Hepp and Speer sectors within modern strategies of sector decomposition

Hepp and Speer sectors were successfully used in the sixties and seventies for proving mathematical theorems on analytically or/and dimensionally regularized and renormalized Feynman integrals at Euclidean external momenta. We describe them within recently developed strategies of introducing iterative sector decompositions. We prove that Speer sectors are reproduced within one of the existing strategies.

[1]  M. Steinhauser,et al.  Fermionic contributions to the three-loop static potential , 2008, 0809.1927.

[2]  D. Maitre,et al.  Master integrals for fermionic contributions to massless three-loop form-factors , 2007, 0711.3590.

[3]  V. Velizhanin.  Leading transcendental contribution to the four-loop universal anomalous dimension in N = 4 SYM , 2009 .

[4]  R. Bonciani,et al.  Two-loop QCD corrections to the heavy-to-light quark decay , 2008, 0809.4687.

[5]  N. N. Bogoliubov,et al.  Introduction to the theory of quantized fields , 1960 .

[6]  T. Binoth,et al.  Numerical evaluation of phase space integrals by sector decomposition , 2004 .

[7]  T. Binoth,et al.  An automatized algorithm to compute infrared divergent multi-loop integrals , 2000 .

[8]  Gudrun Heinrich,et al.  Sector Decomposition , 2008, 0803.4177.

[9]  V. Velizhanin.  Leading transcedentality contributions to the four-loop universal anomalous dimension in N = 4 SYM , 2022 .

[10]  G. Hooft,et al.  Regularization and Renormalization of Gauge Fields , 1972 .

[11]  Y. Kiyo,et al.  ααs) corrections to the γtt̄ vertex at the top quark threshold , 2008, 0810.1597.

[12]  Klaus Hepp,et al.  Proof of the Bogoliubov-Parasiuk theorem on renormalization , 1966 .

[13]  O. I. Zavialov.  Renormalized Quantum Field Theory , 1990 .

[14]  P. Breitenlohner,et al.  Dimensional renormalization and the action principle , 1977 .

[15]  V. Smirnov.  Asymptotic expansions in limits of large momenta and masses , 1990 .

[16]  M. Bergere,et al.  Bogolubov–Parasiuk theorem in the α‐parametric representation , 1976 .

[17]  Y. Kiyo,et al.  ${\cal O}(\alpha\alpha_s)$ corrections to the $\gamma t\bar{t}$ vertex at the top quark threshold , 2008 .

[18]  Christian Bogner,et al.  Blowing up Feynman integrals , 2008, 0806.4307.

[19]  K. Chetyrkin,et al.  Four Loop Massless Propagators: an Algebraic Evaluation of All Master Integrals , 2010, 1004.1153.

[20]  E. Speer.  Ultraviolet and infrared singularity structure of generic Feynman amplitudes , 1975 .

[21]  Master integrals for massless three-loop form factors: One-loop and two-loop insertions , 2006, hep-ph/0607185.

[22]  G. Bell.  NNLO corrections to inclusive semileptonic B decays in the shape-function region , 2008, 0810.5695.

[23]  C. G. Bollini,et al.  Dimensional renorinalization : The number of dimensions as a regularizing parameter , 1972, Il Nuovo Cimento B.

[24]  J. Zuber,et al.  Renormalization of Feynman amplitudes and parametric integral representation , 1974 .

[25]  A. V. Smirnov,et al.  Feynman Integral Evaluation by a Sector decomposiTion Approach (FIESTA) , 2008, Comput. Phys. Commun..

[26]  V. Smirnov.  Applied Asymptotic Expansions in Momenta and Masses , 2001 .

[27]  M. Bergere,et al.  A theorem on asymptotic expansion of Feynman amplitudes , 1978 .

[28]  T. Binoth,et al.  Numerical evaluation of multi-loop integrals by sector decomposition , 2004 .

[29]  中西 襄.  Graph theory and Feynman integrals , 1971 .

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

[31]  K. Pohlmeyer.  Large momentum behavior of the Feynman amplitudes in the φ44 ‐theory , 1982 .

[32]  P. Breitenlohner,et al.  Dimensionally Renormalized Green's functions for theories with massless particles. I , 1977 .