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The 3-loop non-singlet heavy flavor contributions to the structure function \(g_1(x, Q^2)\) at large momentum transfer. (English) Zbl 1329.81362
Summary: We calculate the massive flavor non-singlet Wilson coefficient for the heavy flavor contributions to the polarized structure function \(g_1(x, Q^2)\) in the asymptotic region \(Q^2 \gg m^2\) to 3-loop order in Quantum Chromodynamics at general values of the Mellin variable \(N\) and the momentum fraction \(x\), and derive heavy flavor corrections to the Bjorken sum-rule. Numerical results are presented for the charm quark contribution. Results on the structure function \(g_2(x, Q^2)\) in the twist-2 approximation are also given.
MSC:
81V05 Strong interaction, including quantum chromodynamics
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
81T18 Feynman diagrams
Software:
Fermat; HarmonicSums
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[1] Bethke, S.; Moch, S.; Weinzierl, S., High precision fundamental constants at the TeV scale
[2] Watson, A. D., Z. Phys. C, 12, 123, (1982)
[3] Vogelsang, W., Z. Phys. C, 50, 275, (1991)
[4] Alekhin, S. I.; Blümlein, J., Phys. Lett. B, 594, 299, (2004)
[5] Buza, M.; Matiounine, Y.; Smith, J.; Migneron, R.; van Neerven, W. L., Nucl. Phys. B, 472, 611, (1996)
[6] Buza, M.; Matiounine, Y.; Smith, J.; van Neerven, W. L., Nucl. Phys. B, 485, 420, (1997)
[7] J. Blümlein, et al., in preparation.
[8] Blümlein, J.; Böttcher, H., Nucl. Phys. B, 841, 205, (2010)
[9] Bierenbaum, I.; Blümlein, J.; Klein, S., Nucl. Phys. B, 780, 40, (2007)
[10] 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, (2014)
[11] Bardin, D. Y.; Blümlein, J.; Christova, P.; Kalinovskaya, L., Nucl. Phys. B, 506, 295, (1997)
[12] Lampe, B.; Reya, E., Phys. Rep., 332, 1, (2000)
[13] Blümlein, J., Prog. Part. Nucl. Phys., 69, 28, (2013)
[14] Buza, M.; Matiounine, Y.; Smith, J.; van Neerven, W. L., Eur. Phys. J. C, 1, 301, (1998)
[15] Wandzura, S.; Wilczek, F., Phys. Lett. B, 72, 195, (1977)
[16] Bierenbaum, I.; Blümlein, J.; Klein, S., Nucl. Phys. B, 820, 417, (2009)
[17] J. Lagrange, Nouvelles recherches sur la nature et la propagation du son, Miscellanea Taurinensis, t. II, 1760-61; Oeuvres t. I, p. 263.; C.F. Gauss, Theoria attractionis corporum sphaeroidicorum ellipticorum homogeneorum methodo novo tractate, in: Commentationes societas scientiarum Gottingensis recentiores, Vol III, 1813, Werke Bd. V, pp. 5-7.; G. Green, Essay on the Mathematical Theory of Electricity and Magnetism, Nottingham, 1828 [Green Papers, pp. 1-115.
[18] Matiounine, Y.; Smith, J.; van Neerven, W. L., Phys. Rev. D, 58, 076002, (1998)
[19] von Manteuffel, A.; Studerus, C.; Studerus, C., Comput. Phys. Commun., 181, 1293, (2010)
[20] Lewis, R. H., Computer algebra system
[21] Bauer, C. W.; Frink, A.; Kreckel, R., Symb. Comput., 33, 1, (2002), cs/0004015 [cs-sc]
[22] Schneider, C., Sémin. Lothar. Comb., 56, 1, (2007), article B56b
[23] Schneider, C., Computer algebra in quantum field theory: integration, summation and special functions, (Schneider, C.; Blümlein, J., Texts and Monographs in Symbolic Computation, (2013), Springer Wien), 325, (2013)
[24] Ablinger, J.; Blümlein, J.; Klein, S.; Schneider, C.; Blümlein, J.; Hasselhuhn, A.; Schneider, C.; Schneider, C., Proc. of ACAT 2013, Nucl. Phys. Proc. Suppl., PoS RADCOR, J. Phys. Conf. Ser., 523, 012037, 1, (2014)
[25] M. Round, et al., in preparation.
[26] Ablinger, J.; Ablinger, J.; Ablinger, J.; Ablinger, J.; Blümlein, J.; Schneider, C.; Ablinger, J.; Blümlein, J.; Schneider, C., A computer algebra toolbox for harmonic sums related to particle physics, PoS LL, J. Math. Phys., J. Math. Phys., 54, 082301, (2013), J. Kepler University Linz, Diploma thesis · Zbl 1295.81071
[27] Furmanski, W.; Petronzio, R., Z. Phys. C, 11, 293, (1982), and references therein
[28] van Neerven, W. L.; Zijlstra, E. B., Phys. Lett. B, 272, 127, (1991)
[29] Zijlstra, E. B.; van Neerven, W. L.; Zijlstra, E. B.; van Neerven, W. L.; Zijlstra, E. B.; van Neerven, W. L., Nucl. Phys. B, Nucl. Phys. B, Nucl. Phys. B, 773, 105, (2007), (Erratum)
[30] Moch, S.; Vermaseren, J. A.M.; Vogt, A., Nucl. Phys. B, 813, 220, (2009)
[31] Larin, S. A.; Vermaseren, J. A.M., Phys. Lett. B, 259, 345, (1991)
[32] Baikov, P. A.; Chetyrkin, K. G.; Kühn, J. H., Phys. Rev. Lett., 104, 132004, (2010)
[33] Vermaseren, J. A.M.; Blümlein, J.; Kurth, S., Int. J. Mod. Phys. A, Phys. Rev. D, 60, 014018, (1999)
[34] Blümlein, J., Comput. Phys. Commun., 180, 2218, (2009)
[35] Blümlein, J., (Carey, A.; Ellwood, D.; Paycha, S.; Rosenberg, S., Proceedings of the Workshop Motives, Quantum Field Theory, and Pseudodifferential Operators, Clay Mathematics Institute, Boston University, 2-13 June 2008, Clay Mathematics Proceedings, vol. 12, (2010)), 167-186
[36] Blümlein, J.; Vogt, A., Phys. Rev. D, 58, 014020, (1998)
[37] Blümlein, J.; Blümlein, J.; Moch, S. O., Comput. Phys. Commun., Phys. Lett. B, 614, 53, (2005)
[38] Remiddi, E.; Vermaseren, J. A.M., Int. J. Mod. Phys. A, 15, 725, (2000)
[39] Blümlein, J., Comput. Phys. Commun., 159, 19, (2004)
[40] Blümlein, J.; Kochelev, N., Nucl. Phys. B, 498, 285, (1997)
[41] Jackson, J. D.; Ross, G. G.; Roberts, R. G., Phys. Lett. B, 226, 159, (1989)
[42] Roberts, R. G.; Ross, G. G., Phys. Lett. B, 373, 235, (1996)
[43] Blümlein, J.; Kochelev, N., Phys. Lett. B, 381, 296, (1996)
[44] Blümlein, J.; Ravindran, V.; van Neerven, W. L., Phys. Rev. D, 68, 114004, (2003)
[45] Piccione, A.; Ridolfi, G., Nucl. Phys. B, 513, 301, (1998)
[46] Blümlein, J.; Tkabladze, A., Nucl. Phys. B, 553, 427, (1999)
[47] Blümlein, J.; Robaschik, D., Nucl. Phys. B, 581, 449, (2000)
[48] Blümlein, J.; Robaschik, D.; Geyer, B., Eur. Phys. J. C, 61, 279, (2009)
[49] Blümlein, J.; Robaschik, D., Phys. Rev. D, 65, 096002, (2002)
[50] Kirschner, R.; Lipatov, L. N.; Blümlein, J.; Vogt, A.; Blümlein, J.; Vogt, A., Nucl. Phys. B, Phys. Lett. B, Acta Phys. Pol. B, 27, 1309, (1996)
[51] Kiyo, Y.; Kodaira, J.; Tochimura, H., Z. Phys. C, 74, 631, (1997)
[52] Moch, S.; Vermaseren, J. A.M.; Vogt, A., Nucl. Phys. B, 889, 351, (2014)
[53] Alekhin, S.; Blümlein, J.; Moch, S., Phys. Rev. D, 89, 5, 054028, (2014)
[54] Alekhin, S.; Blümlein, J.; Daum, K.; Lipka, K.; Moch, S., Phys. Lett. B, 720, 172, (2013)
[55] Boer, D.; Diehl, M.; Milner, R.; Venugopalan, R.; Vogelsang, W.; Kaplan, D.; Montgomery, H.; Vigdor, S.; Accardi, A.; Albacete, J. L.; Anselmino, M.; Armesto, N.; Aschenauer, E. C.; Bacchetta, A.; Boer, D.; Brooks, W.
[56] Blümlein, J.; Böttcher, H.; Guffanti, A., Nucl. Phys. B, 774, 182, (2007)
[57] Blümlein, J.; Riemersma, S.; Botje, M.; Pascaud, C.; Zomer, F.; van Neerven, W. L.; Vogt, A.; Blümlein, J.; Riemersma, S.; van Neerven, W. L.; Vogt, A., (Proceedings Future Physics at HERA, Hamburg, (1995/96)), Nucl. Phys. Proc. Suppl., 51C, 97, (1996)
[58] Bjorken, J. D., Phys. Rev. D, 1, 1376, (1970)
[59] Mund, D.; Märkisch, B.; Deissenroth, M.; Krempel, J.; Schumann, M.; Abele, H.; Petoukhov, A.; Soldner, T., Phys. Rev. Lett., 110, 172502, (2013)
[60] Kodaira, J.; Matsuda, S.; Muta, T.; Sasaki, K.; Uematsu, T., Phys. Rev. D, 20, 627, (1979)
[61] Gorishnii, S. G.; Larin, S. A., Phys. Lett. B, 172, 109, (1986)
[62] Blümlein, J.; van Neerven, W. L., Phys. Lett. B, 450, 417, (1999)
[63] van Neerven, W. L., (Blin, A. H.; Hiller, B.; Ruivo, M. C.; de Sousa, C. A.; van Beveren, E., Proceedings of the Workshop Hadron Physics: Effective Theories of Low-Energy QCD, Coimbra, Portugal, 1999, AIP Conf. Proc., vol. 508, (2000)), 162
[64] J. Blümlein, M. Klein, T. Naumann, T. Riemann, Structure Functions, Quark Distributions and \(\operatorname{\Lambda}_{\mathit{QCD}}\) at Hera, PHE-88-01.
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