×

The iterated structure of the all-order result for the two-loop sunrise integral. (English) Zbl 1333.81283

Summary: We present a method to compute the Laurent expansion of the two-loop sunrise integral with equal non-zero masses to arbitrary order in the dimensional regularisation \(\epsilon\). This is done by introducing a class of functions (generalisations of multiple polylogarithms to include the elliptic case) and by showing that all integrations can be carried out within this class of functions.{
©2016 American Institute of Physics}

MSC:

81T18 Feynman diagrams
30B30 Boundary behavior of power series in one complex variable; over-convergence
11G55 Polylogarithms and relations with \(K\)-theory

Software:

Nestedsums
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Hooft, G. ’t; Veltman, M. J. G., Nucl. Phys., B44, 189 (1972) · doi:10.1016/0550-3213(72)90279-9
[2] Bollini, C. G.; Giambiagi, J. J., Nuovo Cim., B12, 20 (1972)
[3] Cicuta, G. M.; Montaldi, E., Lett. Nuovo Cimento, 4, 329 (1972) · doi:10.1007/BF02756527
[4] Goncharov, A. B., Math. Res. Lett., 5, 497 (1998) · Zbl 0961.11040 · doi:10.4310/MRL.1998.v5.n4.a7
[5] Goncharov, A. B., e-print (2001).
[6] Borwein, J. M.; Bradley, D. M.; Broadhurst, D. J.; Lisonek, P., Trans. Am. Math. Soc., 353, 3, 907 (2001) · Zbl 1002.11093 · doi:10.1090/S0002-9947-00-02616-7
[7] Vollinga, J.; Weinzierl, S., Comput. Phys. Commun., 167, 177 (2005) · Zbl 1196.65045 · doi:10.1016/j.cpc.2004.12.009
[8] Moch, S.; Uwer, P.; Weinzierl, S., J. Math. Phys., 43, 3363 (2002) · Zbl 1060.33007 · doi:10.1063/1.1471366
[9] Weinzierl, S., Comput. Phys. Commun., 145, 357 (2002) · Zbl 1001.65025 · doi:10.1016/S0010-4655(02)00261-8
[10] Weinzierl, S., J. Math. Phys., 45, 2656 (2004) · Zbl 1071.33018 · doi:10.1063/1.1758319
[11] Moch, S.; Uwer, P., Comput. Phys. Commun., 174, 759 (2006) · Zbl 1196.68332 · doi:10.1016/j.cpc.2005.12.014
[12] Bierenbaum, I.; Weinzierl, S., Eur. Phys. J. C, 32, 67 (2003) · Zbl 1099.81534 · doi:10.1140/epjc/s2003-01389-7
[13] Brown, F., Commun. Math. Phys., 287, 925 (2008) · Zbl 1196.81130 · doi:10.1007/s00220-009-0740-5
[14] Panzer, E., Comput. Phys. Commun., 188, 148 (2014) · Zbl 1344.81024 · doi:10.1016/j.cpc.2014.10.019
[15] Bogner, C., e-print (2015).
[16] Kotikov, A. V., Phys. Lett. B, 254, 158 (1991) · doi:10.1016/0370-2693(91)90413-K
[17] Kotikov, A. V., Phys. Lett. B, 267, 123 (1991) · doi:10.1016/0370-2693(91)90536-Y
[18] Remiddi, E., Nuovo Cimento A, 110, 1435 (1997)
[19] Gehrmann, T.; Remiddi, E., Nucl. Phys. B, 580, 485 (2000) · Zbl 1071.81089 · doi:10.1016/S0550-3213(00)00223-6
[20] Argeri, M.; Mastrolia, P., Int. J. Mod. Phys. A, 22, 4375 (2007) · Zbl 1141.81325 · doi:10.1142/S0217751X07037147
[21] Müller-Stach, S.; Weinzierl, S.; Zayadeh, R., Commun. Math. Phys., 326, 237 (2014) · Zbl 1285.81029 · doi:10.1007/s00220-013-1838-3
[22] Henn, J. M., Phys. Rev. Lett., 110, 251601 (2013) · doi:10.1103/PhysRevLett.110.251601
[23] Brown, F.; Acad, C. R., Sci. Paris, 342, 949 (2006) · Zbl 1105.11019 · doi:10.1016/j.crma.2006.04.016
[24] Bogner, C.; Brown, F., Commun. Num. Theor. Phys., 09, 189 (2015) · Zbl 1316.81040 · doi:10.4310/CNTP.2015.v9.n1.a3
[25] Broadhurst, D. J.; Fleischer, J.; Tarasov, O., Z. Phys. C, 60, 287 (1993)
[26] Berends, F. A.; Buza, M.; Böhm, M.; Scharf, R., Z. Phys. C, 63, 227 (1994) · doi:10.1007/bf01411014
[27] Bauberger, S.; Böhm, M.; Weiglein, G.; Berends, F. A.; Buza, M., Nucl. Phys. B, Proc. Suppl., 37, 95 (1994) · doi:10.1016/0920-5632(94)90665-3
[28] Bauberger, S.; Berends, F. A.; Böhm, M.; Buza, M., Nucl. Phys. B, 434, 383 (1995) · doi:10.1016/0550-3213(94)00475-T
[29] Bauberger, S.; Böhm, M., Nucl. Phys. B, 445, 25 (1995) · doi:10.1016/0550-3213(95)00199-3
[30] Caffo, M.; Czyz, H.; Laporta, S.; Remiddi, E., Nuovo Cimento A, 111, 365 (1998)
[31] Laporta, S.; Remiddi, E., Nucl. Phys. B, 704, 349 (2005) · Zbl 1119.81356 · doi:10.1016/j.nuclphysb.2004.10.044
[32] Groote, S.; Körner, J. G.; Pivovarov, A. A., Ann. Phys., 322, 2374 (2007) · Zbl 1148.81020 · doi:10.1016/j.aop.2006.11.001
[33] Groote, S.; Körner, J.; Pivovarov, A., Eur. Phys. J. C, 72, 2085 (2012) · doi:10.1140/epjc/s10052-012-2085-z
[34] Bailey, D. H.; Borwein, J. M.; Broadhurst, D.; Glasser, M. L., J. Phys. A, 41, 205203 (2008)
[35] Müller-Stach, S.; Weinzierl, S.; Zayadeh, R., Commun. Num. Theor. Phys., 6, 203 (2012) · Zbl 1275.81069 · doi:10.4310/CNTP.2012.v6.n1.a5
[36] Adams, L.; Bogner, C.; Weinzierl, S., J. Math. Phys., 54, 052303 (2013) · Zbl 1282.81193 · doi:10.1063/1.4804996
[37] Bloch, S.; Vanhove, P., J. Num. Theory, 148, 328 (2015) · Zbl 1319.81044 · doi:10.1016/j.jnt.2014.09.032
[38] Remiddi, E.; Tancredi, L., Nucl. Phys. B, 880, 343 (2014) · Zbl 1284.81139 · doi:10.1016/j.nuclphysb.2014.01.009
[39] Adams, L.; Bogner, C.; Weinzierl, S., J. Math. Phys., 55, 102301 (2014) · Zbl 1298.81204 · doi:10.1063/1.4896563
[40] Adams, L.; Bogner, C.; Weinzierl, S., J. Math. Phys., 56, 072303 (2015) · Zbl 1320.81059 · doi:10.1063/1.4926985
[41] Caffo, M.; Czyz, H.; Remiddi, E., Nucl. Phys. B, 634, 309 (2002) · Zbl 0995.81079 · doi:10.1016/S0550-3213(02)00315-2
[42] Pozzorini, S.; Remiddi, E., Comput. Phys. Commun., 175, 381 (2006) · Zbl 1196.81075 · doi:10.1016/j.cpc.2006.05.005
[43] Caffo, M.; Czyz, H.; Gunia, M.; Remiddi, E., Comput. Phys. Commun., 180, 427 (2009) · Zbl 1198.81011 · doi:10.1016/j.cpc.2008.10.011
[44] Tarasov, O. V., Phys. Rev. D, 54, 6479 (1996)
[45] Tarasov, O. V., Nucl. Phys. B, 502, 455 (1997) · doi:10.1016/S0550-3213(97)00376-3
[46] Bern, Z.; Dixon, L. J.; Kosower, D. A., Nucl. Phys. B, 412, 751 (1994) · Zbl 1007.81512 · doi:10.1016/0550-3213(94)90398-0
[47] Lu, H. J. and Perez, C. A., Report SLAC-PUB-5809, 1992.
[48] Bogner, C.; Weinzierl, S., Comput. Phys. Commun., 178, 596 (2008) · Zbl 1196.81010 · doi:10.1016/j.cpc.2007.11.012
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.