Evaluating multi-loop Feynman integrals numerically through differential equations

[1]  P. Mastrolia,et al.  Decomposition of Feynman integrals on the maximal cut by intersection numbers , 2019, Proceedings of 14th International Symposium on Radiative Corrections — PoS(RADCOR2019).

[2]  Matthias Steinhauser,et al.  Double Higgs boson production at NLO in the high-energy limit: complete analytic results , 2019, Journal of High Energy Physics.

[3]  M. Mühlleitner,et al.  Gluon fusion into Higgs pairs at NLO QCD and the top mass scheme , 2018, The European Physical Journal C.

[4]  M. Steinhauser,et al.  Double Higgs boson production at NLO in the high-energy limit: complete analytic results , 2018, Journal of High Energy Physics.

[5]  Li Lin Yang,et al.  Towards a new approximation for pair-production and associated-production of the Higgs boson , 2018, Journal of High Energy Physics.

[6]  P. Mastrolia,et al.  Feynman integrals and intersection theory , 2018, Journal of High Energy Physics.

[7]  Long-Bin Chen,et al.  Three-loop planar master integrals for heavy-to-light form factors , 2018, Physics Letters B.

[8]  Ramona Gröber,et al.  Analytical Method for Next-to-Leading-Order QCD Corrections to Double-Higgs Production. , 2018, Physical review letters.

[9]  J. Blumlein,et al.  Heavy quark form factors at three loops in the planar limit , 2018, Physics Letters B.

[10]  M. Steinhauser,et al.  Three-loop massive form factors: complete light-fermion and large-Nc corrections for vector, axial-vector, scalar and pseudo-scalar currents , 2018, Journal of High Energy Physics.

[11]  Daniel Hulme,et al.  Systematic approximation of multi-scale Feynman integrals , 2018, Journal of High Energy Physics.

[12]  G. Luisoni,et al.  Next-to-Leading-Order QCD Corrections to Higgs Boson Plus Jet Production with Full Top-Quark Mass Dependence. , 2018, Physical review letters.

[13]  P. Mastrolia,et al.  Master integrals for the NNLO virtual corrections to μe scattering in QED: the non-planar graphs , 2017, Journal of High Energy Physics.

[14]  Stephan Jahn,et al.  pySecDec: A toolbox for the numerical evaluation of multi-scale integrals , 2017, Comput. Phys. Commun..

[15]  R. Bonciani,et al.  Two-loop master integrals for the planar QCD massive corrections to di-photon and di-jet hadro-production , 2017, 1712.02537.

[16]  Yan-Qing Ma,et al.  A Systematic and Efficient Method to Compute Multi-loop Master Integrals , 2017, 1711.09572.

[17]  P. Mastrolia,et al.  Master integrals for the NNLO virtual corrections to μe scattering in QED: the planar graphs , 2017, 1709.07435.

[18]  A. Smirnov,et al.  Solving differential equations for Feynman integrals by expansions near singular points , 2017, 1709.07525.

[19]  R. Schabinger,et al.  Numerical multi-loop calculations via finite integrals and one-mass EW-QCD Drell-Yan master integrals , 2017, 1701.06583.

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

[21]  R. Bonciani,et al.  Two-loop planar master integrals for Higgs → 3 partons with full heavy-quark mass dependence , 2016, 1609.06685.

[22]  G.Heinrich,et al.  Full top quark mass dependence in Higgs boson pair production at NLO , 2016, 1608.04798.

[23]  Jun Gao,et al.  NNLO QCD corrections to t -channel single top quark production and decay , 2016, 1606.08463.

[24]  S. Borowka,et al.  Higgs Boson Pair Production in Gluon Fusion at Next-to-Leading Order with Full Top-Quark Mass Dependence. , 2016, Physical review letters.

[25]  C. Anastasiou,et al.  High precision determination of the gluon fusion Higgs boson cross-section at the LHC , 2016, 1602.00695.

[26]  Q. Yan,et al.  Efficient numerical evaluation of Feynman integrals , 2015, 1508.02512.

[27]  G. Zanderighi,et al.  Fully differential vector-boson fusion Higgs pair production at next-to-next-to-leading order , 2018, Physical Review D.

[28]  C. Anastasiou,et al.  Higgs boson gluon-fusion production in QCD at three loops. , 2015, Physical review letters.

[29]  A. V. Smirnov,et al.  FIRE5: A C++ implementation of Feynman Integral REduction , 2014, Comput. Phys. Commun..

[30]  K. Melnikov,et al.  On the NNLO QCD corrections to single-top production at the LHC , 2014, 1404.7116.

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

[32]  R. N. Lee.  LiteRed 1.4: a powerful tool for reduction of multiloop integrals , 2013, 1310.1145.

[33]  C. Huot.  Iterative structure of finite loop integrals , 2014 .

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

[35]  A. Mitov,et al.  Total top-quark pair-production cross section at hadron colliders through O(αS(4)). , 2013, Physical review letters.

[36]  V. Smirnov.  Analytic Tools for Feynman Integrals , 2013 .

[37]  Mario Mulansky,et al.  Odeint - Solving ordinary differential equations in C++ , 2011, ArXiv.

[38]  F. Maltoni,et al.  Higgs boson production via vector-boson fusion at next-to-next-to-leading order in QCD. , 2010, Physical review letters.

[39]  Takahiro Ueda,et al.  A geometric method of sector decomposition , 2009, Comput. Phys. Commun..

[40]  M. Czakon.  Tops from light quarks : Full mass dependence at two-loops in QCD , 2008, 0803.1400.

[41]  M. Czakon,et al.  Double fermionic contributions to the heavy-quark vacuum polarization , 2007, 0712.2762.

[42]  Christian Bogner,et al.  Operating system: Unix , 1983 .

[43]  M. Czakon,et al.  NNLO fermionic corrections to the charm quark mass dependent matrix elements in B̄ → Xsγ , 2007, 0707.3090.

[44]  C. Anastasiou,et al.  Evaluating multi-loop Feynman diagrams with infrared and threshold singularities numerically , 2007, hep-ph/0703282.

[45]  H. Czyz,et al.  Numerical evaluation of the general massive 2-loop sunrise self-mass master integrals from differential equations , 2002, hep-ph/0203256.

[46]  Arnold Neumaier,et al.  Introduction to Numerical Analysis , 2001 .

[47]  T. Binoth,et al.  An automatized algorithm to compute infrared divergent multi-loop integrals , 2000, hep-ph/0004013.

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

[49]  D. Soper.  Techniques for QCD calculations by numerical integration , 1999, hep-ph/9910292.

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

[51]  D. Graudenz,et al.  HIGGS BOSON PRODUCTION AT THE LHC , 1995, hep-ph/9504378.

[52]  Zerwas,et al.  QCD corrections to Higgs-boson production at proton-proton colliders. , 1993, Physical review letters.

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

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

[55]  E. Fehlberg.  Classical Fifth-, Sixth-, Seventh-, and Eighth-Order Runge-Kutta Formulas with Stepsize Control , 1968 .

[56]  L. Landau.  On analytic properties of vertex parts in quantum field theory , 1959 .