Jul 16 – 22, 2009
Kraków, Poland
Europe/Warsaw timezone

Why dispersion relations help in description of pion-pion amplitudes and lead to precise determination of the f0(600) (sigma) parameters?

Jul 18, 2009, 11:40 AM
Exhibition room B (Kraków, Poland)

Exhibition room B

Kraków, Poland

The Auditorium Maximum of the Jagiellonian University 33 Krupnicza Street 31-123 Kraków
QCD in hadronic physics VI. QCD in Hadronic Physics


Dr Robert Kaminski (Insititute of Nuclear Physics PAN)


Significant progress in description of pi-pi amplitudes has been recently made [1,2]. We present amplitudes fitted both to well known and to newest experimental data. In fits we use additional theoretical constraints from forward dispersion relations, sum rules and from twice and once subtracted dispersion relations. The latter two (so called Roy's and GKPY equations) are derived with imposed crossing symmetry condition for the pi-pi S and P waves and provide strong constraints for errors of phase shifts and inelasticities below 1 GeV. In this way very demanding and model independent test for pi-pi amplitudes fitted to experimental data is constructed and proposed. We show that constraints from this test imposed on the pi-pi amplitudes lead to very precise determination of parameters of the f0(600) (sigma) pole and pi-pi threshold parameters in good agreement with ChPT. We compare once and twice subtracted dispersion relations and conclude that the former ones provide more stringent consistency check for parameterizations of the pi-pi amplitudes. Our analysis is based only on unitarity, analyticity and crossing symmetry. References: [1] B. Ananthanarayan et al., Phys. Rept. 353, 207 (2001). [2] R. Kaminski, J.R. Pelaez and F.J. Yndurain, Phys. Rev. D 77, 054015 (2008).

Primary author

Dr Robert Kaminski (Insititute of Nuclear Physics PAN)


Dr Jose Pelaez (Departamento de Physica Teorica II, Universidad Complutense de Madrid, Spain) Dr Ruben Garcia-Martin (Departamento de Physica Teorica II, Universidad Complutense de Madrid, Spain)

Presentation materials