Garcia Martin, R.Kamiński, RobertPeláez Sagredo, José Ramón2023-06-202023-06-2020081. W. M. Yao, et al., J. Phys. G33, 1–1232 (2006). 2. A. Dobado, and J. R. Peláez, Phys. Rev. D56, 3057–3073 (1997), hep-ph/9604416. 3. Z. Y. Zhou, et al., JHEP 02, 043 (2005), hep-ph/0406271. 4. S. M. Roy, Phys. Lett. B36, 353 (1971). 5. I. Caprini, G. Colangelo, and H. Leutwyler, Phys. Rev. Lett. 96, 132001 (2006), hep-ph/0512364. 6. S. Pislak, et al., Phys. Rev. Lett. 87, 221801 (2001), hep- ex/0106071. 7. J. R. Batley, et al. (2008), cERN-PH-EP-2007-035. 8. J. R. Peláez, On this conference (2008). 9. F. J. Ynduráin, R. García-Martín, and J. R. Peláez, Phys. Rev. D76, 074034 (2007), hep-ph/ 0701025. 10. R. Kaminski, J. R. Peláez, and F. J. Ynduráin (2008), arXiv:0710.1150[hep-ph]. 11. I. Caprini (2008), 0804.2108.978-0-7354-0554-710.1063/1.2973510https://hdl.handle.net/20.500.14352/53482ISSN: 0094-243X ©Amer Inst Physics. Workshop on Scalar Mesons and Related Topics (2008. Lisboa, Portugal). We thank Prof. F. J. Ynduráin for his comments and suggestions, the organizers for creating the nice scientific atmosphere of the workshop and the Spanish research contracts PR27/05-13955-BSCH, FPA2004-02602, UCM-CAM 910309 and BFM2003-00856 for partial financial support.We review how the use of recent precise data on kaon decays together with forward dispersion relations (FDR) and Roy’s equations allow us to determine the σ resonance pole position very precisely, by using only experimental input. In addition, we present preliminary results for a modified set of Roy-like equations with only one subtraction, that showaremarkable improvement in the precision around the σ region. For practical applications, these results are shown to be very well approximated by a very simple conformal expansionengbook parthttp://dx.doi.org/10.1063/1.2973510http://scitation.aip.orgopen access538.9Roy's equationsDispersion relationsSigmaScalar MesonsMeson-meson scatteringFísica-Modelos matemáticosFísica matemática