Numerical solution of Q2 evolution equation for the transversity distribution ΔTq

Computer Physics Communications

Volumn 111, Issue 1-3, 1998, Pages 150-166

  Hirai, M ^a   Kumano, S ^a   Miyama, M ^a  

^a SAGA UNIVERSITY   (Japan)

Author keywords

Chiral odd structure function; Numerical solution; Polarized parton distribution; Q2 evolution; Transversity distribution

Indexed keywords

ELEMENTARY PARTICLES; FORTRAN (PROGRAMMING LANGUAGE); INTEGRODIFFERENTIAL EQUATIONS; PROBLEM SOLVING;

CHIRAL ODD FUNCTIONS; LEADING ORDER (LO) EVOLUTION EQUATIONS; NEXT TO LEADING ORDER (NLO) EVOLUTION EQUATIONS; POLARIZED PARTON DISTRIBUTIONS;

QUANTUM THEORY;

EID: 0032094814     PISSN: 00104655     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0010-4655(98)00028-9     Document Type: Article

References (47)

1. Y. Goto, N. Hayashi, M. Hirai, H. Horikawa S. Kumano, M. Miyama, T. Morii, N, Saito, T.-A. Shibata, E. Taniguchi, T. Yamanishi, RHIC-SPIN-J working group on parametrization, research in progress.
2. J.P. Ralston, D.E. Soper, Nucl. Phys. B 152 (1979) 109.
3. R.L. Jaffe, X. Ji, Phys. Rev. Lett. 67 (1991) 552; Nucl. Phys. B 375 (1992) 527; X. Ji, Phys. Lett. B 284 (1992) 137.
4. R.L. Jaffe, X. Ji, Phys. Rev. Lett. 67 (1991) 552; Nucl. Phys. B 375 (1992) 527; X. Ji, Phys. Lett. B 284 (1992) 137.
5. R.L. Jaffe, X. Ji, Phys. Rev. Lett. 67 (1991) 552; Nucl. Phys. B 375 (1992) 527; X. Ji, Phys. Lett. B 284 (1992) 137.
6. J.L. Cortes, B. Pire, J.P. Ralston, Z. Phys. C 55 (1992) 409; J.C. Collins, S.F. Heppelmann, G.A. Ladinsky, Nucl. Phys. B 420 (1994) 565; B. Kamal, Phys. Rev. D 53 (1996) 1142; R.L. Jaffe, N. Saito, Phys. Lett. B 382 (1996) 165.
7. J.L. Cortes, B. Pire, J.P. Ralston, Z. Phys. C 55 (1992) 409; J.C. Collins, S.F. Heppelmann, G.A. Ladinsky, Nucl. Phys. B 420 (1994) 565; B. Kamal, Phys. Rev. D 53 (1996) 1142; R.L. Jaffe, N. Saito, Phys. Lett. B 382 (1996) 165.
8. J.L. Cortes, B. Pire, J.P. Ralston, Z. Phys. C 55 (1992) 409; J.C. Collins, S.F. Heppelmann, G.A. Ladinsky, Nucl. Phys. B 420 (1994) 565; B. Kamal, Phys. Rev. D 53 (1996) 1142; R.L. Jaffe, N. Saito, Phys. Lett. B 382 (1996) 165.
9. J.L. Cortes, B. Pire, J.P. Ralston, Z. Phys. C 55 (1992) 409; J.C. Collins, S.F. Heppelmann, G.A. Ladinsky, Nucl. Phys. B 420 (1994) 565; B. Kamal, Phys. Rev. D 53 (1996) 1142; R.L. Jaffe, N. Saito, Phys. Lett. B 382 (1996) 165.
10. RHIC-Spin collaboration, Proposal on spin physics using the RHIC polarized collider, August 1992; update Sept. 2, 1993.
11. P.J. Mulders, R.D. Tangerman, Nucl. Phys. B 461 (1996) 197.
12. B.L. Ioffe, A. Khodjamirian, Phys. Rev. D 51 (1995) 3373; J. Soffer, Phys. Rev. Lett. 74 (1995) 1292; S. Aoki, M. Doui, T. Hatsuda, Y. Kuramashi, Phys. Rev. D 56 (1997) 433; A.Y. Umnikov, H. He, F.C. Khanna, Phys. Lett. B 398 (1997) 6; R. Kirschner, L. Mankiewicz, A. Schäfer, L. Szymanowski, Z. Phys. C 74 (1997) 501; M. Meyer-Hermann, A. Schäfer, hep-ph/9709349; K. Suzuki, T. Shigetani, hep-ph/9709394; R.L. Jaffe, X. Jin, J. Tang, hep-ph/9709322.
13. B.L. Ioffe, A. Khodjamirian, Phys. Rev. D 51 (1995) 3373; J. Soffer, Phys. Rev. Lett. 74 (1995) 1292; S. Aoki, M. Doui, T. Hatsuda, Y. Kuramashi, Phys. Rev. D 56 (1997) 433; A.Y. Umnikov, H. He, F.C. Khanna, Phys. Lett. B 398 (1997) 6; R. Kirschner, L. Mankiewicz, A. Schäfer, L. Szymanowski, Z. Phys. C 74 (1997) 501; M. Meyer-Hermann, A. Schäfer, hep-ph/9709349; K. Suzuki, T. Shigetani, hep-ph/9709394; R.L. Jaffe, X. Jin, J. Tang, hep-ph/9709322.
14. B.L. Ioffe, A. Khodjamirian, Phys. Rev. D 51 (1995) 3373; J. Soffer, Phys. Rev. Lett. 74 (1995) 1292; S. Aoki, M. Doui, T. Hatsuda, Y. Kuramashi, Phys. Rev. D 56 (1997) 433; A.Y. Umnikov, H. He, F.C. Khanna, Phys. Lett. B 398 (1997) 6; R. Kirschner, L. Mankiewicz, A. Schäfer, L. Szymanowski, Z. Phys. C 74 (1997) 501; M. Meyer-Hermann, A. Schäfer, hep-ph/9709349; K. Suzuki, T. Shigetani, hep-ph/9709394; R.L. Jaffe, X. Jin, J. Tang, hep-ph/9709322.
15. B.L. Ioffe, A. Khodjamirian, Phys. Rev. D 51 (1995) 3373; J. Soffer, Phys. Rev. Lett. 74 (1995) 1292; S. Aoki, M. Doui, T. Hatsuda, Y. Kuramashi, Phys. Rev. D 56 (1997) 433; A.Y. Umnikov, H. He, F.C. Khanna, Phys. Lett. B 398 (1997) 6; R. Kirschner, L. Mankiewicz, A. Schäfer, L. Szymanowski, Z. Phys. C 74 (1997) 501; M. Meyer-Hermann, A. Schäfer, hep-ph/9709349; K. Suzuki, T. Shigetani, hep-ph/9709394; R.L. Jaffe, X. Jin, J. Tang, hep-ph/9709322.
16. B.L. Ioffe, A. Khodjamirian, Phys. Rev. D 51 (1995) 3373; J. Soffer, Phys. Rev. Lett. 74 (1995) 1292; S. Aoki, M. Doui, T. Hatsuda, Y. Kuramashi, Phys. Rev. D 56 (1997) 433; A.Y. Umnikov, H. He, F.C. Khanna, Phys. Lett. B 398 (1997) 6; R. Kirschner, L. Mankiewicz, A. Schäfer, L. Szymanowski, Z. Phys. C 74 (1997) 501; M. Meyer-Hermann, A. Schäfer, hep-ph/9709349; K. Suzuki, T. Shigetani, hep-ph/9709394; R.L. Jaffe, X. Jin, J. Tang, hep-ph/9709322.
17. B.L. Ioffe, A. Khodjamirian, Phys. Rev. D 51 (1995) 3373; J. Soffer, Phys. Rev. Lett. 74 (1995) 1292; S. Aoki, M. Doui, T. Hatsuda, Y. Kuramashi, Phys. Rev. D 56 (1997) 433; A.Y. Umnikov, H. He, F.C. Khanna, Phys. Lett. B 398 (1997) 6; R. Kirschner, L. Mankiewicz, A. Schäfer, L. Szymanowski, Z. Phys. C 74 (1997) 501; M. Meyer-Hermann, A. Schäfer, hep-ph/9709349; K. Suzuki, T. Shigetani, hep-ph/9709394; R.L. Jaffe, X. Jin, J. Tang, hep-ph/9709322.
18. B.L. Ioffe, A. Khodjamirian, Phys. Rev. D 51 (1995) 3373; J. Soffer, Phys. Rev. Lett. 74 (1995) 1292; S. Aoki, M. Doui, T. Hatsuda, Y. Kuramashi, Phys. Rev. D 56 (1997) 433; A.Y. Umnikov, H. He, F.C. Khanna, Phys. Lett. B 398 (1997) 6; R. Kirschner, L. Mankiewicz, A. Schäfer, L. Szymanowski, Z. Phys. C 74 (1997) 501; M. Meyer-Hermann, A. Schäfer, hep-ph/9709349; K. Suzuki, T. Shigetani, hep-ph/9709394; R.L. Jaffe, X. Jin, J. Tang, hep-ph/9709322.
19. B.L. Ioffe, A. Khodjamirian, Phys. Rev. D 51 (1995) 3373; J. Soffer, Phys. Rev. Lett. 74 (1995) 1292; S. Aoki, M. Doui, T. Hatsuda, Y. Kuramashi, Phys. Rev. D 56 (1997) 433; A.Y. Umnikov, H. He, F.C. Khanna, Phys. Lett. B 398 (1997) 6; R. Kirschner, L. Mankiewicz, A. Schäfer, L. Szymanowski, Z. Phys. C 74 (1997) 501; M. Meyer-Hermann, A. Schäfer, hep-ph/9709349; K. Suzuki, T. Shigetani, hep-ph/9709394; R.L. Jaffe, X. Jin, J. Tang, hep-ph/9709322.
20. M. Göckeler, R. Horsley, H. Perlt, P. Rakow, G. Schierholz, A. Schiller, P. Stephenson, hep-ph/9711245.
21. V.N. Gribov, L.N. Lipatov, Sov. J. Nucl. Phys. 15 (1972) 438, 675; G. Altarelli, G. Parisi, Nucl. Phys. B 126 (1977) 298; Yu.L. Dokshitzer, Sov. Phys. JETP 46 (1977) 641.
22. V.N. Gribov, L.N. Lipatov, Sov. J. Nucl. Phys. 15 (1972) 438, 675; G. Altarelli, G. Parisi, Nucl. Phys. B 126 (1977) 298; Yu.L. Dokshitzer, Sov. Phys. JETP 46 (1977) 641.
23. V.N. Gribov, L.N. Lipatov, Sov. J. Nucl. Phys. 15 (1972) 438, 675; G. Altarelli, G. Parisi, Nucl. Phys. B 126 (1977) 298; Yu.L. Dokshitzer, Sov. Phys. JETP 46 (1977) 641.
24. X. Artru, M. Mekhfi, Z. Phys. C 45 (1990) 669.
25. V. Barone, T. Calarco, A. Drago, Phys. Lett. B 390 (1997) 287.
26. S. Kumano, M. Miyama, Phys. Rev. D 56 (1997) 2504.
27. W. Vogelsang, hep-ph/9706511, Phys. Rev. D, in press.
28. A. Hayashigaki, Y. Kanazawa, Y. Koike, hep-ph/9707208, Phys. Rev. D, in press; numerical analysis in progress.
29. S. Scopetta, V. Vento, hep-ph/9707250.
30. C. Bourrely, J. Soffer, O.V. Teryaev, hep-ph/9710224.
31. O. Martin, A. Schäfer, M. Stratmann, W. Vogelsang, hep-ph/9710300.
32. G.P. Ramsey, J. Comput. Phys. 60 (1985) 97; J. Blümlein, G. Ingelman, M. Klein, R. Rückl, Z. Phys. C 45 (1990) 501; S. Kumano, J.T. Londergan, Comput. Phys. Commun. 69 (1992) 373; R. Kobayashi, M. Konuma, S. Kumano, Comput. Phys. Commun. 86 (1995) 264.
33. G.P. Ramsey, J. Comput. Phys. 60 (1985) 97; J. Blümlein, G. Ingelman, M. Klein, R. Rückl, Z. Phys. C 45 (1990) 501; S. Kumano, J.T. Londergan, Comput. Phys. Commun. 69 (1992) 373; R. Kobayashi, M. Konuma, S. Kumano, Comput. Phys. Commun. 86 (1995) 264.
34. G.P. Ramsey, J. Comput. Phys. 60 (1985) 97; J. Blümlein, G. Ingelman, M. Klein, R. Rückl, Z. Phys. C 45 (1990) 501; S. Kumano, J.T. Londergan, Comput. Phys. Commun. 69 (1992) 373; R. Kobayashi, M. Konuma, S. Kumano, Comput. Phys. Commun. 86 (1995) 264.
35. G.P. Ramsey, J. Comput. Phys. 60 (1985) 97; J. Blümlein, G. Ingelman, M. Klein, R. Rückl, Z. Phys. C 45 (1990) 501; S. Kumano, J.T. Londergan, Comput. Phys. Commun. 69 (1992) 373; R. Kobayashi, M. Konuma, S. Kumano, Comput. Phys. Commun. 86 (1995) 264.
36. M. Miyama, S. Kumano, Comput. Phys. Commun. 94 (1996) 185; M. Hirai, S. Kumano, M. Miyama, hep-ph/9707220, Comput Phys. Commun., in press.
37. M. Miyama, S. Kumano, Comput. Phys. Commun. 94 (1996) 185; M. Hirai, S. Kumano, M. Miyama, hep-ph/9707220, Comput Phys. Commun., in press.
38. J. Blümlein, B. Geyer, D. Robaschik, hep-ph/9711405.
39. B. Carnahan, H.A. Luther, J.O. Wilkes, Applied Numerical Methods (Wiley, New York, 1969).
40. T. Gehrmann, W.J. Stirling, Phys. Rev. D. 53 (1996) 6100.
41. G.E. Forsythe, M.A. Malcolm, C.B. Moler, Computer Methods for Mathematical Computations (Prentice-Hall, Englewoods Cliffs, NJ, 1977).
42. B.-Q. Ma, I. Schmidt, J. Soffer, hep-ph/9710247.
43. M. Glück, E. Reya, M. Stratmann, W. Vogelsang, Phys. Rev. D 53 (1996) 4775.
44. S. Kumano, hep-ph/9702367.
45. N. Saito, in: Spin Structure of the Nucleon, T.-A. Shibata, S. Ohta, N. Saito, eds. (World Scientific, 1996) pp. 40-49; J. Soffer, J.-M. Virey, hep-ph/9706229; B. Kamal, hep-ph/9710374.
46. N. Saito, in: Spin Structure of the Nucleon, T.-A. Shibata, S. Ohta, N. Saito, eds. (World Scientific, 1996) pp. 40-49; J. Soffer, J.-M. Virey, hep-ph/9706229; B. Kamal, hep-ph/9710374.
47. N. Saito, in: Spin Structure of the Nucleon, T.-A. Shibata, S. Ohta, N. Saito, eds. (World Scientific, 1996) pp. 40-49; J. Soffer, J.-M. Virey, hep-ph/9706229; B. Kamal, hep-ph/9710374.