Four-loop non-singlet splitting functions in QCD are computed analytically for the first time, with numerical representations provided.
Usovitsch,Factorization of denominators in integration-by-parts reductions, 2002.08173
7 Pith papers cite this work. Polarity classification is still indexing.
7
Pith papers citing it
abstract
We present a Mathematica package which finds a basis of master integrals for the Feynman integral reduction. In this basis the dependence on the dimensional regularization in the denominators factorizes in kinematic independent polynomials.
citation-role summary
background 1
method 1
citation-polarity summary
representative citing papers
N3LO calculation of the B to Xs gamma photon spectrum including complete light-fermion corrections, two massive fermion loops, and large-Nc terms, with improved results in kinetic and MSR mass schemes.
An algorithm reconstructs symbolic IBP reduction coefficients via intermediate bases, demonstrated on massive box-triangle and pentagon-triangle integrals using 3289 and 13013 samplings versus over a million unknowns.
Kira 2.0 implements finite-field coefficient reconstruction for IBP reductions and improved user-equation handling, yielding lower memory use and faster performance on state-of-the-art problems.
Algorithms that factor denominators in IBP coefficients inside the FUEL interface reduce reconstruction cost and improve robustness of large-scale Feynman integral reductions.
AMFlow 2.0 cuts symbolic and numerical cost of multi-loop Feynman integral evaluation via an FT recursion mode, a C++ DE solver, and modern IBP reducers, demonstrated on a three-loop five-point family.
Feynman integrals with mixed geometries (K3 surfaces, curves, points) can be computed more efficiently by extracting and using their algebraic geometric properties.
citing papers explorer
-
The four-loop non-singlet splitting functions in QCD
Four-loop non-singlet splitting functions in QCD are computed analytically for the first time, with numerical representations provided.
-
The photon-energy spectrum in $B\to X_s\gamma$ to N$^3$LO: light-fermion and large-$N_{\rm c}$ corrections
N3LO calculation of the B to Xs gamma photon spectrum including complete light-fermion corrections, two massive fermion loops, and large-Nc terms, with improved results in kinetic and MSR mass schemes.
-
Taming Symbolic IBP Reduction with Intermediate Bases
An algorithm reconstructs symbolic IBP reduction coefficients via intermediate bases, demonstrated on massive box-triangle and pentagon-triangle integrals using 3289 and 13013 samplings versus over a million unknowns.
-
Integral Reduction with Kira 2.0 and Finite Field Methods
Kira 2.0 implements finite-field coefficient reconstruction for IBP reductions and improved user-equation handling, yielding lower memory use and faster performance on state-of-the-art problems.
-
Factorization of denominators as a `fuel' for Feynman integral reduction
Algorithms that factor denominators in IBP coefficients inside the FUEL interface reduce reconstruction cost and improve robustness of large-scale Feynman integral reductions.
-
AMFlow 2.0: significant algorithmic and software improvements for Feynman integral evaluation
AMFlow 2.0 cuts symbolic and numerical cost of multi-loop Feynman integral evaluation via an FT recursion mode, a C++ DE solver, and modern IBP reducers, demonstrated on a three-loop five-point family.
-
From geometry to phenomenology
Feynman integrals with mixed geometries (K3 surfaces, curves, points) can be computed more efficiently by extracting and using their algebraic geometric properties.