R. Cutkosky, Singularities and Discontinuities of Feynman Amplitudes, Journal of Mathematical Physics, vol.1, issue.5, pp.429-433, 1960.
DOI : 10.1063/1.1703676

R. Eden, P. Landshoff, D. Olive, and J. Polkinghorne, The Analytic S-Matrix, American Journal of Physics, vol.35, issue.11, 1966.
DOI : 10.1119/1.1973770

L. Landau, On analytic properties of vertex parts in quantum field theory, Nuclear Physics, vol.13, issue.1, pp.181-192, 1959.
DOI : 10.1016/0029-5582(59)90154-3

Z. Bern, L. J. Dixon, and D. A. Kosower, One-loop amplitudes for e+e??? to four partons, Nuclear Physics B, vol.513, issue.1-2, pp.3-86, 1998.
DOI : 10.1016/S0550-3213(97)00703-7

R. Britto, F. Cachazo, and B. Feng, Generalized unitarity and one-loop amplitudes in super-Yang???Mills, Nuclear Physics B, vol.725, issue.1-2, pp.725-275, 2005.
DOI : 10.1016/j.nuclphysb.2005.07.014

D. Forde, Direct extraction of one-loop integral coefficients, Physical Review D, vol.75, issue.12, p.75, 2007.
DOI : 10.1103/PhysRevD.75.125019

D. A. Kosower and K. J. Larsen, Maximal unitarity at two loops, Physical Review D, vol.85, issue.4, p.85
DOI : 10.1103/PhysRevD.85.045017

URL : http://arxiv.org/abs/1108.1180

S. Caron-huot and K. J. Larsen, Uniqueness of two-loop master contours, Journal of High Energy Physics, vol.01, issue.10
DOI : 10.1007/JHEP10(2012)026

H. Johansson, D. A. Kosower, and K. J. Larsen, Two-loop maximal unitarity with external masses, Physical Review D, vol.87, issue.2, 2013.
DOI : 10.1103/PhysRevD.87.025030

H. Johansson, D. A. Kosower, and K. J. Larsen, Maximal unitarity for the four-mass double box, Physical Review D, vol.89, issue.12, p.89, 2014.
DOI : 10.1103/PhysRevD.89.125010

M. Søgaard and Y. Zhang, Elliptic functions and maximal unitarity, Physical Review D, vol.91, issue.8, p.91, 2015.
DOI : 10.1103/PhysRevD.91.081701

K. J. Larsen and Y. Zhang, Integration-by-parts reductions from unitarity cuts and algebraic geometry, Physical Review D, vol.93, issue.4, 2016.
DOI : 10.1103/PhysRevD.93.041701

URL : http://arxiv.org/abs/1511.01071

H. Ita, Two-loop integrand decomposition into master integrals and surface terms, Physical Review D, vol.94, issue.11, 2016.
DOI : 10.1103/PhysRevD.94.116015

URL : http://arxiv.org/abs/1510.05626

E. Remiddi and L. Tancredi, Differential equations and dispersion relations for Feynman amplitudes. The two-loop massive sunrise and the kite integral, Nuclear Physics B, vol.907, pp.400-444, 2016.
DOI : 10.1016/j.nuclphysb.2016.04.013

A. Primo and L. Tancredi, On the maximal cut of Feynman integrals and the solution of their differential equations, Nuclear Physics B, vol.916, pp.916-94, 2017.
DOI : 10.1016/j.nuclphysb.2016.12.021

H. Frellesvig and C. G. Papadopoulos, Cuts of Feynman Integrals in Baikov representation, 1701, p.7356

T. Dennen, M. Spradlin, and A. Volovich, Landau singularities and symbology: one- and two-loop MHV amplitudes in SYM theory, Journal of High Energy Physics, vol.01, issue.3
DOI : 10.1007/JHEP03(2016)069

M. Veltman, Diagrammatica: The Path to Feynman rules, Cambridge Lect, Notes Phys, vol.4, pp.1-284, 1994.
DOI : 10.1017/CBO9780511564079

E. Remiddi, Dispersion Relations for Feynman Graphs, Helv.Phys.Acta, vol.54, issue.364, 1982.

S. Mandelstam, Analytic Properties of Transition Amplitudes in Perturbation Theory, Physical Review, vol.115, issue.6, pp.1741-1751, 1959.
DOI : 10.1103/PhysRev.115.1741

P. Ball, V. M. Braun, and H. G. Dosch, Form-factors of semileptonic D decays from QCD sum rules, Phys.Rev, pp.44-3567, 1991.

S. Abreu, R. Britto, C. Duhr, and E. Gardi, From multiple unitarity cuts to the coproduct of Feynman integrals, Journal of High Energy Physics, vol.338, issue.10
DOI : 10.1007/JHEP10(2014)125

URL : https://hal.archives-ouvertes.fr/cea-00996371

S. Abreu, R. Britto, and H. Grönqvist, Cuts and coproducts of massive triangle diagrams, Journal of High Energy Physics, vol.41, issue.7, 2015.
DOI : 10.1007/JHEP07(2015)111

URL : https://hal.archives-ouvertes.fr/cea-01201809

F. Cachazo, Sharpening The Leading Singularity, 0803, 1988.

N. Arkani-hamed, F. Cachazo, and J. Kaplan, What is the simplest quantum field theory?, Journal of High Energy Physics, vol.46, issue.9
DOI : 10.1007/JHEP09(2010)016

D. B. Fairlie, P. V. Landshoff, J. Nuttall, and J. C. Polkinghorne, Singularities of the Second Type, Journal of Mathematical Physics, vol.3, issue.4, 1962.
DOI : 10.1063/1.1724262

D. B. Fairlie, P. V. Landshoff, J. Nuttall, and J. C. Polkinghorne, Physical sheet properties of second type singularities, Physics Letters, vol.3, issue.1, p.55, 1962.
DOI : 10.1016/0031-9163(62)90200-7

D. Fotiadi, M. Froissart, J. Lascoux, and F. Pham, Applications of an isotopy theorem, Topology, vol.4, issue.2, pp.159-191, 1965.
DOI : 10.1016/0040-9383(65)90063-7

R. C. Hwa and V. L. Teplitz, Homology and Feynman integrals, 1966.

J. Leray, Le calcul différential et intégral sur une variété analytique complexe. Probì eme de Cauchy. III, Bull. S. M. F, vol.87, pp.81-180, 1959.
DOI : 10.24033/bsmf.1515

URL : http://archive.numdam.org/article/BSMF_1959__87__81_0.pdf

Z. Bern, L. J. Dixon, and D. A. Kosower, Dimensionally regulated one-loop integrals, Physics Letters B, vol.302, issue.2-3, pp.302-299, 1993.
DOI : 10.1016/0370-2693(93)90400-C

URL : http://doi.org/10.1016/0370-2693(93)90400-c

O. V. Tarasov, Connection between Feynman integrals having different values of the space-time dimension, Physical Review D, vol.54, issue.10, pp.6479-6490, 1996.
DOI : 10.1103/PhysRevD.54.6479

R. N. Lee, Space???time dimensionality as complex variable: Calculating loop integrals using dimensional recurrence relation and analytical properties with respect to, Nuclear Physics B, vol.830, issue.3, pp.474-492, 2010.
DOI : 10.1016/j.nuclphysb.2009.12.025

M. Spradlin and A. Volovich, Symbols of one-loop integrals from mixed Tate motives, Journal of High Energy Physics, vol.50, issue.11, pp.84-1105, 2011.
DOI : 10.1007/JHEP11(2011)084

P. A. Baikov, Explicit solutions of the multiloop integral recurrence relations and its application, Nucl. Instrum. Meth, pp.389-347, 1997.

R. N. Lee, Calculating multiloop integrals using dimensional recurrence relation and D-analyticity, Nucl. Phys, Proc. Suppl, pp.205-206, 2010.

A. G. Grozin, INTEGRATION BY PARTS: AN INTRODUCTION, International Journal of Modern Physics A, vol.26, issue.17, pp.2807-2854, 2011.
DOI : 10.1142/S0217751X11053687

R. K. Ellis and G. Zanderighi, Scalar one-loop integrals for QCD, Journal of High Energy Physics, vol.25, issue.02, 2008.
DOI : 10.1103/PhysRevD.62.095014

URL : http://arxiv.org/abs/0712.1851

M. Abramowitz and A. S. Irene, Handbook of Mathematical Functions, American Journal of Physics, vol.34, issue.2, 1972.
DOI : 10.1119/1.1972842

S. Moch, P. Uwer, and S. Weinzierl, Nested sums, expansion of transcendental functions, and multiscale multiloop integrals, Journal of Mathematical Physics, vol.43, issue.6, pp.3363-3386, 2002.
DOI : 10.1063/1.1471366

D. Fotiadi and F. Pham, Analytic Properties of Some Integrals over Complex Manifolds, 1966.

S. Caron-huot and J. M. Henn, Iterative structure of finite loop integrals, Journal of High Energy Physics, vol.15, issue.6, 2014.
DOI : 10.1007/JHEP06(2014)114

D. Fotiadi and F. Pham, Analytic study of Some Feynman Graphs by Homological Methods, 1966.

E. Panzer, Feynman integrals and hyperlogarithms, Humboldt U, pp.2015-1506

C. Bogner and S. Weinzierl, FEYNMAN GRAPH POLYNOMIALS, International Journal of Modern Physics A, vol.25, issue.13, pp.25-2585, 2010.
DOI : 10.1142/S0217751X10049438

S. Bloch and D. Kreimer, Cutkosky Rules and Outer Space

J. B. Boyling, ???????????????????????????? ???????????? ?? ?????????????????????????????? ?????????????????????????? ????????????????????, Il Nuovo Cimento A, vol.65, issue.825, pp.351-374, 1968.
DOI : 10.1007/BF02800115

P. V. Landshoff, D. Olive, and J. C. Polkinghorne, The hierarchical principle in perturbation theory, Il Nuovo Cimento A Series 10, vol.3, issue.2, pp.444-453, 1966.
DOI : 10.1007/BF02752870

F. V. Tkachov, A Theorem on Analytical Calculability of Four Loop Renormalization Group Functions, Phys. Lett, pp.100-65, 1981.

K. Chetyrkin and F. Tkachov, Integration by parts: The algorithm to calculate ??-functions in 4 loops, Nuclear Physics B, vol.192, issue.1, pp.192-159, 1981.
DOI : 10.1016/0550-3213(81)90199-1

R. N. Lee, Group structure of the integration-by-part identities and its application to the reduction of multiloop integrals, Journal of High Energy Physics, vol.2008, issue.07, p.31, 2008.
DOI : 10.1088/1126-6708/2008/07/031

C. Anastasiou and K. Melnikov, Higgs boson production at hadron colliders in NNLO QCD, Nuclear Physics B, vol.646, issue.1-2, pp.220-256, 2002.
DOI : 10.1016/S0550-3213(02)00837-4

C. Anastasiou and K. Melnikov, Pseudoscalar Higgs boson production at hadron colliders in NNLO QCD, Phys. Rev, vol.67, issue.037501, 2003.
DOI : 10.2172/801784

C. Anastasiou, L. J. Dixon, and K. Melnikov, NLO Higgs boson rapidity distributions at hadron colliders, Nucl. Phys, Proc. Suppl, pp.193-197193, 2002.
DOI : 10.2172/808704

URL : http://arxiv.org/pdf/hep-ph/0211141v1.pdf

C. Anastasiou, L. J. Dixon, K. Melnikov, and F. Petriello, Dilepton Rapidity Distribution in the Drell-Yan Process at Next-to-Next-to-Leading Order in QCD, Physical Review Letters, vol.91, issue.18, p.182002, 2003.
DOI : 10.1103/PhysRevLett.91.182002

C. Anastasiou, L. J. Dixon, K. Melnikov, and F. Petriello, High precision QCD at hadron colliders: Electroweak gauge boson rapidity distributions at NNLO, Phys. Rev, vol.094008, p.69, 2004.
DOI : 10.2172/826683

URL : http://arxiv.org/abs/hep-ph/0312266

C. Anastasiou, C. Duhr, F. Dulat, and B. Mistlberger, Soft triple-real radiation for Higgs production at N3LO, Journal of High Energy Physics, vol.68, issue.7
DOI : 10.1007/JHEP07(2013)003

URL : http://arxiv.org/abs/1302.4379

R. N. Lee and V. A. Smirnov, The dimensional recurrence and analyticity method for multicomponent master integrals: using unitarity cuts to construct homogeneous solutions, Journal of High Energy Physics, vol.11, issue.206, 2012.
DOI : 10.1007/JHEP12(2012)104

H. P. Stapp, Inclusive Cross Sections Are Discontinuities, Physical Review D, vol.3, issue.12, pp.3177-3184, 1971.
DOI : 10.1103/PhysRevD.3.3177

J. C. Polkinghorne, ???????????????????? ???????????????????? ?????????????? ?? ??????????????, Il Nuovo Cimento A, vol.3, issue.3, pp.555-566, 1972.
DOI : 10.1007/BF02734212

S. Caron-huot and M. Wilhelm, Renormalization group coefficients and the S-matrix, Journal of High Energy Physics, vol.04, issue.12
DOI : 10.1007/JHEP12(2016)010

A. V. Smirnov and A. V. Petukhov, The Number of Master Integrals is Finite, Letters in Mathematical Physics, vol.183, issue.1, pp.37-44, 2011.
DOI : 10.1007/s11005-010-0450-0

R. N. Lee and A. A. Pomeransky, Critical points and number of master integrals, Journal of High Energy Physics, vol.634, issue.206, 2013.
DOI : 10.1007/JHEP11(2013)165

A. V. Kotikov, Differential equations method. New technique for massive Feynman diagram calculation, Physics Letters B, vol.254, issue.1-2, pp.254-158, 1991.
DOI : 10.1016/0370-2693(91)90413-K

A. V. Kotikov, Differential equations method: the calculation of vertex-type Feynman diagrams, Physics Letters B, vol.259, issue.3, pp.259-314, 1991.
DOI : 10.1016/0370-2693(91)90834-D

A. V. Kotikov, Differential equation method. The calculation of N-point Feynman diagrams, Physics Letters B, vol.267, issue.1, pp.267-123, 1991.
DOI : 10.1016/0370-2693(91)90536-Y

T. Gehrmann and E. Remiddi, Differential equations for two-loop four-point functions, Nuclear Physics B, vol.580, issue.1-2, pp.580-485, 2000.
DOI : 10.1016/S0550-3213(00)00223-6

J. M. Henn, Multiloop Integrals in Dimensional Regularization Made Simple, Physical Review Letters, vol.110, issue.25, 1304.
DOI : 10.1103/PhysRevLett.110.251601

P. Federbush, Calculation of Some Homology Groups Relevant to Sixth???Order Feynman Diagrams, Journal of Mathematical Physics, vol.6, issue.6, p.941, 1965.
DOI : 10.1063/1.1704354

A. Goncharov, Volumes of hyperbolic manifolds and mixed Tate motives, alg-geom, 9601021.