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  • Letter
  • Open Access

Rigorous Roy-Steiner equation analysis of πK scattering at unphysical quark masses

Xiong-Hui Cao1,*, Feng-Kun Guo1,2,3,4,†, Zhi-Hui Guo5,‡, and Qu-Zhi Li6,§

  • *Contact author: xhcao@itp.ac.cn
  • †Contact author: fkguo@itp.ac.cn
  • ‡Contact author: zhguo@hebtu.edu.cn
  • §Contact author: liquzhi@scu.edu.cn
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Phys. Rev. D 112, L031503 – Published 29 August, 2025

DOI: https://doi.org/10.1103/38b9-m57d

Abstract

We perform a rigorous analysis of the πK scattering at an unphysical pion mass 391 MeV using the Roy-Steiner equations, which satisfy unitarity, analyticity, and crossing symmetry, for the first time. Stable solutions of the Roy-Steiner equations with different quantum numbers of isospin and angular momentum are obtained in the elastic energy region, by taking inputs from the πK lattice data in the inelastic region, the lattice data from the crossed ππ→KK¯ channels, the masses of f0(500) and K* at the same pion mass from previous study, and the Regge model. Predictions on the elastic πK scattering phase shifts and the K0*(700) pole content are made. Contrary to the virtual pole scenario obtained using the K-matrix method in the literature, we find that lightest strange scalar meson K0*(700) remains a broad resonance at mπ=391  MeV. The cross-channel dynamics is found to play a crucial role in deriving the proper pole position.

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References (47)

  1. R. A. Briceño, J. J. Dudek, and R. D. Young, Scattering processes and resonances from lattice QCD, Rev. Mod. Phys. 90, 025001 (2018).
  2. M. Mai, M. Döring, and A. Rusetsky, Multi-particle systems on the lattice and chiral extrapolations: A brief review, Eur. Phys. J. Special Topics 230, 1623 (2021).
  3. H. Yan, M. Garofalo, M. Mai, U.-G. Meißner, and C. Urbach, The ω-meson from lattice QCD, Phys. Rev. Lett. 133, 211906 (2024).
  4. C. Hanhart, J. R. Peláez, and G. Ríos, Quark mass dependence of the rho and sigma from dispersion relations and Chiral Perturbation Theory, Phys. Rev. Lett. 100, 152001 (2008).
  5. M. Cleven, F.-K. Guo, C. Hanhart, and U.-G. Meißner, Light meson mass dependence of the positive parity heavy-strange mesons, Eur. Phys. J. A 47, 19 (2011).
  6. M.-L. Du, M. Albaladejo, P. Fernandez-Soler, F.-K. Guo, C. Hanhart, U.-G. Meißner, J. Nieves, and D.-L. Yao, Towards a new paradigm for heavy-light meson spectroscopy, Phys. Rev. D 98, 094018 (2018).
  7. M. Niehus, M. Hoferichter, B. Kubis, and J. Ruiz de Elvira, Two-loop analysis of the pion mass dependence of the ρ meson, Phys. Rev. Lett. 126, 102002 (2021).
  8. R. Molina and J. Ruiz de Elvira, Light- and strange-quark mass dependence of the ρ(770) meson revisited, J. High Energy Phys. 11 (2020) 017.
  9. S. M. Roy, Exact integral equation for pion pion scattering involving only physical region partial waves, Phys. Lett. 36B, 353 (1971).
  10. G. E. Hite and F. Steiner, New dispersion relations and their application to partial-wave amplitudes, Nuovo Cimento A 18, 237 (1973).
  11. B. Ananthanarayan, G. Colangelo, J. Gasser, and H. Leutwyler, Roy equation analysis of ππ scattering, Phys. Rep. 353, 207 (2001).
  12. I. Caprini, G. Colangelo, and H. Leutwyler, Mass and width of the lowest resonance in QCD, Phys. Rev. Lett. 96, 132001 (2006).
  13. R. García-Martín, R. Kamiński, J. R. Peláez, J. Ruiz de Elvira, and F. J. Ynduráin, The pion-pion scattering amplitude. IV: Improved analysis with once subtracted Roy-like equations up to 1100 MeV, Phys. Rev. D 83, 074004 (2011).
  14. B. Moussallam, Couplings of light I=0 scalar mesons to simple operators in the complex plane, Eur. Phys. J. C 71, 1814 (2011).
  15. I. Caprini, G. Colangelo, and H. Leutwyler, Regge analysis of the ππ scattering amplitude, Eur. Phys. J. C 72, 1860 (2012).
  16. R. García-Martín, R. Kamiński, J. R. Peláez, and J. Ruiz de Elvira, Precise determination of the f0(600) and f0(980) pole parameters from a dispersive data analysis, Phys. Rev. Lett. 107, 072001 (2011).
  17. J. R. Peláez, From controversy to precision on the sigma meson: A review on the status of the non-ordinary f0(500) resonance, Phys. Rep. 658, 1 (2016).
  18. P. Buettiker, S. Descotes-Genon, and B. Moussallam, A new analysis of πK scattering from Roy and Steiner type equations, Eur. Phys. J. C 33, 409 (2004).
  19. S. Descotes-Genon and B. Moussallam, The K0*(800) scalar resonance from Roy-Steiner representations of πK scattering, Eur. Phys. J. C 48, 553 (2006).
  20. J. R. Peláez and A. Rodas, Determination of the lightest strange resonance K0*(700) or κ, from a dispersive data analysis, Phys. Rev. Lett. 124, 172001 (2020).
  21. J. R. Peláez and A. Rodas, Dispersive πK→πK and ππ→KK¯ amplitudes from scattering data, threshold parameters, and the lightest strange resonance κ or K0*(700), Phys. Rep. 969, 1 (2022).
  22. M. Hoferichter, J. Ruiz de Elvira, B. Kubis, and U.-G. Meißner, Roy–Steiner-equation analysis of pion–nucleon scattering, Phys. Rep. 625, 1 (2016).
  23. X.-H. Cao, Q.-Z. Li, and H.-Q. Zheng, A possible subthreshold pole in S11 channel from πN Roy-Steiner equation analyses, J. High Energy Phys. 12 (2022) 073.
  24. M. Hoferichter, J. R. de Elvira, B. Kubis, and U.-G. Meißner, Nucleon resonance parameters from Roy–Steiner equations, Phys. Lett. B 853, 138698 (2024).
  25. X.-H. Cao, Q.-Z. Li, Z.-H. Guo, and H.-Q. Zheng, Roy equation analyses of ππ scatterings at unphysical pion masses, Phys. Rev. D 108, 034009 (2023).
  26. A. Rodas, J. J. Dudek, and R. G. Edwards (Hadron Spectrum Collaboration), Determination of crossing-symmetric ππ scattering amplitudes and the quark mass evolution of the σ constrained by lattice QCD, Phys. Rev. D 109, 034513 (2024).
  27. R. A. Briceño, J. J. Dudek, R. G. Edwards, and D. J. Wilson, Isoscalar ππ scattering and the σ meson resonance from QCD, Phys. Rev. Lett. 118, 022002 (2017).
  28. R. A. Briceño, J. J. Dudek, R. G. Edwards, and D. J. Wilson, Isoscalar ππ,KK¯,ηη scattering and the σ,f0,f2 mesons from QCD, Phys. Rev. D 97, 054513 (2018).
  29. D. J. Wilson, R. A. Briceño, J. J. Dudek, R. G. Edwards, and C. E. Thomas, The quark-mass dependence of elastic πK scattering from QCD, Phys. Rev. Lett. 123, 042002 (2019).
  30. J. J. Dudek, R. G. Edwards, and C. E. Thomas, S and D-wave phase shifts in isospin-2ππ scattering from lattice QCD, Phys. Rev. D 86, 034031 (2012).
  31. J. J. Dudek, R. G. Edwards, and C. E. Thomas (Hadron Spectrum Collaboration), Energy dependence of the ρ resonance in ππ elastic scattering from lattice QCD, Phys. Rev. D 87, 034505 (2013); 90, 099902(E) (2014).
  32. J. J. Dudek, R. G. Edwards, C. E. Thomas, and D. J. Wilson (Hadron Spectrum Collaboration), Resonances in coupled πK−ηK scattering from quantum chromodynamics, Phys. Rev. Lett. 113, 182001 (2014).
  33. D. J. Wilson, J. J. Dudek, R. G. Edwards, and C. E. Thomas, Resonances in coupled πK,ηK scattering from lattice QCD, Phys. Rev. D 91, 054008 (2015).
  34. K. M. Watson, The effect of final state interactions on reaction cross-sections, Phys. Rev. 88, 1163 (1952).
  35. N. I. Muskhelishvili, Singular Integral Equations: Boundary Problems of Functions Theory and Their Applications to Mathematical Physics (Wolters-Noordhoff Publishing, Groningen, 1953).
  36. R. Omnès, On the solution of certain singular integral equations of quantum field theory, Nuovo Cimento 8, 316 (1958).
  37. G. Veneziano, Construction of a crossing-symmetric, Regge behaved amplitude for linearly rising trajectories, Nuovo Cimento A 57, 190 (1968).
  38. C. Lovelace, A novel application of Regge trajectories, Phys. Lett. 28B, 264 (1968).
  39. J. A. Shapiro, Narrow-resonance model with Regge behavior for ππ scattering, Phys. Rev. 179, 1345 (1969).
  40. X.-H. Cao, F.-K. Guo, Z.-H. Guo, and Q.-Z. Li, companion paper, Revisiting Roy-Steiner-equation analysis of pion-kaon scattering from lattice QCD data, Phys. Rev. D 112, 034042 (2025).
  41. M. Luscher, Two particle states on a torus and their relation to the scattering matrix, Nucl. Phys. B354, 531 (1991).
  42. V. Bernard, N. Kaiser, and U.-G. Meißner, πK scattering in chiral perturbation theory to one loop, Nucl. Phys. B357, 129 (1991).
  43. A. Gomez Nicola and J. R. Peláez, Meson meson scattering within one loop chiral perturbation theory and its unitarization, Phys. Rev. D 65, 054009 (2002).
  44. J. Bijnens and G. Ecker, Mesonic low-energy constants, Annu. Rev. Nucl. Part. Sci. 64, 149 (2014).
  45. H. Q. Zheng, Z. Y. Zhou, G. Y. Qin, Z. Xiao, J. J. Wang, and N. Wu, The κ resonance in s wave πK scatterings, Nucl. Phys. A733, 235 (2004).
  46. D.-L. Yao, L.-Y. Dai, H.-Q. Zheng, and Z.-Y. Zhou, A review on partial-wave dynamics with chiral effective field theory and dispersion relation, Rep. Prog. Phys. 84, 076201 (2021).
  47. J. Nebreda and J. R. Peláez, Strange and non-strange quark mass dependence of elastic light resonances from SU(3) unitarized chiral perturbation theory to one loop, Phys. Rev. D 81, 054035 (2010).

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Phys. Rev. D 112, L031503– Published 29 August, 2025
  • Received 8 December 2024
  • Accepted 29 July 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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