur and McLeod, Andrew J. and Schwartz, Matthew D. and Vergu, Cristian", title = "{Sequential Discontinuities of Feynman Integrals and the Monodromy Group}", eprint = "2007.13747", archivePrefix = "arXiv", primaryClass = "hep-th", doi = "10.1007/JHEP01(2021)205", journal = "JHEP", volume = "01", pages = "205", year = "2021" } @article{Blanton:2020gmf, author = "Blanton, Tyler D. and Sharpe, Stephen R.", title = "{Relativistic three-particle quantization condition for nondegenerate scalars}", eprint = "2011.05520", archivePrefix = "arXiv", primaryClass = "hep-lat", doi = "10.1103/PhysRevD.103.054503", journal = "Phys. Rev. D", volume = "103", number = "5", pages = "054503", year = "2021" } @article{Arndt:2006bf, author = "Arndt, R. A. and Briscoe, W. J. and Strakovsky, I. I. and Workman, R. L.", title = "{Extended partial-wave analysis of piN scattering data}", eprint = "nucl-th/0605082", archivePrefix = "arXiv", doi = "10.1103/PhysRevC.74.045205", journal = "Phys. Rev. C", volume = "74", pages = "045205", year = "2006" } @article{ALBALADEJO2022103981, title = {Novel approaches in hadron spectroscopy}, journal = {Progress in Particle and Nuclear Physics}, volume = {127}, pages = {103981}, year = {2022}, issn = {0146-6410}, doi = {https://doi.org/10.1016/j.ppnp.2022.103981}, url = {https://www.sciencedirect.com/science/article/pii/S0146641022000424}, author = {Miguel Albaladejo and Łukasz Bibrzycki and Sebastian M. Dawid and César Fernández-Ramírez and Sergi Gonzàlez-Solís and Astrid N. Hiller Blin and Andrew W. Jackura and Vincent Mathieu and Mikhail Mikhasenko and Victor I. Mokeev and Emilie Passemar and Alessandro Pilloni and Arkaitz Rodas and Jorge A. Silva-Castro and Wyatt A. Smith and Adam P. Szczepaniak and Daniel Winney}, keywords = {Hadron spectroscopy, Exotic hadrons, Three-body scattering, Resonance production}, abstract = {The last two decades have witnessed the discovery of a myriad of new and unexpected hadrons. The future holds more surprises for us, thanks to new-generation experiments. Understanding the signals and determining the properties of the states requires a parallel theoretical effort. To make full use of available and forthcoming data, a careful amplitude modeling is required, together with a sound treatment of the statistical uncertainties, and a systematic survey of the model dependencies. We review the contributions made by the Joint Physics Analysis Center to the field of hadron spectroscopy.} } @Article{Grisaru:1966xyz, Title = {Three-Particle Contributions to Elastic Scattering}, Author = {Grisaru, M. 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B", volume = "823", pages = "136773", year = "2021" } @article{Frederico:2021wej, author = "Frederico, T. and Ydrefors, E.", title = "{Three-Bosons in a Finite 4D Euclidean Volume}", doi = "10.1007/s00601-021-01594-4", journal = "Few Body Syst.", volume = "62", number = "1", pages = "8", year = "2021" } @article{Wang:2020ojz, author = "Wang, Ziyue and Jiang, Shao-Jian and Jiang, Yin", title = "{Relativistic Borromean States}", eprint = "2004.05997", archivePrefix = "arXiv", primaryClass = "hep-ph", doi = "10.1088/1674-1137/abe197", journal = "Chin. Phys. C", volume = "45", number = "4", pages = "041006", year = "2021" } @article{Ydrefors:2019jvu, author = "Ydrefors, E. and Alvarenga Nogueira, J. H. and Karmanov, V. A. and Frederico, T.", title = "{Solving the three-body bound-state Bethe-Salpeter equation in Minkowski space}", eprint = "1903.01741", archivePrefix = "arXiv", primaryClass = "hep-ph", doi = "10.1016/j.physletb.2019.02.046", journal = "Phys. Lett. B", volume = "791", pages = "276--280", year = "2019" } @article{Ydrefors:2017nnc, author = "Ydrefors, E. and Alvarenga Nogueira, J. H. and Gigante, V. and Frederico, T. and Karmanov, V. A.", title = "{Three-body bound states with zero-range interaction in the Bethe\textendash{}Salpeter approach}", eprint = "1703.07981", archivePrefix = "arXiv", primaryClass = "nucl-th", doi = "10.1016/j.physletb.2017.04.035", journal = "Phys. Lett. B", volume = "770", pages = "131--137", year = "2017" } @article{Pazy:2020ufm, author = "Pazy, Ehoud", title = "{Fractal geometry and the mapping of Efimov states to Bloch states}", eprint = "2005.12350", archivePrefix = "arXiv", primaryClass = "nucl-th", doi = "10.1103/PhysRevE.102.022136", journal = "Phys. Rev. E", volume = "102", number = "2", pages = "022136", year = "2020" } %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % EFIMOV STATES PAPERS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @article{Frederico:2023fee, author = "Frederico, Tobias and Gattobigio, Mario", title = "{Universal tetramer limit-cycle at the unitarity limit}", eprint = "2303.14952", archivePrefix = "arXiv", primaryClass = "physics.atm-clus", month = "3", year = "2023" } @article{Rosa:2022vql, author = "Rosa, D. S. and Frederico, T. and Krein, G. and Yamashita, M. T.", title = "{D-dimensional three-body bound-state problem with zero-range interactions}", eprint = "2209.00575", archivePrefix = "arXiv", primaryClass = "physics.atom-ph", doi = "10.1103/PhysRevA.106.023311", journal = "Phys. Rev. A", volume = "106", number = "2", pages = "023311", year = "2022" } @article{Pricoupenko:2023nak, author = "Pricoupenko, Ludovic", title = "{Universality of isolated $N$-body resonances at large scattering length}", eprint = "2303.12637", archivePrefix = "arXiv", primaryClass = "cond-mat.quant-gas", month = "3", year = "2023" } @article{Hyodo:2013zxa, author = "Hyodo, Tetsuo and Hatsuda, Tetsuo and Nishida, Yusuke", title = "{Universal physics of three bosons with isospin}", reportNumber = "YITP-13-121, RIKEN-QHP-106", doi = "10.1103/PhysRevC.89.032201", journal = "Phys. Rev. C", volume = "89", number = "3", pages = "032201", year = "2014" } @article{Dietz:2021haj, author = {Dietz, Sebastian and Hammer, Hans-Werner and K\"onig, Sebastian and Schwenk, Achim}, title = "{Three-body resonances in pionless effective field theory}", eprint = "2109.11356", archivePrefix = "arXiv", primaryClass = "nucl-th", doi = "10.1103/PhysRevC.105.064002", journal = "Phys. Rev. C", volume = "105", number = "6", pages = "064002", year = "2022" } @article{Deltuva:2021fmj, author = "Deltuva, A.", title = "{Efimov resonances above four-boson threshold}", eprint = "2106.01458", archivePrefix = "arXiv", primaryClass = "nucl-th", doi = "10.1103/PhysRevC.103.064001", journal = "Phys. Rev. C", volume = "103", number = "6", pages = "064001", year = "2021" } @article{Valderrama:2018azi, author = "Valderrama, Manuel Pavon", title = "{$\bar{D}^* \bar{D}^* \Sigma_c$ three-body system}", eprint = "1811.10173", archivePrefix = "arXiv", primaryClass = "hep-ph", doi = "10.1103/PhysRevD.99.034010", journal = "Phys. Rev. D", volume = "99", number = "3", pages = "034010", year = "2019" } @article{Valderrama:2018sap, author = "Valderrama, Manuel Pavon", title = "{$D^* D^* \bar{D}$ and $D^* D^* \bar{D}^*$ three-body systems}", eprint = "1805.10584", archivePrefix = "arXiv", primaryClass = "hep-ph", doi = "10.1103/PhysRevD.98.034017", journal = "Phys. Rev. D", volume = "98", number = "3", pages = "034017", year = "2018" } @article{Canham:2009zq, author = "Canham, David L. and Hammer, H. -W. and Springer, Roxanne P.", title = "{On the scattering of D and D* mesons off the X(3872)}", eprint = "0906.1263", archivePrefix = "arXiv", primaryClass = "hep-ph", reportNumber = "HISKP-TH-09-15", doi = "10.1103/PhysRevD.80.014009", journal = "Phys. Rev. D", volume = "80", pages = "014009", year = "2009" } @article{Braaten:2003he, author = "Braaten, Eric and Kusunoki, Masaoki", title = "{Low-energy universality and the new charmonium resonance at 3870-MeV}", eprint = "hep-ph/0311147", archivePrefix = "arXiv", doi = "10.1103/PhysRevD.69.074005", journal = "Phys. Rev. D", volume = "69", pages = "074005", year = "2004" } @article{Wilbring:2017fwy, author = "Wilbring, E. and Hammer, H. -W. and Mei\ss{}ner, Ulf-G.", title = "{Three-body universality in the B meson sector}", eprint = "1705.06176", archivePrefix = "arXiv", primaryClass = "hep-ph", month = "5", year = "2017" } @article{Konishi:2017mpx, author = "Konishi, Atsunari and Morimatsu, Osamu and Yasui, Shigehiro", title = "{New Universality for Near-Threshold Three-Body Resonances}", eprint = "1705.02569", archivePrefix = "arXiv", primaryClass = "hep-ph", month = "5", year = "2017" } @article{Matsuyama:1991bm, author = "Matsuyama, A. and Yazaki, K.", title = "{S matrix pole trajectory of the three-body system}", doi = "10.1016/0375-9474(91)90464-H", journal = "Nucl. Phys. A", volume = "534", pages = "620--636", year = "1991" } @article{Delfino:1996zz, author = "Delfino, A. and Frederico, T.", title = "{Scaling of three-body S-matrix poles}", doi = "10.1103/PhysRevC.53.62", journal = "Phys. Rev. C", volume = "53", pages = "62--65", year = "1996" } @article{Adhikari:1982zz, author = "Adhikari, Sadhan Kumar and Tomio, Lauro", title = "{Efimov effect in the three-nucleon system}", doi = "10.1103/PhysRevC.26.83", journal = "Phys. Rev. C", volume = "26", pages = "83--86", year = "1982" } @article{PhysRevA.82.043633, title = {Crossover in the Efimov spectrum}, author = {Pricoupenko, Ludovic}, journal = {Phys. Rev. A}, volume = {82}, issue = {4}, pages = {043633}, numpages = {6}, year = {2010}, month = {Oct}, publisher = {American Physical Society}, doi = {10.1103/PhysRevA.82.043633}, url = {https://link.aps.org/doi/10.1103/PhysRevA.82.043633} } @article{PhysRevLett.112.190401, title = {Observation of the Second Triatomic Resonance in Efimov's Scenario}, author = {Huang, Bo and Sidorenkov, Leonid A. and Grimm, Rudolf and Hutson, Jeremy M.}, journal = {Phys. Rev. Lett.}, volume = {112}, issue = {19}, pages = {190401}, numpages = {5}, year = {2014}, month = {May}, publisher = {American Physical Society}, doi = {10.1103/PhysRevLett.112.190401}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.112.190401} } @article{Yamashita:2007cc, author = "Yamashita, M. T. and Frederico, T. and Tomio, L.", title = "{Comment on `Efimov states and their fano resonances in a neutron-rich nucleus'}", eprint = "0711.3684", archivePrefix = "arXiv", primaryClass = "nucl-th", doi = "10.1103/PhysRevLett.99.269201", journal = "Phys. Rev. Lett.", volume = "99", pages = "269201", year = "2007" } @article{Yamashita:2007ej, author = "Yamashita, M. T. and Frederico, T. and Tomio, Lauro", title = "{Trajectory of excited state of neutron$-$neutron$-^{18}C$ system}", eprint = "0704.1461", archivePrefix = "arXiv", primaryClass = "nucl-th", doi = "10.1016/j.physletb.2008.01.008", journal = "Phys. Lett. B", volume = "660", pages = "339--344", year = "2008" } @article{Yamashita:2002zz, author = "Yamashita, M. T. and Frederico, T. and Delfino, A. and Tomio, Lauro", title = "{Scaling limit of virtual states of triatomic systems}", eprint = "physics/0209025", archivePrefix = "arXiv", doi = "10.1103/PhysRevA.66.052702", journal = "Phys. Rev. A", volume = "66", pages = "052702", year = "2002" } @article{Bringas:2004zz, author = "Bringas, F. and Yamashita, M. T. and Frederico, T.", title = "{Triatomic continuum resonances for large negative scattering lengths}", doi = "10.1103/PhysRevA.69.040702", journal = "Phys. Rev. A", volume = "69", pages = "040702", year = "2004" } @article{Kamiya:2017pcq, author = "Kamiya, Yuki and Hyodo, Tetsuo", title = "{Structure of hadron resonances with a nearby zero of the amplitude}", reportNumber = "YITP-17-118", doi = "10.1103/PhysRevD.97.054019", journal = "Phys. Rev. D", volume = "97", number = "5", pages = "054019", year = "2018" } @article{PhysRevLett.102.140401, title = {Evidence for Universal Four-Body States Tied to an Efimov Trimer}, author = {Ferlaino, F. and Knoop, S. and Berninger, M. and Harm, W. and D'Incao, J. P. and N\"agerl, H.-C. and Grimm, R.}, journal = {Phys. Rev. Lett.}, volume = {102}, issue = {14}, pages = {140401}, numpages = {4}, year = {2009}, month = {Apr}, publisher = {American Physical Society}, doi = {10.1103/PhysRevLett.102.140401}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.102.140401} } @article{PhysRevLett.107.120401, title = {Universality of the Three-Body Parameter for Efimov States in Ultracold Cesium}, author = {Berninger, M. and Zenesini, A. and Huang, B. and Harm, W. and N\"agerl, H.-C. and Ferlaino, F. and Grimm, R. and Julienne, P. S. and Hutson, J. M.}, journal = {Phys. Rev. Lett.}, volume = {107}, issue = {12}, pages = {120401}, numpages = {5}, year = {2011}, month = {Sep}, publisher = {American Physical Society}, doi = {10.1103/PhysRevLett.107.120401}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.107.120401} } @article{PhysRevLett.112.250404, title = {Observation of Efimov Resonances in a Mixture with Extreme Mass Imbalance}, author = {Pires, R. and Ulmanis, J. and H\"afner, S. and Repp, M. and Arias, A. and Kuhnle, E. D. and Weidem\"uller, M.}, journal = {Phys. Rev. Lett.}, volume = {112}, issue = {25}, pages = {250404}, numpages = {5}, year = {2014}, month = {Jun}, publisher = {American Physical Society}, doi = {10.1103/PhysRevLett.112.250404}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.112.250404} } @article{PhysRevLett.71.4103, title = {Efimov effect in coordinate space Faddeev equations}, author = {Fedorov, D. V. and Jensen, A. S.}, journal = {Phys. Rev. Lett.}, volume = {71}, issue = {25}, pages = {4103--4106}, numpages = {0}, year = {1993}, month = {Dec}, publisher = {American Physical Society}, doi = {10.1103/PhysRevLett.71.4103}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.71.4103} } @article{PhysRevLett.108.263001, title = {Origin of the Three-Body Parameter Universality in Efimov Physics}, author = {Wang, Jia and D'Incao, J. P. and Esry, B. D. and Greene, Chris H.}, journal = {Phys. Rev. Lett.}, volume = {108}, issue = {26}, pages = {263001}, numpages = {5}, year = {2012}, month = {Jun}, publisher = {American Physical Society}, doi = {10.1103/PhysRevLett.108.263001}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.108.263001} } @article{zaccanti2009observation, title={Observation of an Efimov spectrum in an atomic system}, author={Zaccanti, Matteo and Deissler, Benjamin and D’Errico, Chiara and Fattori, Marco and Jona-Lasinio, Mattia and M{\"u}ller, Stefan and Roati, Giacomo and Inguscio, Massimo and Modugno, Giovanni}, journal={Nature Physics}, volume={5}, number={8}, pages={586--591}, year={2009}, publisher={Nature Publishing Group UK London} } @article{PhysRevLett.103.163202, title = {Observation of Universality in Ultracold $^{7}\mathrm{Li}$ Three-Body Recombination}, author = {Gross, Noam and Shotan, Zav and Kokkelmans, Servaas and Khaykovich, Lev}, journal = {Phys. Rev. Lett.}, volume = {103}, issue = {16}, pages = {163202}, numpages = {4}, year = {2009}, month = {Oct}, publisher = {American Physical Society}, doi = {10.1103/PhysRevLett.103.163202}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.103.163202} } @article{ doi:10.1126/science.1182840, author = {Scott E. Pollack and Daniel Dries and Randall G. Hulet }, title = {Universality in Three- and Four-Body Bound States of Ultracold Atoms}, journal = {Science}, volume = {326}, number = {5960}, pages = {1683-1685}, year = {2009}, doi = {10.1126/science.1182840}, abstract = {As powerful as theoretical physics can be, when it comes to describing the dynamics of several interacting particles, it stumbles at three. This few-body physics is interesting in many contexts, particularly interactions within the nucleus and between atoms and molecules. Although predicted 40 years ago for the special case of resonant interaction, which occurs at the edge of where two-particle bound states start to form, Efimov trimers were only recently observed in ultracold Bose gases. More work followed, revealing evidence of multiple trimer, and even tetramer, states. Now, Pollack et al. (p. 1683, published online 19 November; see the Perspective by Modugno) observe as many as 11 features near a lithium resonance that can be directly related to different few-body processes. The positions of the features with respect to each other are in excellent agreement with the theoretical prediction, although some deviations, attributed to short-range interactions, present a challenge for a future, more detailed theory. Cold lithium gas reveals a universal lineup of Efimov trimers and associated tetramers. Under certain circumstances, three or more interacting particles may form bound states. Although the general few-body problem is not analytically solvable, the so-called Efimov trimers appear for a system of three particles with resonant two-body interactions. The binding energies of these trimers are predicted to be universally connected to each other, independent of the microscopic details of the interaction. By exploiting a Feshbach resonance to widely tune the interactions between trapped ultracold lithium atoms, we find evidence for two universally connected Efimov trimers and their associated four-body bound states. A total of 11 precisely determined three- and four-body features are found in the inelastic-loss spectrum. Their relative locations on either side of the resonance agree well with universal theory, whereas a systematic deviation from universality is found when comparing features across the resonance.}} @article{PhysRevLett.105.103203, title = {Nuclear-Spin-Independent Short-Range Three-Body Physics in Ultracold Atoms}, author = {Gross, Noam and Shotan, Zav and Kokkelmans, Servaas and Khaykovich, Lev}, journal = {Phys. Rev. Lett.}, volume = {105}, issue = {10}, pages = {103203}, numpages = {4}, year = {2010}, month = {Sep}, publisher = {American Physical Society}, doi = {10.1103/PhysRevLett.105.103203}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.105.103203} } @article{Kraemer_2006, doi = {10.1038/nature04626}, url = {https://doi.org/10.1038%2Fnature04626}, year = 2006, month = {mar}, publisher = {Springer Science and Business Media {LLC}}, volume = {440}, number = {7082}, pages = {315--318}, author = {T. Kraemer and M. Mark and P. Waldburger and J. G. Danzl and C. Chin and B. Engeser and A. D. Lange and K. Pilch and A. Jaakkola and H.-C. Nägerl and R. Grimm}, title = {Evidence for Efimov quantum states in an ultracold gas of caesium atoms}, journal = {Nature} } @article{PhysRevLett.102.165302, title = {Three-Body Recombination in a Three-State Fermi Gas with Widely Tunable Interactions}, author = {Huckans, J. H. and Williams, J. R. and Hazlett, E. L. and Stites, R. W. and O'Hara, K. M.}, journal = {Phys. Rev. Lett.}, volume = {102}, issue = {16}, pages = {165302}, numpages = {4}, year = {2009}, month = {Apr}, publisher = {American Physical Society}, doi = {10.1103/PhysRevLett.102.165302}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.102.165302} } @article{PhysRevLett.105.103201, title = {Atom-Dimer Scattering in a Three-Component Fermi Gas}, author = {Lompe, T. and Ottenstein, T. B. and Serwane, F. and Viering, K. and Wenz, A. N. and Z\"urn, G. and Jochim, S.}, journal = {Phys. Rev. Lett.}, volume = {105}, issue = {10}, pages = {103201}, numpages = {4}, year = {2010}, month = {Sep}, publisher = {American Physical Society}, doi = {10.1103/PhysRevLett.105.103201}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.105.103201} } @article{PhysRevLett.103.130404, title = {Evidence for an Excited-State Efimov Trimer in a Three-Component Fermi Gas}, author = {Williams, J. R. and Hazlett, E. L. and Huckans, J. H. and Stites, R. W. and Zhang, Y. and O'Hara, K. M.}, journal = {Phys. Rev. Lett.}, volume = {103}, issue = {13}, pages = {130404}, numpages = {4}, year = {2009}, month = {Sep}, publisher = {American Physical Society}, doi = {10.1103/PhysRevLett.103.130404}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.103.130404} } @article{PhysRevLett.108.145305, title = {Measurements of Tan's Contact in an Atomic Bose-Einstein Condensate}, author = {Wild, R. J. and Makotyn, P. and Pino, J. M. and Cornell, E. A. and Jin, D. S.}, journal = {Phys. Rev. Lett.}, volume = {108}, issue = {14}, pages = {145305}, numpages = {5}, year = {2012}, month = {Apr}, publisher = {American Physical Society}, doi = {10.1103/PhysRevLett.108.145305}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.108.145305} } @article{PhysRevLett.105.023201, title = {Nonuniversal Efimov Atom-Dimer Resonances in a Three-Component Mixture of $^{6}\mathrm{Li}$}, author = {Nakajima, Shuta and Horikoshi, Munekazu and Mukaiyama, Takashi and Naidon, Pascal and Ueda, Masahito}, journal = {Phys. Rev. Lett.}, volume = {105}, issue = {2}, pages = {023201}, numpages = {4}, year = {2010}, month = {Jul}, publisher = {American Physical Society}, doi = {10.1103/PhysRevLett.105.023201}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.105.023201} } @article{PhysRevLett.112.105301, title = {Microscopic Origin and Universality Classes of the Efimov Three-Body Parameter}, author = {Naidon, Pascal and Endo, Shimpei and Ueda, Masahito}, journal = {Phys. Rev. Lett.}, volume = {112}, issue = {10}, pages = {105301}, numpages = {5}, year = {2014}, month = {Mar}, publisher = {American Physical Society}, doi = {10.1103/PhysRevLett.112.105301}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.112.105301} } @article{PhysRevLett.109.073003, title = {$N$-Body Efimov States from Two-Particle Noise}, author = {Nicholson, Amy N.}, journal = {Phys. Rev. Lett.}, volume = {109}, issue = {7}, pages = {073003}, numpages = {5}, year = {2012}, month = {Aug}, publisher = {American Physical Society}, doi = {10.1103/PhysRevLett.109.073003}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.109.073003} } @article{PhysRevA.74.063604, title = {Energetics and structural properties of three-dimensional bosonic clusters near threshold}, author = {Hanna, G. J. and Blume, D.}, journal = {Phys. Rev. A}, volume = {74}, issue = {6}, pages = {063604}, numpages = {11}, year = {2006}, month = {Dec}, publisher = {American Physical Society}, doi = {10.1103/PhysRevA.74.063604}, url = {https://link.aps.org/doi/10.1103/PhysRevA.74.063604} } @article{von_Stecher_2010, doi = {10.1088/0953-4075/43/10/101002}, url = {https://dx.doi.org/10.1088/0953-4075/43/10/101002}, year = {2010}, month = {may}, publisher = {}, volume = {43}, number = {10}, pages = {101002}, author = {Javier von Stecher}, title = {Weakly bound cluster states of Efimov character}, journal = {Journal of Physics B: Atomic, Molecular and Optical Physics}, abstract = {We study the behaviour of weakly bound clusters and their relation to the well-known three-body Efimov states. We adopt a model to describe the universal behaviour of strongly interacting bosonic systems, and we test its validity by reproducing predictions of three- and four-body universal states. Then, we extend our study to larger systems and identify a series of universal cluster states that can be qualitatively interpreted as adding one particle at a time to an Efimov trimer. The properties of these cluster states and their experimental signatures are discussed.} } @article{PhysRevLett.96.112501, title = {Efimov Effect in Nuclear Three-Body Resonance Decays}, author = {Garrido, E. and Fedorov, D. V. and Jensen, A. S.}, journal = {Phys. Rev. Lett.}, volume = {96}, issue = {11}, pages = {112501}, numpages = {4}, year = {2006}, month = {Mar}, publisher = {American Physical Society}, doi = {10.1103/PhysRevLett.96.112501}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.96.112501} } @article{PhysRevD.3.1818, title = {Renormalization Group and Strong Interactions}, author = {Wilson, Kenneth G.}, journal = {Phys. Rev. D}, volume = {3}, issue = {8}, pages = {1818--1846}, numpages = {0}, year = {1971}, month = {Apr}, publisher = {American Physical Society}, doi = {10.1103/PhysRevD.3.1818}, url = {https://link.aps.org/doi/10.1103/PhysRevD.3.1818} } @article{Glazek:2002hq, author = "Glazek, Stanislaw D. and Wilson, Kenneth G.", title = "{Limit cycles in quantum theories}", eprint = "hep-th/0203088", archivePrefix = "arXiv", reportNumber = "IFT-07-02", doi = "10.1103/PhysRevLett.89.230401", journal = "Phys. Rev. Lett.", volume = "89", pages = "230401", year = "2002", note = "[Erratum: Phys.Rev.Lett. 92, 139901 (2004)]" } @article{Dawid:2017ahd, author = "Dawid, Sebastian M. and Gonsior, R. and Kwapisz, J. and Serafin, K. and Tobolski, M. and G\l{}azek, S. D.", title = "{Renormalization group procedure for potential $-g/r^2$}", eprint = "1704.08206", archivePrefix = "arXiv", primaryClass = "quant-ph", doi = "10.1016/j.physletb.2017.12.028", journal = "Phys. Lett. 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