×

zbMATH — the first resource for mathematics

The polarized two-loop massive pure singlet Wilson coefficient for deep-inelastic scattering. (English) Zbl 1435.81226
Summary: We calculate the polarized massive two-loop pure singlet Wilson coefficient contributing to the structure functions \(g_1(x, Q^2)\) analytically in the whole kinematic region. The Wilson coefficient contains Kummer-elliptic integrals. We derive the representation in the asymptotic region \(Q^2 \gg m^2\), retaining power corrections, and in the threshold region. The massless Wilson coefficient is recalculated. The corresponding twist-2 corrections to the structure function \(g_2(x, Q^2)\) are obtained by the Wandzura-Wilczek relation. Numerical results are presented.
MSC:
81U05 \(2\)-body potential quantum scattering theory
81R05 Finite-dimensional groups and algebras motivated by physics and their representations
81Q30 Feynman integrals and graphs; applications of algebraic topology and algebraic geometry
33E05 Elliptic functions and integrals
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Blümlein, J.; Schneider, C., Int. J. Mod. Phys. A, 33, 17, Article 1830015 pp. (2018)
[2] Boer, D., Gluons and the quark sea at high energies: distributions, polarization, tomography
[3] Buza, M.; Matiounine, Y.; Smith, J.; van Neerven, W. L., Nucl. Phys. B, 485, 420-456 (1997)
[4] I. Bierenbaum, J. Blümlein, S. Klein, PoS (ACAT2007) 070.
[5] I. Bierenbaum, J. Blümlein, S. Klein, K. Schönwald, The \(O(\alpha_s^2)\) Polarized Heavy Flavor Production in Deep-Inelastic Scattering at \(Q^2 \gg m^2\), DESY 15-004, DO-TH 15/01.
[6] Eynck, T. O.; Moch, S. O., Phys. Lett. B, 495, 87-97 (2000)
[7] Blümlein, J.; Falcioni, G.; De Freitas, A., Nucl. Phys. B, 910, 568-617 (2016)
[8] Blümlein, J.; van Neerven, W. L., Phys. Lett. B, 450, 417-426 (1999)
[9] Hekhorn, F.; Stratmann, M., Phys. Rev. D, 98, 1, Article 014018 pp. (2018)
[10] Behring, A.; Blümlein, J.; De Freitas, A.; von Manteuffel, A.; Schneider, C., Nucl. Phys. B, 897, 612-644 (2015)
[11] Ablinger, J.; Behring, A.; Blümlein, J.; De Freitas, A.; Hasselhuhn, A.; von Manteuffel, A.; Round, M.; Schneider, C.; Wißbrock, F., Nucl. Phys. B, 886, 733-823 (2014)
[12] Blümlein, J.; De Freitas, A.; Raab, C. G.; Schönwald, K., Nucl. Phys. B, 945, Article 114659 pp. (2019)
[13] Zijlstra, E. B.; van Neerven, W. L., Nucl. Phys. B. Nucl. Phys. B, Nucl. Phys. B. Nucl. Phys. B. Nucl. Phys. B, Nucl. Phys. B, Nucl. Phys. B. Nucl. Phys. B. Nucl. Phys. B, Nucl. Phys. B. Nucl. Phys. B. Nucl. Phys. B, Nucl. Phys. B, Nucl. Phys. B, Nucl. Phys. B, 773, 105-106 (2007), Erratum:
[14] Vogt, A.; Moch, S.; Rogal, M.; Vermaseren, J. A.M., Nucl. Phys. Proc. Suppl., 183, 155-161 (2008)
[15] Larin, S. A., Phys. Lett. B, 303, 113-118 (1993)
[16] ’t Hooft, G.; Veltman, M. J.G., Nucl. Phys. B, 44, 189-213 (1972); Akyeampong, D. A.; Delbourgo, R., Nuovo Cimento A, 17, 578-586 (1973); Akyeampong, D. A.; Delbourgo, R., Nuovo Cimento A, 18, 94-104 (1973); Akyeampong, D. A.; Delbourgo, R., Nuovo Cimento A, 19, 219-224 (1974); Breitenlohner, P.; Maison, D., Commun. Math. Phys., 52, 55-75 (1977)
[17] Matiounine, Y.; Smith, J.; van Neerven, W. L., Phys. Rev. D, 58, Article 076002 pp. (1998)
[18] Moch, S.; Vermaseren, J. A.M.; Vogt, A., Nucl. Phys. B, 889, 351-400 (2014)
[19] Wandzura, S.; Wilczek, F., Phys. Lett. B, 72, 195-198 (1977)
[20] Jackson, J. D.; Ross, G. G.; Roberts, R. G., Phys. Lett. B, 226, 159-166 (1989); Roberts, R. G.; Ross, G. G., Phys. Lett. B, 373, 235-245 (1996)
[21] Blümlein, J.; Kochelev, N., Nucl. Phys. B, 498, 285-309 (1997); Blümlein, J.; Kochelev, N., Phys. Lett. B, 381, 296-304 (1996)
[22] Blümlein, J.; Ravindran, V.; van Neerven, W. L., Phys. Rev. D, 68, Article 114004 pp. (2003)
[23] Blümlein, J.; Robaschik, D., Phys. Rev. D, 65, Article 096002 pp. (2002)
[24] Blümlein, J.; Robaschik, D., Nucl. Phys. B, 581, 449-473 (2000)
[25] Blümlein, J.; Tkabladze, A., Nucl. Phys. B, 553, 427-464 (1999)
[26] Lampe, B.; Reya, E., Phys. Rep., 332, 1-163 (2000)
[27] Blümlein, J.; Geyer, B.; Robaschik, D., Nucl. Phys. B, 755, 112-136 (2006); Blümlein, J.; Geyer, B.; Robaschik, D., Eur. Phys. J. C, 61, 279-298 (2009)
[28] Politzer, H. D., Nucl. Phys. B, 129, 301-318 (1977); Amati, D.; Petronzio, R.; Veneziano, G., Nucl. Phys. B, 140, 54-72 (1978); Amati, D.; Petronzio, R.; Veneziano, G., Nucl. Phys. B, 146, 29-49 (1978); Libby, S. B.; Sterman, G. F., Phys. Rev. D, 18, 4737-4745 (1978); Mueller, A. H., Phys. Rev. D, 18, 3705-3727 (1978); Collins, J. C.; Sterman, G. F., Nucl. Phys. B, 185, 172-188 (1981); Collins, J. C.; Soper, D. E.; Sterman, G. F., Nucl. Phys. B, 261, 104-142 (1985); Bodwin, G. T., Phys. Rev. D. Phys. Rev. D, Phys. Rev. D, 34, 3932-2642 (1986), Erratum:; Collins, J. C.; Soper, D. E.; Sterman, G. F., (Mueller, A. H., Adv. Ser. Direct. High Energy Phys., vol. 5 (1989), World Scientific: World Scientific Singapore), 1-91 (1989)
[29] Zijlstra, E. B.; van Neerven, W. L., Nucl. Phys. B, 383, 525-574 (1992)
[30] Sasaki, K., Prog. Theor. Phys., 54, 1816-1827 (1975)
[31] Ahmed, M. A.; Ross, G. G., Nucl. Phys. B, 111, 441-460 (1976)
[32] Altarelli, G.; Parisi, G., Nucl. Phys. B, 126, 298-318 (1977)
[33] Mertig, R.; van Neerven, W. L., Z. Phys. C, 70, 637-654 (1996)
[34] Vogelsang, W., Phys. Rev. D, 54, 2023-2029 (1996); Vogelsang, W., Nucl. Phys. B, 475, 47-72 (1996)
[35] Remiddi, E.; Vermaseren, J. A.M., Int. J. Mod. Phys. A, 15, 725-754 (2000)
[36] Vermaseren, J. A.M., Int. J. Mod. Phys. A, 14, 2037-2976 (1999)
[37] Blümlein, J.; Kurth, S., Phys. Rev. D, 60, Article 014018 pp. (1999)
[38] Watson, A. D., Z. Phys. C, 12, 123-125 (1982)
[39] Glück, M.; Reya, E.; Vogelsang, W., Nucl. Phys. B, 351, 579-592 (1991)
[40] Vogelsang, W., Z. Phys. C, 50, 275-284 (1991)
[41] Ablinger, J.; Blümlein, J.; Raab, C. G.; Schneider, C., J. Math. Phys., 55, Article 112301 pp. (2014)
[42] C.G. Raab, unpublished.
[43] Koutschan, C., HolonomicFunctions (User’s Guide) (Jan. 2010), University of Linz: University of Linz Austria, Technical report no. 10-01 in RISC Report Series
[44] C.G. Raab, G. Regensburger, The fundamental theorem of calculus in differential rings, in preparation.
[45] C.G. Raab, On the arithmetic of d’Alembertian functions, in preparation.
[46] Guo, Li; Regensburger, G.; Rosenkranz, M., J. Pure Appl. Algebra, 218, 456-473 (2014)
[47] Buza, M.; Matiounine, Y.; Smith, J.; Migneron, R.; van Neerven, W. L., Nucl. Phys. B, 472, 611-658 (1996)
[48] Bierenbaum, I.; Blümlein, J.; Klein, S., Nucl. Phys. B, 780, 40-75 (2007)
[49] Bierenbaum, I.; Blümlein, J.; Klein, S., Nucl. Phys. B, 820, 417-482 (2009)
[50] Blümlein, J.; Böttcher, H., Nucl. Phys. B, 841, 205-230 (2010)
[51] Alekhin, S.; Blümlein, J.; Moch, S.; Placakyte, R., Phys. Rev. D, 96, 1, Article 014011 pp. (2017)
[52] Devoto, A.; Duke, D. W., Riv. Nuovo Cimento, 7, 6, 1-39 (1984); Lewin, L., Dilogarithms and Associated Functions (1958), Macdonald: Macdonald London; Lewin, L., Polylogarithms and Associated Functions (1981), North Holland: North Holland New York
[53] W.L. van Neerven, -code , unpublished.
[54] Collins, J. C.; Vermaseren, J. A.M., Axodraw version 2 · Zbl 1114.68598
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.