Pion-pion scattering amplitude
| dc.contributor.author | Peláez Sagredo, José Ramón | |
| dc.contributor.author | Ynduráin, F. J. | |
| dc.date.accessioned | 2023-06-20T11:06:58Z | |
| dc.date.available | 2023-06-20T11:06:58Z | |
| dc.date.issued | 2005-04 | |
| dc.description | ©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. | |
| dc.description.abstract | 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. | |
| dc.description.department | Depto. de Física Teórica | |
| dc.description.faculty | Fac. de Ciencias Físicas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | CICYT, Spain | |
| dc.description.sponsorship | INTAS | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/35457 | |
| dc.identifier.doi | 10.1103/PhysRevD.71.074016 | |
| dc.identifier.issn | 0556-2821 | |
| dc.identifier.officialurl | http://dx.doi.org/10.1103/PhysRevD.71.074016 | |
| dc.identifier.relatedurl | http://journals.aps.org/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/51728 | |
| dc.issue.number | 7 | |
| dc.journal.title | Physical Review D | |
| dc.language.iso | eng | |
| dc.publisher | American Physical Society | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 51-73 | |
| dc.subject.keyword | Phase-shift analysis | |
| dc.subject.keyword | Gev-c | |
| dc.subject.keyword | Momentum-transfer | |
| dc.subject.keyword | Cross sections | |
| dc.subject.keyword | Mass region | |
| dc.subject.keyword | π&π | |
| dc.subject.keyword | π-P->π-π&N | |
| dc.subject.keyword | Parameters | |
| dc.subject.keyword | Existence | |
| dc.subject.keyword | Unitarity | |
| dc.subject.ucm | Física-Modelos matemáticos | |
| dc.subject.ucm | Física matemática | |
| dc.title | Pion-pion scattering amplitude | |
| dc.type | journal article | |
| dc.volume.number | 71 | |
| dcterms.references | [1] B. Ananthanarayan et al., Phys. Rep. 353, 207 (2001). [2] G. Colangelo, J. Gasser, and H. Leutwyler, Nucl. Phys. B603, 125 (2001). [3] S. M. Roy, Phys. Lett.36B, 353 (1971). [4] N. N. Biswas et al., Phys. Rev. Lett. 18, 273 (1967) [π ̅ π ̅, π ^+ π ̅, and π^0 π ̅ ] D. Cohen et al., Phys. Rev. D 7, 661 (1973) [π ̅ π ̅ ]; W. J. Robertson, W. D. Walker, and J. L. Davis, Phys. Rev. 7, 2554 (1973) [π ̅ π ̅]; W. Hoogland et al., Nucl. Phys. B126, 109 (1977) [π ̅ π ̅]; J. Hanlon et al., Phys. Rev. Lett. 37, 967 (1976) [π ̅ π ̅ ]; H. Abramowicz et al., Nucl. Phys. B166, 62 (1980) [π ̅ π ̅]. These references cover the region between 1.35 and 16 GeV, and agree within errors in the regions where they overlap (with the exception of π ̅ π ̅ below 2.3 GeV, discussion in Ref. [5]). [5] J. R. Peláez and F. J. Ynduráin, Phys. Rev. D 69, 114001 (2004). [6] J. R. Peláez and F. J. Ynduráin, Phys. Rev. D 68, 074005 (2003). [7] F. J. Ynduráin, hep-ph/0310206. [8] S. Descotes, N. H. Fuchs, L. Girlanda, and J. Stern, Eur. Phys. J. C, 24, 469 (2002); R. Kamńiski, L. Leśniak, and B. Loiseau, Phys. Lett. B 551, 241 (2003). [9] J. F. de Trocóniz and F. J. Ynduráin, Phys. Rev. D 65, 093001 (2002); hep-ph/0402285 [Phys. Rev. D (to be published)]. When quoting numbers, we will quote from this last paper. [10] S. D. Protopopescu et al., Phys. Rev. D 7, 1279 (1973). [11] The Cern-Munich experiments (π π scattering). (a) B. Hyams, Nucl. Phys. B64, 134 (1973); G. Grayer et al., Nucl. Phys. B75, 189 (1974); see also the analysis of the same experimental data in P. Estabrooks and A. D. Martin, Nucl. Phys. B79, 301 (1974). (b) B. Hyams et al., Nucl. Phys. B100, 205 (1975). (c) R. Kamiński, L. Lesniak, and K. Rybicki, Z. Phys. C 74, 79 (1997); Eur. Phys. J. direct C 4, 4 (2002). π π → K̅K scattering: (d) W. Wetzel et al., Nucl. Phys. B115, 208 (1976); V. A. Polychromatos et al., Phys. Rev. D 19, 1317 (1979); D. Cohen et al., Phys. Rev. D 22, 2595 (1980); E. Etkin et al., Phys. Rev. D 25, 1786 (1982). [12] M. J. Losty et al., Nucl. Phys. B69, 185 (1974); W. Hoogland et al., Nucl. Phys. B126, 109 (1977); N. B. Durusoy et al., Phys. Lett. B 45, 517 (1973). [13] L. Rosselet et al., Phys. Rev. D 15, 574 (1977); S. Pislak et al., Phys. Rev. Lett. 87, 221801 (2001). [14] For the more recent determination, see A. Aloisio et al., Phys. Lett. B 538, 21 (2002); an older one is P. Pascual and F. J. Ynduráin, Nucl. Phys. B83, 362, (1974). [15] M. R. Pennington, Ann. Phys. (N.Y.) 92, 164 (1975). [16] B. R. Martín, D. Morgan, and G. Shaw, Pion- Pion Interactions in Particle Physics (Academic Press, New York, 1976). [17] F. P. Palou, J. L. Sánchez-Gómez, and F. J. Ynduráin, Z. Phys. A 274, 161 (1975). [18] W. Rarita et al., Phys. Rev. 165, 1615 (1968). [19] C. D. Froggatt and J. L. Petersen, Nucl. Phys. B129, 89 (1977); F. P. Palou and F. J. Ynduráin, Nuovo Cimento 19A, 245 (1974). [20] D. Atkinson et al., Nucl. Phys. B7, 375 (1968); Nucl. Phys. B23, 397 ( 1970). [21] F. J. Ynduráin, Phys. Lett. B 578, 99 (2004); Phys. Lett. B 586, 439(E) (2004); hep-ph/0501104 [Phys. Lett. B (to be published)]. 8 We would | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 70900239-cb8b-49f3-931f-9dc6a8b7d8d5 | |
| relation.isAuthorOfPublication.latestForDiscovery | 70900239-cb8b-49f3-931f-9dc6a8b7d8d5 |
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