Algorithm FIRE—Feynman Integral REduction

The recently developed algorithm FIRE performs the reduction of Feynman integrals to master integrals. It is based on a number of strategies, such as applying the Laporta algorithm, the s-bases algorithm, region-bases and integrating explicitly over loop momenta when possible. Currently it is being used in complicated three-loop calculations.

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

[2]  A. Maier,et al.  The second physical moment of the heavy quark vector correlator at O (α s 3 ) , 2008, 0806.3405.

[3]  M. Steinhauser,et al.  Applying Mellin-Barnes technique and Groebner bases to the three-loop static potential , 2008, 0805.1871.

[4]  R. N. Lee.  Group structure of the integration-by-part identities and its application to the reduction of multiloop integrals , 2008, 0804.3008.

[5]  A. Smirnov,et al.  On the reduction of Feynman integrals to master integrals , 2007, 0707.3993.

[6]  A. Smirnov,et al.  Decoupling of heavy quarks in HQET , 2006, hep-ph/0609280.

[7]  A. Smirnov,et al.  S-bases as a tool to solve reduction problems for Feynman integrals , 2006, hep-ph/0606247.

[8]  A. Smirnov.  An algorithm to construct Gröbner bases for solving integration by parts relations , 2006, hep-ph/0602078.

[9]  A. Smirnov,et al.  Applying Gröbner bases to solve reduction problems for Feynman integrals , 2005, hep-lat/0509187.

[10]  Vladimir P. Gerdt,et al.  A Maple Package for Computing Groebner Bases for Linear Recurrence Relations , 2005, ArXiv.

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

[12]  V. Gerdt.  Gröbner Bases in Perturbative Calculations , 2004 .

[13]  C. Anastasiou,et al.  Automatic integral reduction for higher order perturbative calculations , 2004, hep-ph/0404258.

[14]  Platanenallee DESY Zeuthen,et al.  Computation of Gröbner bases for two-loop propagator type integrals , 2004, hep-ph/0403253.

[15]  M. Steinhauser,et al.  Solving recurrence relations for multi-loop Feynman integrals , 2003, hep-ph/0307088.

[16]  T. Gehrmann,et al.  Two-loop master integrals for jets: the non-planar topologies , 2001, hep-ph/0101124.

[17]  S. Laporta,et al.  HIGH-PRECISION CALCULATION OF MULTILOOP FEYNMAN INTEGRALS BY DIFFERENCE EQUATIONS , 2000, hep-ph/0102033.

[18]  T. Gehrmann,et al.  Two-Loop Master Integrals for $\gamma^* \to 3$ Jets: The planar topologies , 2000, hep-ph/0008287.

[19]  P. Baikov.  Criterion of irreducibility of multi-loop Feynman integrals , 1999, hep-ph/0507053.

[20]  O. Tarasov.  Reduction of Feynman graph amplitudes to a minimal set of basic integrals , 1998, hep-ph/9812250.

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

[22]  P. Baikov.  Explicit solutions of the 3-loop vacuum integral recurrence relations , 1996 .

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

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

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

[26]  B. Buchberger,et al.  Gröbner bases and applications , 1998 .