Small-<span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math></span> behavior of the singlet polarized structure function <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>g</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span> in the double logarithmic approximation

J. Bartels; M. G. Ryskin

doi:10.1103/PhysRevD.65.114012

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Small- $x$ behavior of the singlet polarized structure function $g_{2}$ in the double logarithmic approximation

J. Bartels

M. G. Ryskin

II.Institut f. Theoretische Physik, Universität Hamburg, D-20355 Hamburg, Germany

Petersburg Nuclear Physics Institute, Gatchina, S.-Petersburg 188300, Russia

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Phys. Rev. D 65, 114012 – Published 20 June, 2002

DOI: https://doi.org/10.1103/PhysRevD.65.114012

Abstract

The small- $x$ behavior of the singlet contributions to the polarized structure function $g_{2} {(x, Q}^{2})$ is calculated in the double-logarithmic approximation of perturbative QCD. The dominant contribution is due to the gluons which, in contrast with the unpolarized case, mix with the fermions also in the small- $x$ domain. We find a powerlike growth in $1 / x$ in the odd-signature parts of the amplitude with the same power as in the singlet function $g_{1} {(x, Q}^{2})$ at $x ≪ 1.$

References (24)

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[c1] G. Altarelli and G. Parisi, Nucl. Phys. B126, 297 (1977).

[c2] J. Bartels, B.I. Ermolayev, and M.G. Ryskin, Z. Phys. C 70, 273 (1996).

[c3] J. Bartels, B.I. Ermolayev, and M.G. Ryskin, Z. Phys. C 72, 627 (1996).

[c4] J. Bartels and M.G. Ryskin, Phys. Rev. D 63, 094002 (2001).

[c5] A.J.G. Hey and J.E. Mandula, Phys. Rev. D 5, 2610 (1972).

[c6] S. Wandzura and F. Wilczek, Phys. Lett. 72B, 195 (1977).

[c7] J. Bluemlein and N. Kochelev, Phys. Lett. B 381, 296 (1996); Nucl. Phys. B498, 285 (1997); ibid.J. Blumlein and A. Tkabladze, B553, 427 (1999).

[c8] G. Altarelli, B. Lampe, P. Nason, and G. Ridolfi, Phys. Lett. B 334, 187 (1994).

[c9] A. Harindranath and Wei-Min Zhang, Phys. Lett. B 408, 347 (1997).

[c10] A. Gabrieli and G. Ridolfi, Phys. Lett. B 417, 369 (1998).

[c11] A.P. Bukhvostov, E.A. Kuraev, and L.N. Lipatov, Sov. Phys. JETP 60, 22 (1984).

[c12] J. Kodaira, Y. Yasui, and T. Vematsu, Phys. Lett. B 344, 348 (1995).

[c13] A. Ali, V.M. Braun, and G. Hiller, Phys. Lett. B 266, 117 (1991).

[c14] K. Sasaki, Phys. Rev. D 58, 094007 (1998).

[c15] V.M. Braun, G.P. Korchemsky, and A.N. Manashov, Phys. Lett. B 476, 455 (2000).

[c16] V.M. Braun, G.P. Korchemsky, and A.N. Manashov, Nucl. Phys. B597, 370 (2001); ibid.B603, 69 (2001).

[c17] B. L. Ioffe, V. A. Khoze, and L. N. Lipatov, Hard Processes (North-Holland, Amsterdam, 1984).

[c18] R.L. Heimann, Nucl. Phys. B64, 429 (1973).

[c19] R. Kirschner and L.N. Lipatov, Nucl. Phys. B213, 122 (1983).

[c20] V.N. Gribov, V.G. Gorshkov, G.V. Frolov, and L.N. Lipatov, Sov. J. Nucl. Phys. 6, 95 (1967).

[c21] B.I. Ermolayev, S.I. Manaenko, and M.G. Ryskin, Z. Phys. C 69, 259 (1996).

[c22] L. N. Lipatov (private communication).

[c23] J. Bartels, L.N. Lipatov, and G.P. Vacca, Phys. Lett. B 477, 178 (2000).

[c24] H. Burkhardt and W.N. Cottingham, Ann. Phys. (N.Y.) 56, 453 (1970).

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Small- $x$ behavior of the singlet polarized structure function $g_{2}$ in the double logarithmic approximation

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References (24)

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Small-x behavior of the singlet polarized structure function g2 in the double logarithmic approximation

Abstract

References (24)

Small- $x$ behavior of the singlet polarized structure function $g_{2}$ in the double logarithmic approximation