RT Journal Article
T1 Pion-pion scattering amplitude
A1 Peláez Sagredo, José Ramón
A1 Ynduráin, F. J.
AB We obtain reliable ππ scattering amplitudes consistent with experimental data, both at low and high energies, and fulfilling appropriate analyticity properties. We do this by first fitting experimental low energy [s^(1/2) ≤ (1.42 GeV] phase shifts and inelasticities with expressions that incorporate analyticity and unitarity. In particular, for the S wave with isospin 0, we discuss in detail several sets of experimental data. This provides low energy partial wave amplitudes that summarize the known experimental information. Then, we impose Regge behavior as follows from factorization and experimental data for the imaginary parts of the scattering amplitudes at higher energy, and check fulfillment of dispersion relations up to 0.925 GeV. This allows us to improve our fits. The ensuing ππ scattering amplitudes are then shown to verify dispersion relations up to 1.42 GeV, as well as s  ̶  t  ̶   u  crossing sum rules and other consistency conditions. The improved parametrizations  therefore provide a reliable representation of pion-pion amplitudes with which one can test chiral perturbation theory calculations, pionium decays, or use as input for CP-violating K decays. In this respect, we find [a^(0)_0  ̶ a^(2)_0]^2 = (0.077 ± 0.008) M^(-2)_π  and  δ^(0)_(0) (m^(2)_K  ̶ ̶  δ^(2)_(0) (m^(2)_(K) = 5209 ±1.6º.
PB American Physical Society
SN 0556-2821
YR 2005
FD 2005-04
LK https://hdl.handle.net/20.500.14352/51728
UL https://hdl.handle.net/20.500.14352/51728
LA eng
NO ©2005 The American Physical Society.We are grateful to CICYT, Spain, and to INTAS, for partial financial support. We are also grateful to G. Colangelo and H. Leutwyler, whose questions about the rho residue, 3"t, prompted us to give the alternate derivation and improvement of its values in Appendix B.
NO CICYT, Spain
NO INTAS
DS Docta Complutense
RD 8 abr 2025