Feynman integrals and intersection theory

[1]  R. Sarpong,et al.  Bio-inspired synthesis of xishacorenes A, B, and C, and a new congener from fuscol† †Electronic supplementary information (ESI) available. See DOI: 10.1039/c9sc02572c , 2019, Chemical science.

[2]  B. Page,et al.  Planar two-loop five-parton amplitudes from numerical unitarity , 2018, Journal of High Energy Physics.

[3]  S. Weinzierl,et al.  Analytic results for the planar double box integral relevant to top-pair production with a closed top loop , 2018, Journal of High Energy Physics.

[4]  J. Boehm,et al.  Complete integration-by-parts reductions of the non-planar hexagon-box via module intersections , 2018, Journal of High Energy Physics.

[5]  D. Kosower.  Direct solution of integration-by-parts systems , 2018, Physical Review D.

[6]  D. F. Lodato,et al.  Λ c + production in pp collisions at √s=7 TeV and in p-Pb collisions at √sNN=5.02 TeV , 2017, 1712.09581.

[7]  E. Panzer,et al.  Feynman integral relations from parametric annihilators , 2017, Letters in Mathematical Physics.

[8]  C. Duhr,et al.  Elliptic polylogarithms and iterated integrals on elliptic curves. Part I: general formalism , 2017, Journal of High Energy Physics.

[9]  K. J. Larsen,et al.  Differential equations for loop integrals in Baikov representation , 2017, 1712.03760.

[10]  H. Hartanto,et al.  First Look at Two-Loop Five-Gluon Scattering in QCD. , 2017, Physical review letters.

[11]  Sebastian Mizera.  Scattering Amplitudes from Intersection Theory. , 2017, Physical review letters.

[12]  Sebastian Mizera.  Combinatorics and topology of Kawai-Lewellen-Tye relations , 2017, 1706.08527.

[13]  Peter Uwer,et al.  Kira - A Feynman integral reduction program , 2017, Comput. Phys. Commun..

[14]  R. Schabinger,et al.  Baikov-Lee representations of cut Feynman integrals , 2017, 1705.03478.

[15]  S. Laporta.  High-precision calculation of the 4-loop contribution to the electron g-2 in QED1 , 2017, Journal of Physics: Conference Series.

[16]  L. Tancredi,et al.  Maximal cuts and differential equations for Feynman integrals. An application to the three-loop massive banana graph , 2017, 1704.05465.

[17]  Yang Zhang,et al.  Maximal cuts in arbitrary dimension , 2017, Journal of High Energy Physics.

[18]  C. Duhr,et al.  Algebraic Structure of Cut Feynman Integrals and the Diagrammatic Coaction. , 2017, Physical review letters.

[19]  N. Arkani-Hamed,et al.  Positive geometries and canonical forms , 2017, 1703.04541.

[20]  S. Weinzierl,et al.  Simplifying Differential Equations for Multiscale Feynman Integrals beyond Multiple Polylogarithms. , 2017, Physical review letters.

[21]  M. Zeng.  Differential equations on unitarity cut surfaces , 2017, 1702.02355.

[22]  C. Papadopoulos,et al.  Cuts of Feynman Integrals in Baikov representation , 2017, Journal of High Energy Physics.

[23]  A. Manteuffel,et al.  A non-planar two-loop three-point function beyond multiple polylogarithms , 2017, 1701.05905.

[24]  Yang Zhang,et al.  Azurite : An algebraic geometry based package for finding bases of loop integrals , 2016, Computer Physics Communications.

[25]  Yang Zhang.  Lecture Notes on Multi-loop Integral Reduction and Applied Algebraic Geometry , 2016, 1612.02249.

[26]  L. Tancredi,et al.  On the maximal cut of Feynman integrals and the solution of their differential equations , 2016, 1610.08397.

[27]  T. Peraro.  Scattering amplitudes over finite fields and multivariate functional reconstruction , 2016, 1608.01902.

[28]  T. Hussain,et al.  Measurement of Ds+ production and nuclear modification factor in Pb-Pb collisions at sNN=2.76$$ \sqrt{{\mathrm{s}}_{\mathrm{NN}}}=2.76 $$ TeV , 2016 .

[29]  E. Remiddi,et al.  Differential equations and dispersion relations for Feynman amplitudes. The two-loop massive sunrise and the kite integral , 2016, 1602.01481.

[30]  T. Gehrmann,et al.  Analytic Form of the Two-Loop Planar Five-Gluon All-Plus-Helicity Amplitude in QCD. , 2015, Physical review letters.

[31]  K. J. Larsen,et al.  Integration-by-parts reductions from unitarity cuts and algebraic geometry , 2015, 1511.01071.

[32]  K. Aomoto,et al.  Double filtration of twisted logarithmic complex and Gauss–Manin connection , 2015 .

[33]  Yoshiaki Goto,et al.  Contiguity relations of Lauricella's F_D revisited , 2014, 1412.3256.

[34]  J. Henn.  Lectures on differential equations for Feynman integrals , 2014, 1412.2296.

[35]  R. Lee.  Reducing differential equations for multiloop master integrals , 2014, 1411.0911.

[36]  Y. Goto.  Intersection numbers and twisted period relations for the generalized hypergeometric function ${}_{m+1} F_m$ , 2014, 1406.7464.

[37]  Andreas von Manteuffel,et al.  A novel approach to integration by parts reduction , 2014, ArXiv.

[38]  C. Papadopoulos.  Simplified differential equations approach for Master Integrals , 2014, 1401.6057.

[39]  P. Mastrolia,et al.  Magnus and Dyson series for Master Integrals , 2014, 1401.2979.

[40]  E. Remiddi,et al.  Schouten identities for Feynman graph amplitudes; The Master Integrals for the two-loop massive sunrise graph , 2013, 1311.3342.

[41]  Y. Goto.  TWISTED PERIOD RELATIONS FOR LAURICELLA'S HYPERGEOMETRIC FUNCTIONS FA , 2013, 1310.6088.

[42]  Keiji Matsumoto,et al.  The monodromy representation and twisted period relations for Appell’s hypergeometric function F 4 , 2013, Nagoya Mathematical Journal.

[43]  Keiji Matsumoto.  MONODROMY AND PFAFFIAN OF LAURICELLA'S FD IN TERMS OF THE INTERSECTION FORMS OF TWISTED (CO)HOMOLOGY GROUPS , 2013 .

[44]  Roman N. Lee,et al.  Critical points and number of master integrals , 2013, 1308.6676.

[45]  Y. Goto.  TWISTED CYCLES AND TWISTED PERIOD RELATIONS FOR LAURICELLA'S HYPERGEOMETRIC FUNCTION $F_c$ , 2013, 1308.5535.

[46]  J. Henn.  Multiloop integrals in dimensional regularization made simple. , 2013, Physical review letters.

[47]  R. N. Lee.  Presenting LiteRed: a tool for the Loop InTEgrals REDuction , 2012, 1212.2685.

[48]  Roman N. Lee,et al.  The dimensional recurrence and analyticity method for multicomponent master integrals: using unitarity cuts to construct homogeneous solutions , 2012, 1209.0339.

[49]  A. von Manteuffel,et al.  Reduze 2 - Distributed Feynman Integral Reduction , 2012, 1201.4330.

[50]  Kazuhiko Aomoto,et al.  Theory of Hypergeometric Functions , 2011 .

[51]  A. Grozin.  Integration by parts: An Introduction , 2011, 1104.3993.

[52]  J. Gluza,et al.  Towards a Basis for Planar Two-Loop Integrals , 2010, 1009.0472.

[53]  R. N. Lee.  Calculating multiloop integrals using dimensional recurrence relation and D-analyticity , 2010, 1007.2256.

[54]  R. N. Lee,et al.  Space-time dimensionality D as complex variable: Calculating loop integrals using dimensional recurrence relation and analytical properties with respect to D , 2009, 0911.0252.

[55]  A. Smirnov.  Algorithm FIRE—Feynman Integral REduction , 2008, 0807.3243.

[56]  M. Marcolli.  Motivic renormalization and singularities , 2008, 0804.4824.

[57]  Masaaki Yoshida,et al.  Intersection Theory for Twisted Cycles II ‐ Degenerate Arrangements , 2006 .

[58]  V. Smirnov.  Evaluating Feynman Integrals , 2005 .

[59]  Masaaki Yoshida,et al.  INTERSECTION NUMBERS FOR LOADED CYCLES ASSOCIATED WITH SELBERG-TYPE INTEGRALS , 2004 .

[60]  E. Remiddi,et al.  Analytic treatment of the two loop equal mass sunrise graph , 2004, hep-ph/0406160.

[61]  S. Laporta.  Calculation of Feynman integrals by difference equations , 2003, hep-ph/0311065.

[62]  N. Takayama,et al.  Quadratic relations for confluent hypergeometric functions , 2000 .

[63]  T. Gehrmann,et al.  Differential Equations for Two-Loop Four-Point Functions , 1999, hep-ph/9912329.

[64]  Denis Bernard,et al.  Vertex Operator Solutions of¶2d Dimensionally Reduced Gravity , 1999, solv-int/9902017.

[65]  Keiji Matsumoto.  Intersection numbers for logarithmic k-forms , 1998 .

[66]  E. Remiddi.  Differential equations for Feynman graph amplitudes , 1997, Il Nuovo Cimento A.

[67]  P. Orlik,et al.  Twisted de Rham Cohomology Groups of Logarithmic Forms , 1997 .

[68]  P. Baikov.  Explicit solutions of the multi-loop integral recurrence relations and its application , 1996 .

[69]  Tarasov.  Connection between Feynman integrals having different values of the space-time dimension. , 1996, Physical review. D, Particles and fields.

[70]  Keiji Matsumoto,et al.  Intersection theory for twisted cohomologies and twisted Riemann’s period relations I , 1995, Nagoya Mathematical Journal.

[71]  Keiji Matsumoto.  QUADRATIC IDENTITIES FOR HYPERGEOMETRIC SERIES OF TYPE ( k , l ) , 1994 .

[72]  A. Kotikov.  Differential equation method: The Calculation of N point Feynman diagrams , 1991 .

[73]  A. Kotikov.  Differential equations method. New technique for massive Feynman diagram calculation , 1991 .

[74]  P. Deligné,et al.  Monodromy of hypergeometric functions and non-lattice integral monodromy , 1986 .

[75]  F. Tkachov,et al.  Integration by parts: The algorithm to calculate β-functions in 4 loops , 1981 .

[76]  Kyoji Saito.  Theory of logarithmic differential forms and logarithmic vector fields , 1980 .

[77]  Aomoto Kazuhiko.  Les equations aux differences lineaires et les integrales des fonctions multiformes , 1975 .

[78]  G. Ponzano,et al.  Differential equations for one-loop generalized Feynman integrals , 1973 .

[79]  R. Stephenson.  A and V , 1962, The British journal of ophthalmology.

[80]  E. Remiddi.  Differential Equations and Dispersion Relations for Feynman Amplitudes , 2019 .

[81]  W. Hager,et al.  and s , 2019, Shallow Water Hydraulics.

[82]  A. Frieze,et al.  Differential Equations Method , 2016 .

[83]  A. Nagel,et al.  HYPERGEOMETRIC FUNCTIONS , 2004 .

[84]  N. Takayama,et al.  Quadratic Relations for Generalized Hypergeometric Functions PFP-1 , 2003 .

[85]  Roel Hospel,et al.  Morse Theory , 1999 .

[86]  Masaaki Yoshida,et al.  Hypergeometric functions, my love , 1997 .

[87]  Masaaki Yoshida,et al.  A HYPERGEOMETRIC INTEGRAL ATTACHED TO THE CONFIGURATION OF THE MIRRORS OF THE REFLECTION GROUP Sn+2 ACTING ON Pn , 1995 .

[88]  Masaaki Yoshida,et al.  Intersection Theory for Twisted Cycles , 1994 .

[89]  P. Orlik,et al.  Arrangements Of Hyperplanes , 1992 .

[90]  K. Aomoto.  On the Structure of Integrals of Power Product of Linear Functions , 1977 .

[91]  K. Aomoto.  Equations aux différences linéaires et les intégrales des fonctions multiformes, II. Evanouissement des hypercohomologies et exemples , 1974 .