×

zbMATH — the first resource for mathematics

The transition matrix element \(A_{gq}(N)\) of the variable flavor number scheme at \(O({\alpha}_s^3)\). (English) Zbl 1285.81065
Summary: We calculate the massive unpolarized operator matrix element \(A_{gq}^(3)(N)\) to 3-loop order in Quantum Chromodynamics at general values of the Mellin variable N. This is the first complete transition function needed in the variable flavor number scheme obtained at \(O({\alpha}_s^3)\). A first independent recalculation is performed for the contributions \(\propto N_F\) of the 3-loop anomalous dimension \({\gamma}_{gq}^{(2)}(N\)).

MSC:
81V05 Strong interaction, including quantum chromodynamics
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
81V35 Nuclear physics
Software:
Axodraw; Fermat; MATAD
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Buza, M.; Matiounine, Y.; Smith, J.; van Neerven, W. L., Eur. Phys. J. C, 1, 301, (1998)
[2] Bierenbaum, I.; Blümlein, J.; Klein, S., Nucl. Phys. B, 820, 417, (2009)
[3] Bethke, S., Proceedings of the workshop on precision measurements of \(\alpha_s\), (2011)
[4] Buza, M.; Matiounine, Y.; Smith, J.; Migneron, R.; van Neerven, W. L., Nucl. Phys. B, 472, 611, (1996)
[5] Bierenbaum, I.; Blümlein, J.; Klein, S., Nucl. Phys. B, 780, 40, (2007)
[6] Bierenbaum, I.; Blümlein, J.; Klein, S., Phys. Lett. B, 672, 401, (2009)
[7] Blümlein, J.; Klein, S.; Tödtli, B., Phys. Rev. D, 80, 094010, (2009)
[8] Ablinger, J.; Blümlein, J.; Klein, S.; Schneider, C.; Wissbrock, F., Nucl. Phys. B, 844, 26, (2011)
[9] Blümlein, J.; Hasselhuhn, A.; Klein, S.; Schneider, C., Nucl. Phys. B, 866, 196, (2013)
[10] Bierenbaum, I.; Blümlein, J.; Klein, S.; Schneider, C., Nucl. Phys. B, 803, 1, (2008)
[11] Nogueira, P., J. Comput. Phys., 105, 279, (1993)
[12] Tentyukov, M.; Vermaseren, J. A.M.; Vermaseren, J. A.M., Comput. Phys. Commun., 181, 1419, (2010)
[13] Ablinger, J.; Blümlein, J.; Hasselhuhn, A.; Klein, S.; Schneider, C.; Wissbrock, F., Nucl. Phys. B, 864, 52, (2012)
[14] J. Lagrange, Oeuvres t. I, p. 263.; G. Green, Essay on the Mathematical Theory of Electricity and Magnetism, Nottingham, 1828 [Green Papers, pp. 1-115].
[15] von Manteuffel, A.; Studerus, C.; Studerus, C., Comput. Phys. Commun., 181, 1293, (2010)
[16] Lewis, R. H., Computer algebra system Fermat
[17] Bauer, C.; Frinck, A.; Kreckel, R., J. Symb. Comput., 33, 1, (2002)
[18] Bailey, W. N., Generalized hypergeometric series, (1935), Cambridge University Press Cambridge · JFM 61.0406.01
[19] Slater, L. J., Generalized hypergeometric functions, (1966), Cambridge University Press Cambridge · Zbl 0135.28101
[20] Appell, P.; Kampé de Fériet, J.; Appell, P.; Kampé de Fériet, J.; Exton, H.; Exton, H.; Srivastava, H. M.; Karlsson, P. W., Multiple Gaussian hypergeometric series, (1985), Ellis Horwood Chichester
[21] Hamberg, R., Second order gluonic contributions to physical quantities, (1991), Univ. of Leiden, PhD thesis
[22] Barnes, E. W.; Barnes, E. W.; Mellin, H., Proc. Lond. Math. Soc. (2), Q. J. Math., Math. Ann., 68, 305, (1910)
[23] Czakon, M., Comput. Phys. Commun., 175, 559, (2006)
[24] Smirnov, A. V.; Smirnov, V. A., Eur. Phys. J. C, 62, 445, (2009)
[25] Karr, M., J. ACM, 28, (1981), 1981, p. 305
[26] Schneider, C., Symbolic summation in difference fields, (2001), PhD thesis RISC, Johannes Kepler University, Linz technical report 01-17
[27] Schneider, C., J. Differ. Equ. Appl., 11, 799, (2005)
[28] Schneider, C., J. Algebra Appl., 6, 415, (2007)
[29] Schneider, C., J. Symb. Comput., 43, 611, (2008)
[30] Schneider, C., Appl. Algebra Eng. Commun. Comput., 21, 1, (2010)
[31] Schneider, C., Motives, quantum field theory, and pseudodifferential operators, (Carey, A.; Ellwood, D.; Paycha, S.; Rosenberg, S., Clay Mathematics Proceedings, vol. 12, (2010), Amer. Math. Soc.), 285
[32] Schneider, C., Ann. Comb., 14, (2010)
[33] Schneider, C., (Guitierrez, J.; Schicho, J.; Weimann, M., Lecture Notes in Computer Science, (2013)), in press
[34] Schneider, C., Sémin. Lothar. Comb., 56, B56b, (2007)
[35] 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
[36] Ablinger, J.; Ablinger, J.; Blümlein, J.; Schneider, C., J. Math. Phys., 54, 082301, (2013)
[37] Ablinger, J.
[38] Ablinger, J.; Blümlein, J.; Klein, S.; Schneider, C.; Blümlein, J.; Hasselhuhn, A.; Schneider, C.; Schneider, C., (Proc. of ACAT 2013, (2013)), RADCOR 2011, 32, (2011), in press
[39] M. Round, et al., in preparation.
[40] Apagodu, M.; Zeilberger, D., Adv. Appl. Math., 37, 139, (2006), (Special Regev issue)
[41] Steinhauser, M., Comput. Phys. Commun., 134, 335, (2001)
[42] Blümlein, J.; Broadhurst, D. J.; Vermaseren, J. A.M., Comput. Phys. Commun., 181, 582, (2010)
[43] Vermaseren, J. A.M.; Blümlein, J.; Kurth, S., Int. J. Mod. Phys. A, Phys. Rev. D, 60, 014018, (1999)
[44] Abbott, L. F.; Rebhan, A.; Jegerlehner, F.; Tarasov, O. V., Nucl. Phys. B, Z. Phys. C, Nucl. Phys. B, 549, 481, (1999)
[45] Blümlein, J., Comput. Phys. Commun., 159, 19, (2004)
[46] Vogt, A.; Moch, S.; Vermaseren, J. A.M., Nucl. Phys. B, 691, 129, (2004)
[47] Larin, S. A.; Nogueira, P.; van Ritbergen, T.; Vermaseren, J. A.M.; Retey, A.; Vermaseren, J. A.M., Nucl. Phys. B, Nucl. Phys. B, 604, 281, (2001)
[48] Furmanski, W.; Petronzio, R.; Floratos, E. G.; Kounnas, C.; Lacaze, R.; Floratos, E. G.; Kounnas, C.; Lacaze, R.; Gonzalez-Arroyo, A.; Lopez, C.; Moch, S.; Vermaseren, J. A.M., Phys. Lett. B, Nucl. Phys. B, Phys. Lett. B, Nucl. Phys. B, Nucl. Phys. B, 573, 853, (2000)
[49] Blümlein, J., Comput. Phys. Commun., 180, 2218, (2009)
[50] Blümlein, J., XXI International Workshop on Deep-Inelastic Scattering and Related Subjects, DIS2013 Marseilles, PoS, DIS 2013, 301, (2013)
[51] Gross, D. J.; Wilczek, F.; Fadin, V. S.; Kuraev, E. A.; Lipatov, L. N., Phys. Rev. D, Phys. Lett. B, 60, 50, (1975)
[52] Kirschner, R.; Lipatov, L. N., Nucl. Phys. B, 213, 122, (1983)
[53] Blümlein, J.; Vogt, A., Phys. Lett. B, 370, 149, (1996)
[54] Blümlein, J.; van Neerven, W. L., Phys. Lett. B, 450, 412, (1999)
[55] Blümlein, J.; Vogt, A., Phys. Lett. B, 386, 350, (1996)
[56] Blümlein, J.; Vogt, A., Phys. Rev. D, 58, 014020, (1998)
[57] Blümlein, J., Comput. Phys. Commun., 133, 76, (2000)
[58] Blümlein, J.; Moch, S.-O., Phys. Lett. B, 614, 53, (2005)
[59] Blümlein, J., (Carey, A.; Ellwood, D.; Paycha, S.; Rosenberg, S., Proceedings of the Workshop “Motives, Quantum Field Theory, and Pseudodifferential Operators”, held at the Clay Mathematics Institute, Boston University, June 2-13, 2008, Clay Mathematics Proceedings, vol. 12, (2010)), 167
[60] Remiddi, E.; Vermaseren, J. A.M., Int. J. Mod. Phys. A, 15, 725, (2000)
[61] Gehrmann, T.; Remiddi, E.; Vollinga, J.; Weinzierl, S., Comput. Phys. Commun., Comput. Phys. Commun., 167, 177, (2005)
[62] Gray, N.; Broadhurst, D. J.; Grafe, W.; Schilcher, K.; Chetyrkin, K. G.; Steinhauser, M.; Melnikov, K.; Ritbergen, T.v.; Melnikov, K.; Ritbergen, T.v., Z. Phys. C, Nucl. Phys. B, Phys. Lett. B, Nucl. Phys. B, 591, 515, (2000)
[63] Klein, S.
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.