Low energy analysis of πn → πn

Journal of High Energy Physics

Volumn 5, Issue 6, 2001, Pages 1-85

  Becher, Thomas ^a   Leutwyler, Heinrich ^b  

^a Cornell University Ithaca ^*  (United States)

^b UNIVERSITY OF BERN   (Switzerland)

Author keywords

Chiral Lagrangians; QCD

Indexed keywords

EID: 33744543771     PISSN: 10298479     EISSN: None     Source Type: Journal    
DOI: 10.1088/1126-6708/2001/06/017     Document Type: Article

References (79)

1. E.M. Henley and W. Thirring, Elementary quantum field theory, Part III. Pion Physics, McGraw-Hill, New York 1962.
2. J. Gasser, M.E. Sainio and A. Švarc, Nucleons with chiral loops, Nucl. Phys. B 307 (1988) 779.
3. E. Jenkins and A.V. Manohar, Baryon chiral perturbation theory using a heavy fermion lagrangian, Phys. Lett. B 255 (1991) 558.
4. G. Ecker, The standard model at low energies, Czech. J. Phys. 44 (1995) 405 [hep-ph/9309268].
5. V. Bernard, N. Kaiser and U.-G. Meissner, Chiral dynamics in nucleons and nuclei, Int. J. Mod. Phys. E4 (1995) 193 [hep-ph/9501384].
6. 3 ) in heavy baryon chiral perturbation theory, Eur. Phys. J. C 2 (1998) 181 [hep-ph/9704415].
7. N. Fettes, U.-G. Meissner and S. Steininger, Pion nucleon scattering in chiral perturbation theory. I: isospin-symmetric case, Nucl. Phys. A 640 (1998) 199 [hep-ph/9803266].
8. N. Fettes and U.-G. Meissner, Pion nucleon scattering in chiral perturbation theory. II: fourth order calculation, Nucl. Phys. A 676 (2000) 311 [hep-ph/0002162].
9. T. Becher and H. Leutwyler, Baryon chiral perturbation theory in manifestly Lorentz invariant form, Eur. Phys. J. C 9 (1999) 643.
10. J.L. Goity, D. Lehmann, G. Prezeau and J. Saez, Regularization for effective field theory with two heavy particles, Phys. Lett. B 504 (2001) 21 [hep-ph/0101011];
11. D. Lehmann and G. Prezeau, Effective field theory dimensional regularization, hep-ph/0102161.
12. J. Schweizer, Low energy representation for the axial form factor of the nucleon, Diploma thesis, University of Bern, Bern 2000.
13. B. Kubis and U.-G. Meissner, Low energy analysis of the nucleon electromagnetic form factors, Nucl. Phys. A 679 (2001) 698 [hep-ph/0007056];
14. Baryon form factors in chiral perturbation theory, Eur. Phys. J. C 18 (2001) 747 [hep-ph/0010283];
15. S.-L. Zhu, S. Puglia and M.J. Ramsey-Musolf, Recoil order chiral corrections to baryon octet axial currents, Phys. Rev. D 63 (2001) 034002 [hep-ph/0009159].
16. 4 ) in heavy baryon chiral perturbation theory, J. High Energy Phys. 04 (1999) 031 [hep-ph/9901235].
17. V. Bernard, N. Kaiser and U.-G. Meissner, On the analysis of the pion nucleon sigma-term: the size of the remainder at the Cheng-Dashen point, Phys. Lett. B 389 (1996) 144 [hep-ph/9607245].
18. S.M. Roy, Exact integral equation for pion-pion scattering involving only physical region partial waves, Phys. Lett. B 36 (1971) 353.
19. R. Oehme, Dispersion relations for pion-nucleon scattering, 1. The spin-flip amplitude, Phys. Rev. 100 (1955) 1503;
20. Dispersion relations for pion-nucleon scattering: no-spin-flip amplitude, Phys. Rev. 102 (1956) 1174;
21. R.H. Capps and G. Takeda, Dispersion relations for finite momentum-transfer pion-nucleon scattering, Phys. Rev. 103 (1956) 1877;
22. G.F. Chew, M.L. Goldberger, F.E. Low and Y. Nambu, Relativistic dispersion relation approach to photomeson production, Phys. Rev. 106 (1957) 1345;
23. F. Steiner, On the generalized πN potential – a new representation from fixed t dispersion relations, Fortsch. Physik 18 (1970) 43;
24. Partial wave crossing relations for meson-baryon scattering, Fortsch. Physik 19 (1971) 115;
25. J. Baacke and F. Steiner, πN partial wave relations from fixed-t dispersion relations, Fortsch. Physik, 18 (1970) 67.
26. R. Koch, A calculation of low-energy πN partial waves based on fixed-t analyticity, Nucl. Phys. A 448 (1986) 707.
27. B. Ananthanarayan, G. Colangelo, J. Gasser and H. Leutwyler, Roy equation analysis of ππ scattering, hep-ph/0005297.
28. G. Colangelo, J. Gasser and H. Leutwyler, The ππ S-wave scattering lengths, Phys. Lett. B 488 (2000) 261 [hep-ph/0007112];
29. ππ scattering, Nucl. Phys. B 603 (2001) 125 [hep-ph/0103088].
30. J. Gasser and H. Leutwyler, Chiral perturbation theory to one loop, Ann. Phys. (NY) 158 (1984) 142.
31. G. Ecker, Chiral invariant renormalization of the pion-nucleon interaction, Phys. Lett. B 336 (1994) 508 [hep-ph/9402337];
32. G. Ecker and M. Mojžiš, Low-energy expansion of the pion-nucleon lagrangian, Phys. Lett. B 365 (1996) 312 [hep-ph/9508204].
33. V. Bernard, N. Kaiser, J. Kambor and U.-G. Meissner, Chiral structure of the nucleon, Nucl. Phys. B 388 (1992) 315.
34. J. Gasser, H. Leutwyler and M.E. Sainio, Sigma term update, Phys. Lett. B 253 (1991) 252;
35. Form-factor of the sigma term, Phys. Lett. B 253 (1991) 260.
36. J. Gasser and H. Leutwyler, Chiral perturbation theory to one loop, Ann. Phys. (NY) 158 (1984) 142.
37. C.A. Dominguez, πNN form-factor, chiral symmetry breaking and three-pion resonance, Phys. Rev. D 27 (1983) 1572;
38. The Goldberger-Treiman relation: a probe of the chiral symmetries of quantum chromodynamics, Nuovo Cim. 8N6 (1985) 1;
39. P.A.M. Guichon, G.A. Miller and A.W. Thomas, The axial form-factor of the nucleon and the pion-nucleon vertex function, Phys. Lett. B 124 (1983) 109;
40. P.M. Gensini, Strangeness in the proton wave function?, Nuovo Cim. 102 (1989) 75, erratum ibid. 102A (1989) 1181.
41. N.F. Nasrallah, The Goldberger-Treiman discrepancy, Phys. Rev. D 62 (2000) 036006 [hep-ph/9904358].
42. M.L. Goldberger and S.B. Treiman, Decay of the π meson, Phys. Rev. 110 (1958) 1178.
43. G. Höhler, in Landolt-Börnstein, 9b2, ed. H. Schopper, Springer, Berlin 1983.
44. T.P. Cheng and R. Dashen, Is SU(2) × SU(2) a better symmetry than SU(3)?, Phys. Rev. Lett. 26 (1971) 594.
45. L.S. Brown, W.J. Pardee and R.D. Peccei, Adler-Weisberger theorem reexamined, Phys. Rev. D 4 (1971) 2801.
46. H. Pagels and W.J. Pardee, Nonanalytic behavior of the sigma term in πN scattering, Phys. Rev. D 4 (1971) 3335.
47. M.E. Sainio, Low-energy pion-nucleon interaction and the sigma term, πN Newslett. 13 (1997) 144.
48. R.A. Arndt, R.L. Workman, I.I. Strakovsky and M.M. Pavan, πN elastic scattering analyses and dispersion relation constraints, nucl-th/9807087.
49. J. Stahov, The subthreshold expansion of the πN invariant amplitudes in dispersion theory, πN Newslett. 15 (1999) 13.
50. G.C. Oades, Finite contour dispersion relations and the subthreshold expansion coefficients of the πN invariant amplitudes, πN Newslett. 15 (1999) 307. Note that some of the numerical values listed in this reference are incorrect. We thank G. Oades for providing us with the corrected values.
51. J. Gasser, Chiral perturbation theory and effective lagrangians, Nucl. Phys. B 279 (1987) 65.
52. M. Knecht, B. Moussallam, J. Stern and N.H. Fuchs, The low-energy ππ amplitude to one and two loops, Nucl. Phys. B 457 (1995) 513 [hep-ph/9507319].
53. E. Jenkins and A.V. Manohar, Chiral corrections to the baryon axial currents, Phys. Lett. B 259 (1991) 353;
54. Effective Theories of the Standard Model, ed. U.-G. Meissner, World Scientific, Singapore 1991;
55. J. Kambor, The ∆(1232) as an effective degree of freedom in chiral perturbation theory in proc. Workshop on Chiral dynamics: theory and experiment, Mainz, Germany 1997, A. Bernstein, D. Drechsel and T. Walcher eds., Lecture Notes in Physics, 513, Springer-Verlag, 1998 [hep-ph/9711484];
56. T.R. Hemmert, B.R. Holstein and J. Kambor, Systematic 1/M expansion for spin 3/2 particles in baryon chiral perturbation theory, Phys. Lett. B 395 (1997) 89 [hep-ph/9606456];
57. ∆(1232) and the polarizabilities of the nucleon, Phys. Rev. D 55 (1997) 5598 [hep-ph/9612374];
58. Chiral lagrangians and ∆(1232) interactions: formalism, J. Phys. G 24 (1998) 1831 [hep-ph/9712496];
59. P.J. Ellis and H.-B. Tang, Pion-nucleon scattering in a new approach to chiral perturbation theory, Phys. Rev. C 57 (1998) 3356 [hep-ph/9709354];
60. N. Fettes and U.G. Meissner, Pion-nucleon scattering in an effective chiral field theory with explicit spin-3/2 fields, Nucl. Phys. A 679 (2001) 629 [hep-ph/0006299].
61. V. Antonelli, A. Gall, J. Gasser, A. Rusetsky, Effective lagrangians in bound state calculations, Ann. Phys. (NY) 286 (2001) 108 [hep-ph/0003118].
62. S. Weinberg, Pion scattering lengths, Phys. Rev. Lett. 17 (1966) 616.
63. Proc. 8th Symposium on Meson-Nucleon Physics and the Structure of the Nucleon (MENU 99), Zuoz, Switzerland (1999), πN Newslett. 15 (1999).
64. R. Koch, Improved πN partial waves consistent with analyticity and unitarity, Z. Physik C 29 (1985) 597.
65. H.J. Leisi, Results from pionic hydrogen, πN Newslett. 15 (1999) 258;
66. H.C. Schröder et al., Determination of the πN scattering lengths from pionic hydrogen, Phys. Lett. B 469 (1999) 25.
67. G.F. Chew and S. Mandelstam, Theory of low-energy pion-pion interactions, Phys. Rev. 119 (1960) 467;
68. T.N. Truong, Chiral perturbation theory and final state theorem, Phys. Rev. Lett. 61 (1988) 2526;
69. Remarks on the unitarization methods, Phys. Rev. Lett. 67 (1991) 2260;
70. E. Oset, J.A. Oller, J.R. Pelaez and A. Ramos, Meson meson and meson baryon interactions in a chiral non-perturbative approach, Acta Phys. Polon. B29 (1998) 3101 [hep-ph/9806460];
71. U.-G. Meissner and J.A. Oller, Chiral unitary meson baryon dynamics in the presence of resonances: elastic pion nucleon scattering, Nucl. Phys. A 673 (2000) 311 [nucl-th/9912026];
72. A.G. Nicola, J. Nieves, J.R. Pelaez and E.R. Arriola, Improved unitarized heavy baryon chiral perturbation theory for πN scattering, Phys. Lett. B 486 (2000) 77 [hep-ph/0006043].
73. P.F.A. Goudsmit, H.J. Leisi, E. Matsinos, B.L. Birbrair and A.B. Gridnev, The extended tree level model for the pion-nucleon interaction, Nucl. Phys. A 575 (1994) 673;
74. + p scattering data and a comparison with pionic hydrogen data, hep-ph/0009081;
75. + p data, hep-ph/9902207.
76. J. Gasser, H. Leutwyler, M.P. Locher and M.E. Sainio, Extracting the pion-nucleon sigma term from data, Phys. Lett. B 213 (1988) 85;
77. J. Gasser, H. Leutwyler and M.E. Sainio, Sigma term update, Phys. Lett. B 253 (1991) 252.
78. B. Ananthanarayan and P. Büttiker, Comparison of πK scattering in SU(3) chiral perturbation theory and dispersion relations, Eur. Phys. J. C 19 (2001) 517 [hep-ph/0012023].
79. G. Hite and F. Steiner, New dispersion relations and their applications to partial-wave amplitude, Nuovo Cim. 18 (1973) 237.