Integral equation for spin dependent unintegrated parton distributions incorporating double <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi mathvariant="normal">ln</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mn></mn><mo>(</mo><mn>1</mn><mo>/</mo><mi>x</mi><mo>)</mo><mn></mn></math></span> effects at low <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math></span>

Jan Kwieciński; Martin Maul

doi:10.1103/PhysRevD.67.034014

Access by Xinjiang University

Integral equation for spin dependent unintegrated parton distributions incorporating double $\ln^{2} (1 / x)$ effects at low $x$

Jan Kwieciński

Martin Maul

The Henryk Niewodniczański Institute of Nuclear Physics, Department of Theoretical Physics, Radzikowskiego 152, 31-342 Cracow, Poland

Department of Theoretical Physics, Lund University, Sölvegatan 14A, S - 223 62 Lund, Sweden

PDF

Phys. Rev. D 67, 034014 – Published 19 February, 2003

DOI: https://doi.org/10.1103/PhysRevD.67.034014

Abstract

In this paper we derive an integral equation for the evolution of unintegrated (longitudinally) polarized quark and gluon parton distributions. The conventional Catani-Ciafaloni-Fiorani-Marchesini (CCFM) framework is modified at small x in order to incorporate the QCD expectations concerning the double $\ln^{2} (1 / x)$ resummation at low x for the integrated distributions. Complete Altarelli-Parisi splitting functions are included that makes the formalism compatible with the leading order Altarelli-Parisi evolution at large and moderately small values of x. The obtained modified polarized CCFM equation is shown to be partially diagonalized by the Fourier-Bessel transformation. Results of the numerical solution for this modifed polarized CCFM equation for the nonsinglet quark distributions are presented.

References (19)

Yu.L. Dokshitzer, D.I. Dyakonov, and S.I. Troyan, Phys. Rep. 58, 269 (1980).
M.A. Kimber, A.D. Martin, and M.G. Ryskin, Eur. Phys. J. C 12, 655 (2000); M.A. Kimber, A.D. Martin, J. Kwieciński, and A.M. Staśto, Phys. Rev. D 62, 094006 (2000); ibid.M.A. Kimber, A.D. Martin, and M.G. Ryskin, 63, 114027 (2001).
A.D. Martin and M.G. Ryskin, Phys. Rev. D 64, 094017 (2001); V.A. Khoze, A.D. Martin, and M.G. Ryskin, Eur. Phys. J. C 14, 525 (2000); ibid.19, 477 (2001); ibid.20, 599 (2001).
G. Gustafson, L. Lönnblad, and G. Miu, J. High Energy Phys. 09, 005 (2002).
Small $x$ Collaboration, B. Andersson et al., Eur. Phys. J. C 25, 77 (2002).
M. Ciafaloni, Nucl. Phys. B296, 49 (1988).
S. Catani, F. Fiorani, and G. Marchesini, Phys. Lett. B 234, 339 (1990).
S. Catani, F. Fiorani, and G. Marchesini, Nucl. Phys. B336, 18 (1990).
M. Maul, Phys. Rev. D 65, 094010 (2002).
G. Altarelli and G. Parisi, Nucl. Phys. B126, 298 (1977).
J. Bartels, B.I. Ermolaev, and M.G. Ryskin, Z. Phys. C 70, 273 (1996).
J. Bartels, B.I. Ermolaev, and M.G. Ryskin, Z. Phys. C 72, 627 (1996).
R. Kirschner and L.N. Lipatov, Nucl. Phys. B213, 122 (1983); R. Kirschner, Z. Phys. C 67, 459 (1995).
J. Kwiecinski and B. Ziaja, Phys. Rev. D 60, 054004 (1999).
B.R. Webber, Nucl. Phys. B (Proc. Suppl.) 18C, 38 (1990).
G. Marchesini and B.R. Webber, Nucl. Phys. B386, 215 (1992); B.R. Webber, in Proceedings of the Workshop Physics at HERA, DESY, Hamburg, Germany, 1992, edited by W. Buchmüller and G. Ingelman (DESY, Hamburg, 1992).
M. Glück, E. Reya, M. Stratmann, and W. Vogelsang, Phys. Rev. D 63, 094005 (2001).
M. Glück, E. Reya, and A. Vogt, Eur. Phys. J. C 5, 461 (1998).
H. Jung and G.P. Salam, Eur. Phys. J. C 19, 351 (2001).

[c1] Yu.L. Dokshitzer, D.I. Dyakonov, and S.I. Troyan, Phys. Rep. 58, 269 (1980).

[c2] M.A. Kimber, A.D. Martin, and M.G. Ryskin, Eur. Phys. J. C 12, 655 (2000); M.A. Kimber, A.D. Martin, J. Kwieciński, and A.M. Staśto, Phys. Rev. D 62, 094006 (2000); ibid.M.A. Kimber, A.D. Martin, and M.G. Ryskin, 63, 114027 (2001).

[c3] A.D. Martin and M.G. Ryskin, Phys. Rev. D 64, 094017 (2001); V.A. Khoze, A.D. Martin, and M.G. Ryskin, Eur. Phys. J. C 14, 525 (2000); ibid.19, 477 (2001); ibid.20, 599 (2001).

[c4] G. Gustafson, L. Lönnblad, and G. Miu, J. High Energy Phys. 09, 005 (2002).

[c5] Small $x$ Collaboration, B. Andersson et al., Eur. Phys. J. C 25, 77 (2002).

[c6] M. Ciafaloni, Nucl. Phys. B296, 49 (1988).

[c7] S. Catani, F. Fiorani, and G. Marchesini, Phys. Lett. B 234, 339 (1990).

[c8] S. Catani, F. Fiorani, and G. Marchesini, Nucl. Phys. B336, 18 (1990).

[c9] M. Maul, Phys. Rev. D 65, 094010 (2002).

[c10] G. Altarelli and G. Parisi, Nucl. Phys. B126, 298 (1977).

[c11] J. Bartels, B.I. Ermolaev, and M.G. Ryskin, Z. Phys. C 70, 273 (1996).

[c12] J. Bartels, B.I. Ermolaev, and M.G. Ryskin, Z. Phys. C 72, 627 (1996).

[c13] R. Kirschner and L.N. Lipatov, Nucl. Phys. B213, 122 (1983); R. Kirschner, Z. Phys. C 67, 459 (1995).

[c14] J. Kwiecinski and B. Ziaja, Phys. Rev. D 60, 054004 (1999).

[c15] B.R. Webber, Nucl. Phys. B (Proc. Suppl.) 18C, 38 (1990).

[c16] G. Marchesini and B.R. Webber, Nucl. Phys. B386, 215 (1992); B.R. Webber, in Proceedings of the Workshop Physics at HERA, DESY, Hamburg, Germany, 1992, edited by W. Buchmüller and G. Ingelman (DESY, Hamburg, 1992).

[c17] M. Glück, E. Reya, M. Stratmann, and W. Vogelsang, Phys. Rev. D 63, 094005 (2001).

[c18] M. Glück, E. Reya, and A. Vogt, Eur. Phys. J. C 5, 461 (1998).

[c19] H. Jung and G.P. Salam, Eur. Phys. J. C 19, 351 (2001).

Physical Review D

Export citation

Export citation

Integral equation for spin dependent unintegrated parton distributions incorporating double $\ln^{2} (1 / x)$ effects at low $x$

Abstract

References (19)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation

Integral equation for spin dependent unintegrated parton distributions incorporating double ln2(1/x) effects at low x

Abstract

References (19)

Integral equation for spin dependent unintegrated parton distributions incorporating double $\ln^{2} (1 / x)$ effects at low $x$