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Lattice QCD study of $πΣ-\bar{K}N$ scattering and the $Λ(1405)$ resonance

Published 25 Jul 2023 in hep-lat, hep-ph, nucl-ex, and nucl-th | (2307.13471v3)

Abstract: A lattice QCD computation of the coupled channel $\pi\Sigma-\bar{K}N$ scattering amplitudes in the $\Lambda(1405)$ region is detailed. Results are obtained using a single ensemble of gauge field configurations with $N_{\rm f} = 2+1$ dynamical quark flavors and $m_{\pi} \approx 200$ MeV and $m_K\approx487$ MeV. Hermitian correlation matrices using both single baryon and meson-baryon interpolating operators for a variety of different total momenta and irreducible representations are used. Several parametrizations of the two-channel scattering $K$-matrix are utilized to obtain the scattering amplitudes from the finite-volume spectrum. The amplitudes, continued to the complex energy plane, exhibit a virtual bound state below the $\pi\Sigma$ threshold and a resonance pole just below the $\bar{K}N$ threshold.

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References (61)
  1. R. L. Workman et al. (Particle Data Group), Review of Particle Physics, PTEP 2022, 083C01 (2022).
  2. R. H. Dalitz and S. F. Tuan, Possible resonant state in pion-hyperon scattering, Phys. Rev. Lett. 2, 425 (1959).
  3. R. H. Dalitz and S. F. Tuan, The phenomenological representation of K¯¯𝐾\overline{K}over¯ start_ARG italic_K end_ARG-nucleon scattering and reaction amplitudes, Annals Phys. 10, 307 (1960).
  4. T. Hyodo and D. Jido, The nature of the Λ⁢(1405)Λ1405\Lambda(1405)roman_Λ ( 1405 ) resonance in chiral dynamics, Prog. Part. Nucl. Phys. 67, 55 (2012), arXiv:1104.4474 [nucl-th] .
  5. T. Hyodo and M. Niiyama, QCD and the strange baryon spectrum, Prog. Part. Nucl. Phys. 120, 103868 (2021), arXiv:2010.07592 [hep-ph] .
  6. M. Bazzi et al. (SIDDHARTA), A New Measurement of Kaonic Hydrogen X-rays, Phys. Lett. B 704, 113 (2011), arXiv:1105.3090 [nucl-ex] .
  7. U. G. Meissner, U. Raha, and A. Rusetsky, Spectrum and decays of kaonic hydrogen, Eur. Phys. J. C 35, 349 (2004), arXiv:hep-ph/0402261 .
  8. K. Moriya et al. (CLAS), Measurement of the ΣΣ\Sigmaroman_Σπ𝜋\piitalic_π photoproduction line shapes near the ΛΛ\Lambdaroman_Λ(1405), Phys. Rev. C 87, 035206 (2013), arXiv:1301.5000 [nucl-ex] .
  9. K. Moriya et al. (CLAS), Spin and parity measurement of the Lambda(1405) baryon, Phys. Rev. Lett. 112, 082004 (2014), arXiv:1402.2296 [hep-ex] .
  10. M. Mai and U.-G. Meißner, Constraints on the chiral unitary K¯⁢N¯𝐾𝑁\bar{K}Nover¯ start_ARG italic_K end_ARG italic_N amplitude from π⁢Σ⁢K+𝜋Σsuperscript𝐾\pi\Sigma K^{+}italic_π roman_Σ italic_K start_POSTSUPERSCRIPT + end_POSTSUPERSCRIPT photoproduction data, Eur. Phys. J. A 51, 30 (2015), arXiv:1411.7884 [hep-ph] .
  11. L. Roca and E. Oset, Isospin 0 and 1 resonances from π⁢Σ𝜋Σ\pi\Sigmaitalic_π roman_Σ photoproduction data, Phys. Rev. C 88, 055206 (2013), arXiv:1307.5752 [nucl-th] .
  12. G. Scheluchin et al. (BGOOD), Photoproduction of K+⁢Λ⁢(1405)→K+⁢π0⁢Σ0→superscript𝐾Λ1405superscript𝐾superscript𝜋0superscriptΣ0K^{+}\Lambda(1405)\rightarrow K^{+}\pi^{0}\Sigma^{0}italic_K start_POSTSUPERSCRIPT + end_POSTSUPERSCRIPT roman_Λ ( 1405 ) → italic_K start_POSTSUPERSCRIPT + end_POSTSUPERSCRIPT italic_π start_POSTSUPERSCRIPT 0 end_POSTSUPERSCRIPT roman_Σ start_POSTSUPERSCRIPT 0 end_POSTSUPERSCRIPT extending to forward angles and low momentum transfer, Phys. Lett. B 833, 137375 (2022), arXiv:2108.12235 [nucl-ex] .
  13. S. Acharya et al. (ALICE), Constraining the K¯⁢N¯𝐾𝑁\overline{K}\,Nover¯ start_ARG italic_K end_ARG italic_N coupled channel dynamics using femtoscopic correlations at the LHC, Eur. Phys. J. C 83, 340 (2023), arXiv:2205.15176 [nucl-ex] .
  14. N. Wickramaarachchi, R. A. Schumacher, and G. Kalicy (GlueX), Decay of the ΛΛ\Lambdaroman_Λ(1405) hyperon to Σ0superscriptΣ0\Sigma^{0}roman_Σ start_POSTSUPERSCRIPT 0 end_POSTSUPERSCRIPT π0superscript𝜋0\pi^{0}italic_π start_POSTSUPERSCRIPT 0 end_POSTSUPERSCRIPT measured at GlueX, EPJ Web Conf. 271, 07005 (2022), arXiv:2209.06230 [nucl-ex] .
  15. S. Aikawa et al. (J-PARC E31), Pole position of ΛΛ\Lambdaroman_Λ(1405) measured in d(K−{}^{-}start_FLOATSUPERSCRIPT - end_FLOATSUPERSCRIPT,n)π𝜋\piitalic_π ΣΣ\Sigmaroman_Σ reactions, Phys. Lett. B 837, 137637 (2023), arXiv:2209.08254 [nucl-ex] .
  16. N. Isgur and G. Karl, P Wave Baryons in the Quark Model, Phys. Rev. D 18, 4187 (1978).
  17. J. A. Oller and U. G. Meissner, Chiral dynamics in the presence of bound states: Kaon nucleon interactions revisited, Phys. Lett. B 500, 263 (2001), arXiv:hep-ph/0011146 .
  18. N. Kaiser, P. B. Siegel, and W. Weise, Chiral dynamics and the low-energy kaon - nucleon interaction, Nucl. Phys. A 594, 325 (1995), arXiv:nucl-th/9505043 .
  19. E. Oset and A. Ramos, Nonperturbative chiral approach to s𝑠sitalic_s wave K¯⁢N¯𝐾𝑁\overline{K}Nover¯ start_ARG italic_K end_ARG italic_N interactions, Nucl. Phys. A 635, 99 (1998), arXiv:nucl-th/9711022 .
  20. M. Mai, Status of the Λ⁢(1405)Λ1405\Lambda(1405)roman_Λ ( 1405 ), Few Body Syst. 59, 61 (2018).
  21. M. Mai, Review of the ΛΛ{\Lambda}roman_Λ(1405) A curious case of a strangeness resonance, Eur. Phys. J. ST 230, 1593 (2021), arXiv:2010.00056 [nucl-th] .
  22. T. Ezoe and A. Hosaka, ΛΛ\Lambdaroman_Λ(1405) as a K¯⁢N¯𝐾𝑁\overline{K}Nover¯ start_ARG italic_K end_ARG italic_N Feshbach resonance in the Skyrme model, Phys. Rev. D 102, 014046 (2020), arXiv:2006.03788 [hep-ph] .
  23. K. Miyahara, T. Hyodo, and W. Weise, Construction of a local K¯⁢N−π⁢Σ−π⁢Λ¯𝐾𝑁𝜋Σ𝜋Λ\bar{K}N-\pi\Sigma-\pi\Lambdaover¯ start_ARG italic_K end_ARG italic_N - italic_π roman_Σ - italic_π roman_Λ potential and composition of the Λ⁢(1405)Λ1405\Lambda(1405)roman_Λ ( 1405 ), Phys. Rev. C 98, 025201 (2018), arXiv:1804.08269 [nucl-th] .
  24. K. Miyahara and T. Hyodo, Theoretical study of Λ⁢(1405)Λ1405\Lambda(1405)roman_Λ ( 1405 ) resonance in Ξb0→D0⁢(π⁢Σ)→superscriptsubscriptΞ𝑏0superscript𝐷0𝜋Σ\Xi_{b}^{0}\to D^{0}(\pi\Sigma)roman_Ξ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 0 end_POSTSUPERSCRIPT → italic_D start_POSTSUPERSCRIPT 0 end_POSTSUPERSCRIPT ( italic_π roman_Σ ) decay, Phys. Rev. C 98, 025202 (2018), arXiv:1803.05572 [nucl-th] .
  25. K. Azizi, Y. Sarac, and H. Sundu, Investigation of Λ⁢(1405)Λ1405\Lambda(1405)roman_Λ ( 1405 ) as a molecular pentaquark state,   (2023), arXiv:2306.07393 [hep-ph] .
  26. T. Hyodo and W. Weise, Theory of Kaon-Nuclear Systems, in Handbook of Nuclear Physics, edited by I. Tanihata, H. Toki, and T. Kajino (2022) pp. 1–34, arXiv:2202.06181 [nucl-th] .
  27. P. Gubler, T. T. Takahashi, and M. Oka, Flavor structure of ΛΛ\Lambdaroman_Λ baryons from lattice QCD: From strange to charm quarks, Phys. Rev. D 94, 114518 (2016), arXiv:1609.01889 [hep-lat] .
  28. G. P. Engel, C. B. Lang, and A. Schäfer (BGR (Bern-Graz-Regensburg)), Low-lying ΛΛ\Lambdaroman_Λ baryons from the lattice, Phys. Rev. D 87, 034502 (2013a), arXiv:1212.2032 [hep-lat] .
  29. T. T. Takahashi and M. Oka, Low-lying Lambda Baryons with spin 1/2 in Two-flavor Lattice QCD, Phys. Rev. D 81, 034505 (2010), arXiv:0910.0686 [hep-lat] .
  30. S. Meinel and G. Rendon, Charm-baryon semileptonic decays and the strange Λ*superscriptΛ\Lambda^{*}roman_Λ start_POSTSUPERSCRIPT * end_POSTSUPERSCRIPT resonances: New insights from lattice QCD, Phys. Rev. D 105, L051505 (2022), arXiv:2107.13084 [hep-ph] .
  31. C. Lang and V. Verduci, Scattering in the π⁢N𝜋𝑁\pi Nitalic_π italic_N negative parity channel in lattice QCD, Phys.Rev. D87, 054502 (2013), arXiv:1212.5055 .
  32. D. Mohler, S. Prelovsek, and R. M. Woloshyn, D⁢π𝐷𝜋D\piitalic_D italic_π scattering and D𝐷Ditalic_D meson resonances from lattice QCD, Phys. Rev. D87, 034501 (2013), arXiv:1208.4059 [hep-lat] .
  33. C. W. Bernard and M. F. L. Golterman, Finite volume two pion energies and scattering in the quenched approximation, Phys. Rev. D 53, 476 (1996), arXiv:hep-lat/9507004 .
  34. W. Detmold and A. Nicholson, Low energy scattering phase shifts for meson-baryon systems, Phys. Rev. D93, 114511 (2016), arXiv:1511.02275 [hep-lat] .
  35. M. Bruno et al., Simulation of QCD with N=f{}_{f}=start_FLOATSUBSCRIPT italic_f end_FLOATSUBSCRIPT = 2 +++ 1 flavors of non-perturbatively improved Wilson fermions, JHEP 02, 043, arXiv:1411.3982 [hep-lat] .
  36. M. Luscher and P. Weisz, On-Shell Improved Lattice Gauge Theories, Commun. Math. Phys. 97, 59 (1985), [Erratum: Commun. Math. Phys.98,433(1985)].
  37. J. Bulava and S. Schaefer, Improvement of Nf=3subscript𝑁f3N_{\mathrm{f}}=3italic_N start_POSTSUBSCRIPT roman_f end_POSTSUBSCRIPT = 3 lattice QCD with Wilson fermions and tree-level improved gauge action, Nucl. Phys. B874, 188 (2013), arXiv:1304.7093 [hep-lat] .
  38. M. Lüscher and S. Schaefer, Lattice QCD without topology barriers, JHEP 07, 036, arXiv:1105.4749 [hep-lat] .
  39. M. A. Clark and A. D. Kennedy, Accelerating dynamical fermion computations using the rational hybrid Monte Carlo (RHMC) algorithm with multiple pseudofermion fields, Phys. Rev. Lett. 98, 051601 (2007), arXiv:hep-lat/0608015 [hep-lat] .
  40. D. Mohler and S. Schaefer, Remarks on strange-quark simulations with Wilson fermions, Phys. Rev. D 102, 074506 (2020), arXiv:2003.13359 [hep-lat] .
  41. S. Kuberski, Low-mode deflation for twisted-mass and RHMC reweighting in lattice QCD,  (2023), arXiv:2306.02385 [hep-lat] .
  42. M. Bruno, T. Korzec, and S. Schaefer, Setting the scale for the CLS 2+1212+12 + 1 flavor ensembles, Phys. Rev. D95, 074504 (2017), arXiv:1608.08900 [hep-lat] .
  43. B. Strassberger et al., Scale setting for CLS 2+1 simulations, PoS LATTICE2021, 135 (2022), arXiv:2112.06696 [hep-lat] .
  44. C. Morningstar and M. J. Peardon, Analytic smearing of SU(3) link variables in lattice QCD, Phys. Rev. D69, 054501 (2004), arXiv:hep-lat/0311018 [hep-lat] .
  45. B. Hörz and A. Hanlon, Two- and three-pion finite-volume spectra at maximal isospin from lattice QCD, Phys. Rev. Lett. 123, 142002 (2019), arXiv:1905.04277 [hep-lat] .
  46. M. Cè et al., Window observable for the hadronic vacuum polarization contribution to the muon g-2 from lattice QCD, Phys. Rev. D 106, 114502 (2022), arXiv:2206.06582 [hep-lat] .
  47. C. Michael and I. Teasdale, Extracting Glueball Masses From Lattice QCD, Nucl. Phys. B215, 433 (1983).
  48. M. Luscher and U. Wolff, How to Calculate the Elastic Scattering Matrix in Two-dimensional Quantum Field Theories by Numerical Simulation, Nucl. Phys. B339, 222 (1990).
  49. S. Aoki et al. (CP-PACS), Lattice QCD Calculation of the rho Meson Decay Width, Phys. Rev. D 76, 094506 (2007), arXiv:0708.3705 [hep-lat] .
  50. M. Lüscher, Two particle states on a torus and their relation to the scattering matrix, Nucl. Phys. B354, 531 (1991).
  51. K. Rummukainen and S. A. Gottlieb, Resonance scattering phase shifts on a nonrest frame lattice, Nucl. Phys. B450, 397 (1995), arXiv:hep-lat/9503028 [hep-lat] .
  52. C. H. Kim, C. T. Sachrajda, and S. R. Sharpe, Finite-volume effects for two-hadron states in moving frames, Nucl. Phys. B727, 218 (2005), arXiv:hep-lat/0507006 [hep-lat] .
  53. S. He, X. Feng, and C. Liu, Two particle states and the S-matrix elements in multi-channel scattering, JHEP 07, 011, arXiv:hep-lat/0504019 [hep-lat] .
  54. R. A. Briceno and Z. Davoudi, Moving multichannel systems in a finite volume with application to proton-proton fusion, Phys. Rev. D88, 094507 (2013), arXiv:1204.1110 [hep-lat] .
  55. R. A. Briceno, Two-particle multichannel systems in a finite volume with arbitrary spin, Phys. Rev. D89, 074507 (2014), arXiv:1401.3312 [hep-lat] .
  56. G. Källén, Elementary Particle Physics (Addison-Wesley, 1964).
  57. J. M. Blatt and L. C. Biedenharn, Neutron-Proton Scattering with Spin-Orbit Coupling. 1. General Expressions, Phys. Rev. 86, 399 (1952).
  58. W. I. Jay and E. T. Neil, Bayesian model averaging for analysis of lattice field theory results, Phys. Rev. D 103, 114502 (2021), arXiv:2008.01069 [stat.ME] .
  59. J. D. Hunter, Matplotlib: A 2d graphics environment, Computing in Science & Engineering 9, 90 (2007).
  60. R. G. Edwards and B. Joo (SciDAC), The Chroma software system for lattice QCD, Nucl. Phys. Proc. Suppl. 140, 832 (2005).
  61. https://zenodo.org/records/10425662.

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