User menu

Elliptic polylogarithms and iterated integrals on elliptic curves I: general formalism

  • Open access
  • PDF
  • 702.23 K
  1. Goncharov A.B., Geometry of Configurations, Polylogarithms, and Motivic Cohomology, 10.1006/aima.1995.1045
  2. REMIDDI E., VERMASEREN J. A. M., HARMONIC POLYLOGARITHMS, 10.1142/s0217751x00000367
  3. A.B. Goncharov, Multiple polylogarithms and mixed Tate motives, math/0103059 [ INSPIRE ].
  4. Vollinga Jens, Weinzierl Stefan, Numerical evaluation of multiple polylogarithms, 10.1016/j.cpc.2004.12.009
  5. N. Nielsen, Der Eulersche Dilogarithmus und seine Verallgemeinerungen, Nova Acta Leopoldina (Halle) 90 (1909) 123.
  6. Kummer E.E., Ueber die Transcendenten, welche aus wiederholten Integrationen rationaler Formeln entstehen., 10.1515/crll.1840.21.74
  7. Kummer E.E., Ueber die Transcendenten, welche aus wiederholten Integrationen rationaler Formeln entstehen. (Fortsetzung)., 10.1515/crll.1840.21.193
  8. Kummer E.E., Ueber die Transcendenten, welche aus wiederholten Integrationen rationaler Formeln entstehen. (Fortsetzung)., 10.1515/crll.1840.21.328
  9. Goncharov A. B., Spradlin M., Vergu C., Volovich A., Classical Polylogarithms for Amplitudes and Wilson Loops, 10.1103/physrevlett.105.151605
  10. Ablinger Jakob, Blümlein Johannes, Schneider Carsten, Harmonic sums and polylogarithms generated by cyclotomic polynomials, 10.1063/1.3629472
  11. Duhr Claude, Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes, 10.1007/jhep08(2012)043
  12. Aglietti U., Bonciani R., Grassi L., Remiddi E., The two loop crossed ladder vertex diagram with two massive exchanges, 10.1016/j.nuclphysb.2007.07.019
  13. Caron-Huot Simon, Larsen Kasper J., Uniqueness of two-loop master contours, 10.1007/jhep10(2012)026
  14. Bloch Spencer, Kerr Matt, Vanhove Pierre, Local mirror symmetry and the sunset Feynman integral, 10.4310/atmp.2017.v21.n6.a1
  15. Remiddi Ettore, Tancredi Lorenzo, Schouten identities for Feynman graph amplitudes; The Master Integrals for the two-loop massive sunrise graph, 10.1016/j.nuclphysb.2014.01.009
  16. Laporta S., Remiddi E., Analytic treatment of the two loop equal mass sunrise graph, 10.1016/j.nuclphysb.2004.10.044
  17. Bloch Spencer, Vanhove Pierre, The elliptic dilogarithm for the sunset graph, 10.1016/j.jnt.2014.09.032
  18. L. Adams, C. Bogner and S. Weinzierl, The two-loop sunrise graph with arbitrary masses, J. Math. Phys. 54 (2013) 052303 [ arXiv:1302.7004 ] [ INSPIRE ].
  19. Adams Luise, Bogner Christian, Weinzierl Stefan, The two-loop sunrise graph in two space-time dimensions with arbitrary masses in terms of elliptic dilogarithms, 10.1063/1.4896563
  20. Adams Luise, Bogner Christian, Weinzierl Stefan, The two-loop sunrise integral around four space-time dimensions and generalisations of the Clausen and Glaisher functions towards the elliptic case, 10.1063/1.4926985
  21. L. Adams, C. Bogner and S. Weinzierl, The iterated structure of the all-order result for the two-loop sunrise integral, J. Math. Phys. 57 (2016) 032304 [ arXiv:1512.05630 ] [ INSPIRE ].
  22. Remiddi Ettore, Tancredi Lorenzo, Differential equations and dispersion relations for Feynman amplitudes. The two-loop massive sunrise and the kite integral, 10.1016/j.nuclphysb.2016.04.013
  23. Adams Luise, Bogner Christian, Schweitzer Armin, Weinzierl Stefan, The kite integral to all orders in terms of elliptic polylogarithms, 10.1063/1.4969060
  24. Bonciani Roberto, Del Duca Vittorio, Frellesvig Hjalte, Henn Johannes M., Moriello Francesco, Smirnov Vladimir A., Two-loop planar master integrals for Higgs → 3 partons with full heavy-quark mass dependence, 10.1007/jhep12(2016)096
  25. von Manteuffel Andreas, Tancredi Lorenzo, A non-planar two-loop three-point function beyond multiple polylogarithms, 10.1007/jhep06(2017)127
  26. Primo Amedeo, Tancredi Lorenzo, Maximal cuts and differential equations for Feynman integrals. An application to the three-loop massive banana graph, 10.1016/j.nuclphysb.2017.05.018
  27. J. Ablinger et al., Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams, arXiv:1706.01299 [ INSPIRE ].
  28. Chen Long-Bin, Liang Yi, Qiao Cong-Feng, NNLO QCD corrections to γ + ηc(ηb) exclusive production in electron-positron collision, 10.1007/jhep01(2018)091
  29. Bourjaily Jacob L., McLeod Andrew J., Spradlin Marcus, von Hippel Matt, Wilhelm Matthias, Elliptic Double-Box Integrals: Massless Scattering Amplitudes beyond Polylogarithms, 10.1103/physrevlett.120.121603
  30. L.-B. Chen, J. Jiang and C.-F. Qiao, Two-loop integrals for CP-even heavy quarkonium production and decays: elliptic sectors, arXiv:1712.03516 [ INSPIRE ].
  31. Broedel Johannes, Mafra Carlos R., Matthes Nils, Schlotterer Oliver, Elliptic multiple zeta values and one-loop superstring amplitudes, 10.1007/jhep07(2015)112
  32. Sabry Afaf, Fourth order spectral functions for the electron propagator, 10.1016/0029-5582(62)90535-7
  33. D.J. Broadhurst, The master two loop diagram with masses, Z. Phys. C 47 (1990) 115 [ INSPIRE ].
  34. Bauberger S., Berends F.A., Böhm M., Buza M., Analytical and numerical methods for massive two-loop self-energy diagrams, 10.1016/0550-3213(94)00475-t
  35. Bauberger S., Böhm M., Simple one-dimensional integral representations for two-loop self-energies: the master diagram, 10.1016/0550-3213(95)00199-3
  36. Kniehl B.A., Kotikov A.V., Onishchenko A.I., Veretin O.L., Two-loop sunset diagrams with three massive lines, 10.1016/j.nuclphysb.2006.01.013
  37. Remiddi Ettore, Tancredi Lorenzo, An elliptic generalization of multiple polylogarithms, 10.1016/j.nuclphysb.2017.10.007
  38. M. Hidding and F. Moriello, All orders structure and efficient computation of linearly reducible elliptic Feynman integrals, arXiv:1712.04441 [ INSPIRE ].
  39. Passarino Giampiero, Elliptic polylogarithms and basic hypergeometric functions, 10.1140/epjc/s10052-017-4623-1
  40. Zagier Don, The Bloch-Wigner-Ramakrishnan polylogarithm function, 10.1007/bf01453591
  41. S.J. Bloch, Higher regulators, algebraic K-theory, and zeta functions of elliptic curves, American Mathematical Society, U.S.A. (2000).
  42. LEVIN ANDREY, 10.1023/a:1000193320513
  43. A. Beilinson and A. Levin, The elliptic polylogarithm, in Proceedings of Symposium in Pure Mathematics 55, Part II, J.P.S.U. Jannsen, S.L. Kleiman eds., American Mathematical Society, U.S.A. (1994).
  44. A. Levin and G. Racinet, Towards multiple elliptic polylogarithms, math/0703237 .
  45. F. Brown and A. Levin, Multiple elliptic polylogarithms, arXiv:1110.6917 .
  46. J. Broedel, C. Duhr, F. Dulat and L. Tancredi, Elliptic polylogarithms and iterated integrals on elliptic curves II: an application to the sunrise integral, arXiv:1712.07095 .
  47. J. A. Lappo-Danilevski, Résolution algorithmique des problèmes réguliers de Poincaré et de Riemann ( Mémoire premier: Le problème de poincaré, concernant la construction d’un groupe de monodromie d’un système donné d’équations différentielles linéaires aux intégrales régulières), J. Soc. Phys.-Math. Léningrade 2 (1928) 94.
  48. Silverman Joseph H., The Arithmetic of Elliptic Curves, ISBN:9781475719222, 10.1007/978-1-4757-1920-8
  49. N. Matthes, Elliptic multiple Zeta values, Ph.D. thesis, Universität Hamburg, Hamburg, Germany (2016).
  50. Bloch Spencer, Kerr Matt, Vanhove Pierre, A Feynman integral via higher normal functions, 10.1112/s0010437x15007472
  51. Ablinger J., Blümlein J., Raab C. G., Schneider C., Iterated binomial sums and their associated iterated integrals, 10.1063/1.4900836
  52. Aglietti U., Bonciani R., Master integrals with 2 and 3 massive propagators for the 2-loop electroweak form factor—planar case, 10.1016/j.nuclphysb.2004.07.018
  53. Bonciani R., Degrassi G., Vicini A., On the generalized harmonic polylogarithms of one complex variable, 10.1016/j.cpc.2011.02.011
  54. E. Panzer, Various guises of elliptic iterated integrals, talk give at The elliptic/missing Feynman integrals, June 5-9, ETH Zürich, Switzerland (2017).
  55. F. Brown, Multiple modular values and the relative completion of the fundamental group of m1,1, arXiv:1407.5167 .
  56. J. Broedel, N. Matthes and O. Schlotterer, Relations between elliptic multiple zeta values and a special derivation algebra, J. Phys. A 49 (2016) 155203 [ arXiv:1507.02254 ] [ INSPIRE ].
  57. N. Matthes, Linear independence of indefinite iterated Eisenstein integrals, arXiv:1601.05743 [ INSPIRE ].
  58. N. Matthes, Decomposition of elliptic multiple zeta values and iterated Eisenstein integrals, arXiv:1703.09597 .
  59. Matthes Nils, On the algebraic structure of iterated integrals of quasimodular forms, 10.2140/ant.2017.11.2113
  60. Brown Francis, The Massless Higher-Loop Two-Point Function, 10.1007/s00220-009-0740-5
  61. Panzer Erik, Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals, 10.1016/j.cpc.2014.10.019
Bibliographic reference Duhr, Claude ; et. al. Elliptic polylogarithms and iterated integrals on elliptic curves I: general formalism. In: Journal of High Energy Physics, Vol. 2018, no.93, p.
Permanent URL http://hdl.handle.net/2078.1/198940