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Revisiting Roy-Steiner-equation analysis of pion-kaon scattering from lattice QCD data

Xiong-Hui Cao ^1,2,*, Feng-Kun Guo ^2,3,4,5,†, Zhi-Hui Guo^6,‡, and Qu-Zhi Li^1,§

¹Institute for Particle and Nuclear Physics, College of Physics, Sichuan University, Chengdu, Sichuan 610065, China
²Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
³School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
⁴Peng Huanwu Collaborative Center for Research and Education, Beihang University, Beijing 100191, China
⁵Southern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences, Huizhou 516000, China
⁶Department of Physics and Hebei Key Laboratory of Photophysics Research and Application, Hebei Normal University, Shijiazhuang 050024, China

^*Contact author: xhcao@itp.ac.cn
^†Contact author: fkguo@itp.ac.cn
^‡Contact author: zhguo@hebtu.edu.cn
^§Contact author: liquzhi@scu.edu.cn

Phys. Rev. D 112, 034042 – Published 29 August, 2025

DOI: https://doi.org/10.1103/hn8j-95vn

Abstract

A comprehensive analysis of $π K \to π K$ and $π π \to K \bar{K}$ amplitudes at large unphysical pion mass for all important partial waves is presented. A set of crossing-symmetric partial-wave hyperbolic dispersion relations is used to describe lattice quantum chromodynamics (QCD) data at $m_{π} = 391 MeV$ . In the present analysis, the amplitudes for the $S$ - and $P$ -waves are formulated by combining the constraints of analyticity, unitarity, and crossing symmetry, fulfilling Roy-Steiner-type equations. We use these results to investigate the low-lying strange-meson resonances and resolve the instability problem tied to analytic continuation in prior lattice QCD studies based on the $K$ -matrix formalism. At $m_{π} = 391 MeV$ , the rigorous Roy-Steiner-type equation approach allows us to determine the $S$ -wave scattering lengths, $m_{π} a_{0}^{1 / 2} = (0.9 2_{- 0.28}^{+ 0.06})$ , $m_{π} a_{0}^{3 / 2} = - (0.3 2_{- 0.02}^{+ 0.05})$ , and the $κ$ [also known as $K_{0}^{*} (700)$ ] pole position, $\sqrt{s_{κ}} = (96 6_{- 24}^{+ 41} - i 19 8_{- 17}^{+ 38}) MeV$ . We also provide a detailed analysis of the complex validity domain of the Roy-Steiner-type equations.

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References (120)

M. Lüscher, Volume dependence of the energy spectrum in massive quantum field theories. 1. Stable particle states, Commun. Math. Phys. 104, 177 (1986).
M. Lüscher, Volume dependence of the energy spectrum in massive quantum field theories. 2. Scattering states, Commun. Math. Phys. 105, 153 (1986).
M. Lüscher, Two particle states on a torus and their relation to the scattering matrix, Nucl. Phys. B354, 531 (1991).
R. A. Briceño, J. J. Dudek, and R. D. Young, Scattering processes and resonances from lattice QCD, Rev. Mod. Phys. 90, 025001 (2018).
C. Miao, X. Du, G. Meng, and C. Liu, Lattice study on kaon pion scattering length in the I = $3 / 2$ channel, Phys. Lett. B 595, 400 (2004).
S. R. Beane, P. F. Bedaque, T. C. Luu, K. Orginos, E. Pallante, A. Parreno, and M. J. Savage, $π K$ scattering in full QCD with domain-wall valence quarks, Phys. Rev. D 74, 114503 (2006).
J. Nagata, S. Muroya, and A. Nakamura, Lattice study of $K π$ scattering in $I = 3 / 2$ and $1 / 2$ , Phys. Rev. C 80, 045203 (2009); 84, 019904(E) (2011).
Z. Fu, Lattice study on $π K$ scattering with moving wall source, Phys. Rev. D 85, 074501 (2012).
C. B. Lang, L. Leskovec, D. Mohler, and S. Prelovsek, $K π$ scattering for isospin $1 / 2$ and $3 / 2$ in lattice QCD, Phys. Rev. D 86, 054508 (2012).
K. Sasaki, N. Ishizuka, M. Oka, and T. Yamazaki (PACS-CS Collaboration), Scattering lengths for two pseudoscalar meson systems, Phys. Rev. D 89, 054502 (2014); 105, 019901(E) (2022).
C. Helmes, C. Jost, B. Knippschild, B. Kostrzewa, L. Liu, F. Pittler, C. Urbach, and M. Werner (ETM Collaboration), Hadron-hadron interactions from $N_{f} = 2 + 1 + 1$ Lattice QCD: $I = 3 / 2$ $π K$ scattering length, Phys. Rev. D 98, 114511 (2018).
S. Prelovsek, T. Draper, C. B. Lang, M. Limmer, K.-F. Liu, N. Mathur, and D. Mohler, Lattice study of light scalar tetraquarks with I=0,2,1/2,3/2: Are $σ$ and $κ$ tetraquarks?, Phys. Rev. D 82, 094507 (2010).
C. Alexandrou, J. O. Daldrop, M. Dalla Brida, M. Gravina, L. Scorzato, C. Urbach, and M. Wagner, Lattice investigation of the scalar mesons $a_{0} (980)$ and $κ$ using four-quark operators, J. High Energy Phys. 04 (2013) 137.
F.-K. Guo, L. Liu, U.-G. Meißner, and P. Wang, Tetraquarks, hadronic molecules, meson-meson scattering and disconnected contributions in lattice QCD, Phys. Rev. D 88, 074506 (2013).
Z. Fu and K. Fu, Lattice QCD study on $K^{*} (892)$ meson decay width, Phys. Rev. D 88, 094507 (2012).
Z. Fu, Studying $κ$ meson with a MILC fine lattice, Int. J. Mod. Phys. A 28, 1350059 (2013).
S. Prelovsek, L. Leskovec, C. B. Lang, and D. Mohler, K $π$ Scattering and the K* decay width from lattice QCD, Phys. Rev. D 88, 054508 (2013).
G. S. Bali, S. Collins, A. Cox, G. Donald, M. Göckeler, C. B. Lang, and A. Schäfer (RQCD Collaboration), $ρ$ and $K^{*}$ resonances on the lattice at nearly physical quark masses and $N_{f} = 2$ , Phys. Rev. D 93, 054509 (2016).
R. Brett, J. Bulava, J. Fallica, A. Hanlon, B. Hörz, and C. Morningstar, Determination of $s$ - and $p$ -wave $I = 1 / 2$ $K π$ scattering amplitudes in $N_{f} = 2 + 1$ lattice QCD, Nucl. Phys. B932, 29 (2018).
G. Rendon, L. Leskovec, S. Meinel, J. Negele, S. Paul, M. Petschlies, A. Pochinsky, G. Silvi, and S. Syritsyn, $I = 1 / 2$ $S$ -wave and $P$ -wave $K π$ scattering and the $κ$ and $K^{*}$ resonances from lattice QCD, Phys. Rev. D 102, 114520 (2020).
J. J. Dudek, R. G. Edwards, C. E. Thomas, and D. J. Wilson (Hadron Spectrum Collaboration), Resonances in coupled $π K - η K$ scattering from quantum chromodynamics, Phys. Rev. Lett. 113, 182001 (2014).
D. J. Wilson, J. J. Dudek, R. G. Edwards, and C. E. Thomas, Resonances in coupled $π K, η K$ scattering from lattice QCD, Phys. Rev. D 91, 054008 (2015).
D. J. Wilson, R. A. Briceño, J. J. Dudek, R. G. Edwards, and C. E. Thomas, The quark-mass dependence of elastic $π K$ scattering from QCD, Phys. Rev. Lett. 123, 042002 (2019).
P. Boyle, F. Erben, V. Gülpers, M. T. Hansen, F. Joswig, M. Marshall, N. P. Lachini, and A. Portelli, Light and strange vector resonances from lattice QCD at physical quark masses, Phys. Rev. Lett. 134, 111901 (2025).
P. Boyle, F. Erben, V. Gülpers, M. T. Hansen, F. Joswig, M. Marshall, N. P. Lachini, and A. Portelli, Physical-mass calculation of $ρ (770)$ and K*(892) resonance parameters via $π π$ and $K π$ scattering amplitudes from lattice QCD, Phys. Rev. D 111, 054510 (2025).
S. M. Dawid, Z. T. Draper, A. D. Hanlon, B. Hörz, C. Morningstar, F. Romero-López, S. R. Sharpe, and S. Skinner, Two- and three-meson scattering amplitudes with physical quark masses from lattice QCD, Phys. Rev. D 112, 014505 (2025).
S. M. Dawid, Z. T. Draper, A. D. Hanlon, B. Hörz, C. Morningstar, F. Romero-López, S. R. Sharpe, and S. Skinner, QCD predictions for physical multimeson scattering amplitudes, Phys. Rev. Lett. 135, 021903 (2025).
M. Döring and U.-G. Meißner, Finite volume effects in pion-kaon scattering and reconstruction of the $κ (800)$ resonance, J. High Energy Phys. 01 (2012) 009.
M. Döring, U.-G. Meißner, E. Oset, and A. Rusetsky, Scalar mesons moving in a finite volume and the role of partial wave mixing, Eur. Phys. J. A 48, 114 (2012).
D. Zhou, E.-L. Cui, H.-X. Chen, L.-S. Geng, and L.-H. Zhu, $K π$ interaction in finite volume and the K* resonance, Phys. Rev. D 91, 094505 (2015).
M. Sadl, S. Collins, Z.-H. Guo, M. Padmanath, S. Prelovsek, and L.-W. Yan, Charmoniumlike channels $1 +$ with isospin 1 from lattice and effective field theory, Phys. Rev. D 111, 054513 (2025).
L.-W. Yan, Z.-H. Guo, F.-K. Guo, D.-L. Yao, and Z.-Y. Zhou, Reconciling experimental and lattice data of $Z_{c} (3900)$ in a $J / ψ π − {DD}^{- *}$ coupled-channel analysis, Phys. Rev. D 109, 014026 (2024).
Z.-H. Guo, L. Liu, U.-G. Meißner, J. A. Oller, and A. Rusetsky, Towards a precise determination of the scattering amplitudes of the charmed and light-flavor pseudoscalar mesons, Eur. Phys. J. C 79, 13 (2019).
Z.-H. Guo, L. Liu, U.-G. Meißner, J. A. Oller, and A. Rusetsky, Chiral study of the $a_{0} (980)$ resonance and $π η$ scattering phase shifts in light of a recent lattice simulation, Phys. Rev. D 95, 054004 (2017).
A. Asokan, M.-N. Tang, F.-K. Guo, C. Hanhart, Y. Kamiya, and U.-G. Meißner, Can the two-pole structure of the $D_{0}^{*} (2300)$ be understood from recent lattice data?, Eur. Phys. J. C 83, 850 (2023).
R. A. Briceño, J. J. Dudek, R. G. Edwards, and D. J. Wilson, Isoscalar $π π$ scattering and the $σ$ meson resonance from QCD, Phys. Rev. Lett. 118, 022002 (2017).
R. A. Briceño, J. J. Dudek, R. G. Edwards, and D. J. Wilson, Isoscalar $π π, K \bar{K}, η η$ scattering and the $σ, f_{0}, f_{2}$ mesons from QCD, Phys. Rev. D 97, 054513 (2018).
X.-H. Cao, Q.-Z. Li, Z.-H. Guo, and H.-Q. Zheng, Roy equation analyses of $π π$ scatterings at unphysical pion masses, Phys. Rev. D 108, 034009 (2023).
H. Q. Zheng, Z. Y. Zhou, G. Y. Qin, Z. Xiao, J. J. Wang, and N. Wu, The kappa resonance in s wave $π K$ scatterings, Nucl. Phys. A733, 235 (2004).
Z. Y. Zhou and H. Q. Zheng, An improved study of the kappa resonance and the non-exotic $s$ wave $π K$ scatterings up to $\sqrt{s} = 2.1 GeV$ of LASS data, Nucl. Phys. A775, 212 (2006).
Büettiker, S. Descotes-Genon, and B. Moussallam, A new analysis of $π K$ scattering from Roy and Steiner type equations, Eur. Phys. J. C 33, 409 (2004).
S. Descotes-Genon and B. Moussallam, The $K_{0}^{*} (800)$ scalar resonance from Roy-Steiner representations of $π K$ scattering, Eur. Phys. J. C 48, 553 (2006).
J. R. Peláez and A. Rodas, $π π \to K \bar{K}$ scattering up to 1.47 GeV with hyperbolic dispersion relations, Eur. Phys. J. C 78, 897 (2018).
J. R. Peláez and A. Rodas, Determination of the lightest strange resonance $K_{0}^{*} (700)$ or $κ$ , from a dispersive data analysis, Phys. Rev. Lett. 124, 172001 (2020).
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).
J. R. Peláez and A. Rodas, Dispersive $π K \to π K$ and $π π \to K \bar{K}$ amplitudes from scattering data, threshold parameters, and the lightest strange resonance $κ$ or $K_{0}^{*} (700)$ , Phys. Rep. 969, 1 (2022).
S. M. Roy, Exact integral equation for pion pion scattering involving only physical region partial waves, Phys. Lett. 36B, 353 (1971).
B. Ananthanarayan, G. Colangelo, J. Gasser, and H. Leutwyler, Roy equation analysis of $π π$ scattering, Phys. Rep. 353, 207 (2001).
G. Colangelo, J. Gasser, and H. Leutwyler, $π π$ scattering, Nucl. Phys. B603, 125 (2001).
R. Garcia-Martin, R. Kaminski, J. R. Peláez, J. Ruiz de Elvira, and F. J. Yndurain, The Pion-pion scattering amplitude. IV: Improved analysis with once subtracted Roy-like equations up to 1100 MeV, Phys. Rev. D 83, 074004 (2011).
I. Caprini, G. Colangelo, and H. Leutwyler, Mass and width of the lowest resonance in QCD, Phys. Rev. Lett. 96, 132001 (2006).
B. Moussallam, Couplings of light $I = 0$ scalar mesons to simple operators in the complex plane, Eur. Phys. J. C 71, 1814 (2011).
R. García-Martín, R. Kamiński, J. R. Peláez, and J. Ruiz de Elvira, Precise determination of the $f_{0} (600)$ and $f_{0} (980)$ pole parameters from a dispersive data analysis, Phys. Rev. Lett. 107, 072001 (2011).
J. R. Peláez, From controversy to precision on the sigma meson: A review on the status of the non-ordinary $f_{0} (500)$ resonance, Phys. Rep. 658, 1 (2016).
G. E. Hite and F. Steiner, New dispersion relations and their application to partial-wave amplitudes, Nuovo Cimento Soc. Ital. Fis. 18A, 237 (1973).
C. Ditsche, M. Hoferichter, B. Kubis, and U.-G. Meißner, Roy-Steiner equations for pion-nucleon scattering, J. High Energy Phys. 06 (2012) 043.
M. Hoferichter, C. Ditsche, B. Kubis, and U.-G. Meißner, Dispersive analysis of the scalar form factor of the nucleon, J. High Energy Phys. 06 (2012) 063.
M. Hoferichter, J. Ruiz de Elvira, B. Kubis, and U.-G. Meißner, High-precision determination of the pion-nucleon $σ$ term from Roy-Steiner equations, Phys. Rev. Lett. 115, 092301 (2015).
M. Hoferichter, J. Ruiz de Elvira, B. Kubis, and U.-G. Meißner, Matching pion-nucleon Roy-Steiner equations to chiral perturbation theory, Phys. Rev. Lett. 115, 192301 (2015).
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).
M. Hoferichter, B. Kubis, J. Ruiz de Elvira, H. W. Hammer, and U. G. Meißner, On the $π π$ continuum in the nucleon form factors and the proton radius puzzle, Eur. Phys. J. A 52, 331 (2016).
J. Ruiz de Elvira, M. Hoferichter, B. Kubis, and U.-G. Meißner, Extracting the $σ$ -term from low-energy pion-nucleon scattering, J. Phys. G 45, 024001 (2018).
M. Hoferichter, B. Kubis, J. Ruiz de Elvira, and P. Stoffer, Nucleon matrix elements of the antisymmetric quark tensor, Phys. Rev. Lett. 122, 122001 (2019); 124, 199901(E) (2020).
Y.-F. Wang, D.-L. Yao, and H.-Q. Zheng, New insights on low energy $π N$ scattering amplitudes, Eur. Phys. J. C 78, 543 (2018).
X.-H. Cao, Q.-Z. Li, and H.-Q. Zheng, A possible subthreshold pole in $S_{11}$ channel from $π N$ Roy-Steiner equation analyses, J. High Energy Phys. 12 (2022) 073.
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).
A. Rodas, J. J. Dudek, and R. G. Edwards (Hadron Spectrum Collaboration), Determination of crossing-symmetric $π π$ scattering amplitudes and the quark mass evolution of the $σ$ constrained by lattice QCD, Phys. Rev. D 109, 034513 (2024).
J. J. Dudek, R. G. Edwards, and C. E. Thomas, $S$ and $D$ -wave phase shifts in isospin- $2 π π$ scattering from lattice QCD, Phys. Rev. D 86, 034031 (2012).
J. J. Dudek, R. G. Edwards, and C. E. Thomas (Hadron Spectrum Collaboration), Energy dependence of the $ρ$ resonance in $π π$ elastic scattering from lattice QCD, Phys. Rev. D 87, 034505 (2013); 90, 099902(E) (2014).
X.-H. Cao, F.-K. Guo, Z.-H. Guo, and Q.-Z. Li, companion paper, Rigorous Roy-Steiner equation analysis of $π K$ scattering at unphysical quark masses, Phys. Rev. D 112, 031503 (2025).
C. B. Lang, The $π K$ scattering and related processes, Fortschr. Phys. 26, 509 (1978).
A. D. Martin and T. D. Spearman, Elementary Particle Theory (North-Holland, Amsterdam, 1970).
H. Nielsen and G. C. Oades, A phenomenological investigation of pion-kaon scattering, Nucl. Phys. B55, 301 (1973).
J. P. Ader, C. Meyers, and B. Bonnier, General features of low energy $K π$ scattering from physical region method, Phys. Lett. 46B, 403 (1973).
N. O. Johannesson and J. L. Petersen, Coupled channel study of the S wave $π π \to K \bar{K}$ interaction, Nucl. Phys. B68, 397 (1974).
N. Hedegaard-Jensen, A phenomenological investigation of $π π \to K \bar{K}$ partial wave amplitudes from hyperbolic dispersion relations, Nucl. Phys. B77, 173 (1974).
N. Johannesson and G. Nilsson, An analysis of low-energy $π K$ scattering, Nuovo Cimento Soc. Ital. Fis. 43A, 376 (1978).
N. Johannesson and L. Sollin, A soluble realistic model for low-energy $π K$ scattering, Nuovo Cimento Soc. Ital. Fis. 43A, 389 (1978).
B. Ananthanarayan and P. Büettiker, Comparison of pion kaon scattering in SU(3) chiral perturbation theory and dispersion relations, Eur. Phys. J. C 19, 517 (2001).
B. Ananthanarayan, Büettiker, and B. Moussallam, $π K$ sum rules and the SU(3) chiral expansion, Eur. Phys. J. C 22, 133 (2001).
M. Froissart, Asymptotic behavior and subtractions in the Mandelstam representation, Phys. Rev. 123, 1053 (1961).
A. Martin, Unitarity and high-energy behavior of scattering amplitudes, Phys. Rev. 129, 1432 (1963).
P. D. B. Collins, An Introduction to Regge Theory and High-Energy Physics (Cambridge University Press, Cambridge, England, 2009).
J. R. Taylor, Scattering Theory: The Quantum Theory of Nonrelativistic Collisions (John Wiley & Sons, Inc., New York, 1972).
J. Kennedy and T. D. Spearman, Singularities in partial-wave amplitudes for two ingoing and two outgoing particles, Phys. Rev. 126, 1596 (1962).
A. Martin, Scattering Theory: Unitarity, Analyticity and Crossing (Springer, Berlin, Heidelberg, 1969), Vol. 3.
G. Sommer, Present state of rigorous analytic properties of scattering amplitudes, Fortschr. Phys. 18, 577 (1970).
H. Lehmann, Analytic properties of scattering amplitudes as functions of momentum transfer, Nuovo Cimento 10, 579 (1958).
A. Martin, Extension of the axiomatic analyticity domain of scattering amplitudes by unitarity. 1., Nuovo Cimento A 42, 930 (1965).
A. Martin, Extension of the axiomatic analyticity domain of scattering amplitudes by unitarity. 2., Nuovo Cimento A 44, 1219 (1966).
M. Hoferichter, D. R. Phillips, and C. Schat, Roy-Steiner equations for $γ γ \to π π$ , Eur. Phys. J. C 71, 1743 (2011).
M. Hoferichter, B. Kubis, and D. Sakkas, Extracting the chiral anomaly from $γ π \to π π$ , Phys. Rev. D 86, 116009 (2012).
S. Mandelstam, Determination of the pion—nucleon scattering amplitude from dispersion relations and unitarity. General theory, Phys. Rev. 112, 1344 (1958).
K. M. Watson, The effect of final state interactions on reaction cross-sections, Phys. Rev. 88, 1163 (1952).
S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
T. Regge, Introduction to complex orbital momenta, Nuovo Cimento 14, 951 (1959).
S. Donnachie, H. G. Dosch, O. Nachtmann, and P. Landshoff, Pomeron Physics and QCD (Cambridge University Press, Cambridge, England, 2004).
V. N. Gribov, The Theory of Complex Angular Momenta: Gribov Lectures on Theoretical Physics (Cambridge University Press, Cambridge, England, 2007).
G. Veneziano, Construction of a crossing—symmetric, Regge behaved amplitude for linearly rising trajectories, Nuovo Cimento A 57, 190 (1968).
C. Lovelace, A novel application of Regge trajectories, Phys. Lett. B 28, 264 (1968).
J. A. Shapiro, Narrow-resonance model with regge behavior for $π π$ scattering, Phys. Rev. 179, 1345 (1969).
K. Kawarabayashi, S. Kitakado, and H. Yabuki, Veneziano’s model and nonet scheme for $1^{-}$ and $2^{+}$ mesons, Phys. Lett. B 28, 432 (1969).
K. Kawarabayashi, S. Kitakado, and H. Yabuki, Note on the consistency condition due to the partial conservation of axial-vector current in the Veneziano model, Phys. Rev. 184, 1956 (1969).
N. I. Muskhelishvili, Singular Integral Equations: Boundary Problems of Functions Theory and Their Applications to Mathematical Physics (Wolters-Noordhoff Publishing, Groningen, 1953).
R. Omnès, On the solution of certain singular integral equations of quantum field theory, Nuovo Cimento 8, 316 (1958).
J. Gasser and G. Wanders, One channel Roy equations revisited, Eur. Phys. J. C 10, 159 (1999).
G. Wanders, The role of the input in Roy’s equations for $π π$ scattering, Eur. Phys. J. C 17, 323 (2000).
A. Schenk, Absorption and dispersion of pions at finite temperature, Nucl. Phys. B363, 97 (1991).
V. Bernard, N. Kaiser, and U.-G. Meißner, $π K$ scattering in chiral perturbation theory to one loop, Nucl. Phys. B357, 129 (1991).
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).
J. Bijnens and G. Ecker, Mesonic low-energy constants, Annu. Rev. Nucl. Part. Sci. 64, 149 (2014).
J. Gasser and H. Leutwyler, Chiral perturbation theory: Expansions in the mass of the strange quark, Nucl. Phys. A250, 465 (1985).
S. L. Adler, Consistency conditions on the strong interactions implied by a partially conserved axial vector current, Phys. Rev. 137, B1022 (1965).
R. Blankenbecler, M. L. Goldberger, S. W. MacDowell, and S. B. Treiman, Singularities of scattering amplitudes on unphysical sheets and their interpretation, Phys. Rev. 123, 692 (1961).
Z. Y. Zhou, G. Y. Qin, P. Zhang, Z. Xiao, H. Q. Zheng, and N. Wu, The pole structure of the unitary, crossing symmetric low energy $π π$ scattering amplitudes, J. High Energy Phys. 02 (2005) 043.
L.-Y. Dai, X.-W. Kang, T. Luo, and U.-G. Meißner, A study on the correlation between poles and cuts in $π π$ scattering, Commun. Theor. Phys. 71, 1309 (2019).
Y.-L. Lyu, Q.-Z. Li, Z. Xiao, and H.-Q. Zheng, Revisiting O(N) $σ$ model at unphysical pion masses and high temperatures, Phys. Rev. D 109, 094026 (2024).
Y.-L. Lyu, Q.-Z. Li, Z. Xiao, and H.-Q. Zheng, Revisiting O(N) $σ$ model at unphysical pion masses and high temperatures. II. The vacuum structure and thermal $σ$ pole trajectory with cross-channel improvements, Phys. Rev. D 110, 094054 (2024).
Q.-Z. Li and H.-Q. Zheng, Singularities and accumulation of singularities of $π N$ scattering amplitudes, Commun. Theor. Phys. 74, 115203 (2022).
A. Dobado and J. R. Peláez, Inverse amplitude method in chiral perturbation theory, Phys. Rev. D 56, 3057 (1997).

Phys. Rev. D 112, 034042– Published 29 August, 2025

Vol. 112, Iss. 3 — 1 August 2025

Received 13 June 2025
Accepted 30 July 2025

DOI: https://doi.org/10.1103/hn8j-95vn

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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Revisiting Roy-Steiner-equation analysis of pion-kaon scattering from lattice QCD data

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