Precision of chiral-dispersive calculations of ππ scattering

Physical Review D

Volumn 68, Issue 7, 2003, Pages

  Pelaez J R ^a,c   Yndurain F J ^b  

^a UNIVERSITY OF FLORENCE   (Italy)

^b UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

^c UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ACCURACY; ARTICLE; CALCULATION; CHIRALITY; MOLECULAR DYNAMICS; MOLECULAR PHYSICS;

EID: 0345356291     PISSN: 05562821     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevD.68.074005     Document Type: Article

References (45)

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. π ≃= 139.57 MeV.
5. The method of the Froissart-Gribov representation to calculate scattering lengths and effective ranges was introduced in [6,7]. It is also discussed in some detail in [8].
6. F. P. Palou and F. J. Yndurain, Nuovo Cimento A 19, 245 (1974).
7. F. P. Palou, J. L. Sánchez-Gómez, and F. J. Ynduráin, Z. Phys. A 274, 161 (1975).
8. F. J. Ynduráin, "Low energy pion interactions," FTUAM02-28, hep-ph/0212282.
9. We are actually simplifying in that Eqs. (2) and (3) should take into account the different isospin structure of s and it channels, which the reader may find in, e.g. the text of Martin, Morgan, and Shaw [10].
10. B. R. Martin, D. Morgan, and G. Shaw, Pion-Pion Interactions in Particle Physics (Academic, New York, 1976).
11. D. Atkinson, Nucl. Phys. B7, 375 (1968);
12. D. Atkinson, Nucl. Phys. B23, 397 (1970).
13. For analyticity properties of ππ scattering see for example [10].
14. 2/DOF of the I = 0 S wave corrects an error there. We send to this reference for details on the fitting procedure.
15. For the more recent determination, see A. Aloisio et al., Phys. Lett. B 538, 21 (2002);
16. the older one is from P. Pascual and F. J. Ynduráin, Nucl. Phys. B83, 362 (1974).
17. J. F. de Trocóniz and F. J. Yndurâin, Phys. Rev. D 65, 093001 (2002).
18. 1 stays essentially constant). Including systematic errors makes the determinations of the pion from factor in the time-like and spacelike regions more compatible one with another, and this allows a more precise determination of low energy parameters.
19. S. D. Protopopescu el al., Phys. Rev. D 7, 1279 (1973).
20. B. Hyams et al., Nucl. Phys. B64, 134 (1973);
21. G. Grayer et al., Nucl. Phys. ibid. B75, 189 (1974);
22. see also the analysis of the same experimental data in P. Estabrooks and A. D. Martin, Nucl. Phys.ibid. B79, 301 (1974).
23. Equation (21) corrects a mistake in the corresponding wave in [8].
24. M. J. Losty et al., Nucl. Phys. B69, 185 (1974);
25. W. Hoogland et al., Nucl. Phys. ibid. B126, 109 (1977).
26. M. Gell-Mann, Phys. Rev. Lett. 8, 263 (1962);
27. V. N. Gribov and I. Ya. Pomeranchuk, Phys. Rev. Lett. ibid. 8, 343 (1962);
28. for more references in general Regge theory, see V. D. Barger and D. B. Cline, Phenomenological Theories of High Energy Scattering (Benjamin, New York, 1969);
29. for references to the QCD analysis, F. J. Yndurain, The Theory of Quark and Gliton Interactions (Springer, Berlin, 1999).
30. In potential theory the proof can be made mathematically rigorous; in relativistic theory, it follows from extended unitarity or, in QCD, in the DGLAP formalism, as is intuitively obvious from Fig. 3.
31. W. Rarita et al., Phys. Rev. 165, 1615 (1968).
32. Fits to deep inelastic scattering processes, and references to previous literature, may be found in the book by Yndurdin in [21].
33. (lt)(t); see [6,23]. For the small values of ; in which we are interested, our expressions are sufficiently accurate.
34. -2, not far from the value 1.01 GeV 2 that the actual fits give, and which we have used here.
35. -, τ decay or J/Φ decay, and the inelasticities in both cases are also quite different.
36. Particle Data Group, D. E. Groom et al., Eur. Phys. J. C 15, 1 (2000).
37. D. Atkinson, G. Mahoux, and R J. Yndurdin, Nucl. Phys. B54, 263 (1973);
38. B98, 521 (1975).
39. M. R. Pennington, Ann. Phys. (N.Y.) 92, 164 (1975).
40. This should not be taken as a criticism of the work of Pennington; at that time the data, very poor, did indeed suggest possible deviations of Regge behavior for ππ. On the other hand, the fact that QCD also implies factorization was of course unknown.
41. This fit is actually a refinement of that of Eq. (7.6.2) in [8]; more details about this will be presented in a separate publication.
42. J. Gasser and H. Leutwyler, Ann. Phys. (N.Y.) 158, 142 (1984).
43. S. Descotes, N. H. Fuchs, L. Girlanda, and J. Stern, Eur. Phys. J. C 24, 469 (2002).
44. 2(1270) resonance is as large as the nominal error due to only the errors in the parameters in Eq. (20).
45. I. Caprini, G. Colangelo, J. Gasser, and H. Leutwyler, following paper, Phys. Rev. D 68, 074006 (2003).