Photon- and pion-nucleon interactions in a unitary and causal effective field theory based on the chiral Lagrangian

Nuclear Physics A

Volumn 848, Issue 1-2, 2010, Pages 126-182

  Gasparyan, A ^a,b   Lutz, M F M ^a  

^a GSI HELMHOLTZZENTRUM FÜR SCHWERIONENFORSCHUNG GMBH   (Germany)

^b INSTITUTE FOR THEORETICAL AND EXPERIMENTAL PHYSICS   (Russian Federation)

Author keywords

Causality; Chiral symmetry; Effective field theory; Nucleon; Photon; Pion; Unitarity

Indexed keywords

EID: 78049302119     PISSN: 03759474     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nuclphysa.2010.08.006     Document Type: Article

References (95)

1. Bernard V., Kaiser N., Meißner U.-G. Chiral dynamics in nucleons and nuclei. Int. J. Mod. Phys. E 1995, 4:193-346.
2. Bernard V. Chiral perturbation theory and baryon properties. Prog. Part. Nucl. Phys. 2008, 60:82-160.
3. Pascalutsa V., Vanderhaeghen M., Yang S.N. Electromagnetic excitation of the Δ(1232)-resonance. Phys. Rep. 2007, 437:125-232.
4. Bernard V., Kaiser N., Meissner U.-G. Determination of the low-energy constants of the next-to-leading order chiral pion nucleon Lagrangian. Nucl. Phys. A 1997, 615:483-500.
5. Fettes N., Meissner U.-G., Steininger S. Pion nucleon scattering in chiral perturbation theory. I: Isospin-symmetric case. Nucl. Phys. A 1998, 640:199-234.
6. Fettes N., Meissner U.-G. Pion nucleon scattering in chiral perturbation theory. II: Fourth order calculation. Nucl. Phys. A 2000, 676:311.
7. Bernard V., Kaiser N., Meissner U.G. Threshold pion photoproduction in chiral perturbation theory. Nucl. Phys. B 1992, 383:442-496.
8. Bernard V., Kaiser N., Meissner U.-G. Neutral pion photoproduction off nucleons revisited. Z. Phys. C 1996, 70:483-498.
9. Bernard V., Kaiser N., Meissner U.-G. Chiral corrections to the Kroll-Ruderman theorem. Phys. Lett. B 1996, 383:116-120.
10. Fearing H.W., Hemmert T.R., Lewis R., Unkmeir C. Radiative pion capture by a nucleon. Phys. Rev. C 2000, 62:054006.
11. Beane S.R., Malheiro M., McGovern J.A., Phillips D.R., van Kolck U. Compton scattering on the proton, neutron, and deuteron in chiral perturbation theory to O(Q4). Nucl. Phys. A 2005, 747:311-361.
12. Scholten O., Korchin A.Y., Pascalutsa V., Van Neck D. Pion and photon induced reactions on the nucleon in a unitary model. Phys. Lett. B 1996, 384:13-19.
13. Krehl O., Hanhart C., Krewald S., Speth J. What is the structure of the Roper resonance?. Phys. Rev. C 2000, 62:025207.
14. Penner G., Mosel U. Vector meson production and nucleon resonance analysis in a coupled-channel approach for energies mN
15. Gasparyan A.M., Haidenbauer J., Hanhart C., Speth J. Pion nucleon scattering in a meson exchange model. Phys. Rev. C 2003, 68:045207.
16. Shklyar V., Lenske H., Mosel U., Penner G. Coupled-channel analysis of the ω-meson production in ΠN and γN reactions for cm energies up to 2-GeV. Phys. Rev. C 2005, 71:055206.
17. Matsuyama A., Sato T., Lee T.S.H. Dynamical coupled-channel model of meson production reactions in the nucleon resonance region. Phys. Rep. 2007, 439:193-253.
18. Drechsel D., Kamalov S.S., Tiator L. Unitary isobar model - MAID2007. Eur. Phys. J. A 2007, 34:69-97.
19. Datta A., Pakvasa S. Pion nucleon phase shifts in heavy baryon chiral perturbation theory. Phys. Rev. D 1997, 56:4322-4327.
20. Ellis P.J., Tang H.-B. Pion nucleon scattering in a new approach to chiral perturbation theory. Phys. Rev. C 1998, 57:3356-3375.
21. Fettes N., Meissner U.G. Pion nucleon scattering in an effective chiral field theory with explicit spin-3/2 fields. Nucl. Phys. A 2001, 679:629-670.
22. Lutz M.F.M., Kolomeitsev E.E. Relativistic chiral SU(3) symmetry, large N(c) sum rules and meson baryon scattering. Nucl. Phys. A 2002, 700:193-308.
23. Torikoshi K., Ellis P.J. Low energy pion nucleon scattering in the heavy baryon and infrared schemes. Phys. Rev. C 2003, 67:015208.
24. Pascalutsa V., Phillips D.R. Effective theory of the Δ(1232) in Compton scattering off the nucleon. Phys. Rev. C 2003, 67:055202.
25. Pascalutsa V., Vanderhaeghen M. Chiral effective-field theory in the Δ(1232) region. I: Pion electroproduction on the nucleon. Phys. Rev. D 2006, 73:034003.
26. Pascalutsa V. The Delta(1232) resonance in chiral effective field theory. Prog. Part. Nucl. Phys. 2008, 61:27-33.
27. Long B., van Kolck U. πN scattering in the γ(1232) region in an effective field theory. Nucl. Phys. A 2010, 840:39-75.
28. Meissner U.-G., Oller J.A. Chiral unitary meson baryon dynamics in the presence of resonances: Elastic pion nucleon scattering. Nucl. Phys. A 2000, 673:311-334.
29. Nicola A.Gomez, Pelaez J.R. Unitarized pion nucleon scattering within heavy baryon chiral perturbation theory. Phys. Rev. D 2000, 62:017502.
30. Nicola A.Gomez, Nieves J., Pelaez J.R., Arriola E. Ruiz Improved unitarized heavy baryon chiral perturbation theory for πN scattering. Phys. Lett. B 2000, 486:77-85.
31. Nicola A.G., Nieves J., Pelaez J.R., Arriola E.R. Improved unitarized heavy baryon chiral perturbation theory for πN scattering to fourth order. Phys. Rev. D 2004, 69:076007.
32. Weinberg S. Nuclear forces from chiral Lagrangians. Phys. Lett. B 1990, 251:288-292.
33. Weinberg S. Effective chiral Lagrangians for nucleon-pion interactions and nuclear forces. Nucl. Phys. B 1991, 363:3-18.
34. M.F.M. Lutz, E.E. Kolomeitsev, Baryon resonances in the hadrogenesis conjecture, in preparation.
35. van Antwerpen C.H.M., Afnan I.R. A gauge invariant unitary theory for pion photoproduction. Phys. Rev. C 1995, 52:554-567.
36. MacDowell S.W. Analytic properties of partial amplitudes in meson-nucleon scattering. Phys. Rev. 1959, 116:774-778.
37. Mandelstam S. Determination of the pion-nucleon scattering amplitude from dispersion relations and unitarity. General Theory Phys. Rev. 1958, 112:1344-1360.
38. Ball J.S. Application of the Mandelstam representation to photoproduction of pions from nucleons. Phys. Rev. 1961, 124:2014-2028.
39. Nakanishi N. Proof of partial-wave dispersion relations in perturbation theory. Phys. Rev. 1962, 126(3):1225-1226.
40. Sommer G. Present state of rigorous analytic properties of scattering amplitudes. Fortsch. Phys. 1970, 18:577-688.
41. Chen C.K. Generalized partial-wave dispersion relation and the n/d method. Phys. Rev. D 1972, 5:1464-1471.
42. Johnson P.W., Warnock R.L. Solution of the unitarity equation with overlapping left and right cuts: A tool for study of the s* and similar systems. J. Math. Phys. 1981, 22:385.
43. Chew G.F., Mandelstam S. Theory of low-energy pion-pion interactions. Phys. Rev. 1960, 119:467-477.
44. Frye G., Warnock R.L. Analysis of partial-wave dispersion relations. Phys. Rev. 1963, 130(1):478-494.
45. Rinat (Reiner) A.S., Stingl M. Multichannel N/D approach to nuclear reactions amongst light nuclei. I. General theory. Ann. Phys. 1971, 65:141-180.
46. Collins P.D.B., Squires E.J. Regge Poles in Particle Physics 1968, Springer-Verlag, Berlin.
47. Stingl M., Rinat A.S. Partial wave dispersion relations for the nonrelativistic five nucleon system. Phys. Rev. C 1974, 10:1253.
48. Castillejo L., Dalitz R.H., Dyson F.J. Low's scattering equation for the charged and neutral scalar theories. Phys. Rev. 1956, 101:453-458.
49. Frazer W.R. Applications of conformal mapping to the phenomenological representation of scattering amplitudes. Phys. Rev. 1961, 123:2180-2182.
50. Kennedy J., Spearman T.D. Singularities in partial-wave amplitudes for two ingoing and two outgoing particles. Phys. Rev. 1962, 126(4):1596-1602.
51. Koch R. A calculation of low-energy πN partial waves based on fixed t analyticity. Nucl. Phys. A 1986, 448:707.
52. Arndt R.A., Briscoe W.J., Strakovsky I.I., Workman R.L. Extended partial-wave analysis of πN scattering data. Phys. Rev. C 2006, 74:045205.
53. Timmermans R.G.E., Rijken T.A., de Swart J.J. Determination of the charged pion coupling constant from data on the charge exchange reaction anti-p p → anti-n n. Phys. Rev. Lett. 1991, 67:1074-1077.
54. Zachariasen F. Relativistic model field theory with finite self-masses. Phys. Rev. 1961, 121(6):1851-1862.
55. Bart G.R., Warnock R.L. Empirical n/d potential and Castillejo-Dalitz-Dyson poles in the pion-nucleon p(11) state. Phys. Rev. Lett. 1969, 22:1081-1084.
56. Pearce B.C., Afnan I.R. Three-body unitarity, the cloudy bag model and the Roper resonance. Phys. Rev. C 1989, 40:220-236.
57. Matsinos E. Isospin violation in the πN system at low energies. Phys. Rev. C 1997, 56:3014-3025.
58. Meissner U.-G., Raha U., Rusetsky A. Isospin-breaking corrections in the pion deuteron scattering length. Phys. Lett. B 2006, 639:478-482.
59. Krebs H., Epelbaum E., Meissner U.-G. Nuclear forces with Delta-excitations up to next-to-next-to-leading order I: Peripheral nucleon-nucleon waves. Eur. Phys. J. A 2007, 32:127-137.
60. Rentmeester M.C.M., Timmermans R.G.E., de Swart J.J. Determination of the chiral coupling constants c(3) and c(4) in new pp and np partial-wave analyses. Phys. Rev. C 2003, 67:044001.
61. Procura M., Musch B.U., Wollenweber T., Hemmert T.R., Weise W. Nucleon mass: From lattice QCD to the chiral limit. Phys. Rev. D 2006, 73:114510.
62. Buettiker P., Meissner U.-G. Pion nucleon scattering inside the Mandelstam triangle. Nucl. Phys. A 2000, 668:97-112.
63. Arndt R.A., Briscoe W.J., Strakovsky I.I., Workman R.L. Analysis of pion photoproduction data. Phys. Rev. C 2002, 66:055213.
64. Watson K.M. Some general relations between the photoproduction and scattering of pi mesons. Phys. Rev. 1954, 95:228-236.
65. R. Leukel, PhD thesis, Mainz, 2001, http://wwwa2.kph.uni-maiz.de/A2/.
66. I. Preobrajenski, PhD thesis, Mainz, 2001, http://wwwa2.kph.uni-maiz.de/A2/.
67. Shafi A., et al. Measurement of inverse pion photoproduction at energies spanning the N(1440) resonance. Phys. Rev. C 2004, 70:035204.
68. 0), and p(πpolarized,Π+). Phys. Rev. C 2001, 64:025203.
69. Bergstrom J.C., et al. Measurement of the H-1 (γ, π0) cross-section near threshold. Phys. Rev. C 1996, 53:1052-1056.
70. Schmidt A., et al. Test of low-energy theorems for p(γ(pol.),π0)p in the threshold region. Phys. Rev. Lett. 2001, 87:232501.
71. Bernard V., Kaiser N., Meissner U.-G. Aspects of near threshold neutral pion photoproduction off protons. Eur. Phys. J. A 2001, 11:209-216.
72. Korkmaz E., et al. Measurement of the γp→π+n reaction near threshold. Phys. Rev. Lett. 1999, 83:3609-3612.
73. Kovash M.A. Total cross-sections for γp→πn at 10-MeV to 20-MeV. πN Newslett. 1997, 12(3):51-55.
74. Bernard V., Kaiser N., Meissner U.-G. Chiral symmetry and the reaction γp→π0p. Phys. Lett. B 1996, 378:337-341.
75. A. Schmidt, PhD thesis, Mainz, 2001, 2001. http://wwwa2.kph.uni-maiz.de/A2/.
76. Bergstrom J.C., Igarashi R., Vogt J.M. Measurement of the H-1 (γ,π0) cross-section near threshold. II: Pion angular distributions. Phys. Rev. C 1997, 55:2016-2023.
77. Hanstein O., Drechsel D., Tiator L. A dispersion theoretical approach to the threshold amplitudes of pion photoproduction. Phys. Lett. B 1997, 399:13-21.
78. Kamalov S.S., Chen G.-Y., Yang S.-N., Drechsel D., Tiator L. π0 photo- and electroproduction at threshold within a dynamical model. Phys. Lett. B 2001, 522:27-36.
79. Fernandez-Ramirez C., Bernstein A.M., Donnelly T.W. The unexpected impact of D waves in low-energy neutral pion photoproduction from the proton and the extraction of multipoles. Phys. Rev. C 2009, 80:065201.
80. D. Hornidge, Proposal for an experiment, MAMI-A2/6-03.
81. A. Berstein, Proposal for an experiment, MAMI-A2/10-09.
82. Olmos de Leon V., et al. Low-energy Compton scattering and the polarizabilities of the proton. Eur. Phys. J. A 2001, 10:207-215.
83. Hallin E.L., et al. Compton scattering from the proton. Phys. Rev. C 1993, 48:1497-1507.
84. Wolf S., et al. Compton scattering by the proton using a large-acceptance arrangement. Eur. Phys. J. A 2001, 12:231-252.
85. Babusci D., Giordano G., L'vov A.I., Matone G., Nathan A.M. Low-energy Compton scattering of polarized photons on polarized nucleons. Phys. Rev. C 1998, 58:1013-1041.
86. L'vov A.I., Petrun'kin V.A., Schumacher M. Dispersion theory of proton Compton scattering in the first and second resonance regions. Phys. Rev. C 1997, 55:359-377.
87. Schumacher M. Polarizability of the nucleon and Compton scattering. Prog. Part. Nucl. Phys. 2005, 55:567-646.
88. Lensky V., Pascalutsa V. Predictive powers of chiral perturbation theory in Compton scattering off protons. Eur. Phys. J. C 2010, 65:195-209.
89. V. Baru, et al., Precision calculation of the π- deuteron scattering length and its impact on threshold π-N scattering.
90. Chew G.F., Goldberger M.L., Low F.E., Nambu Y. Relativistic dispersion relation approach to photomeson production. Phys. Rev. 1957, 106:1345-1355.
91. Jacob M., Wick G.C. On the general theory of collisions for particles with spin. Ann. Phys. 1959, 7:404-428.
92. Bardeen W.A., Tung W.K. Invariant amplitudes for photon processes. Phys. Rev. 1968, 173:1423-1433.
93. Donnachie A., Shaw G. Photopion production, disperion relations, and γ-ρ-π coupling. Ann. Phys. 1966, 37:333-364.
94. Arndt R.A., Workman R.L., Li Z., Roper L.D. Partial wave analysis of pion photoproduction. Phys. Rev. C 1990, 42:1853-1863.
95. Pfeil W., Rollnik H., Stankowski S. A partial-wave analysis for proton Compton scattering in the Δ(1232) energy region. Nucl. Phys. B 1974, 73:166-188.