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.
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Laporta,High-precision calculation of multiloop Feynman integrals by difference equations,Int
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Method
69% of classified citations
abstract
We describe a new method of calculation of generic multi-loop master integrals based on the numerical solution of systems of difference equations in one variable. We show algorithms for the construction of the systems using integration-by-parts identities and methods of solutions by means of expansions in factorial series and Laplace's transformation. We also describe new algorithms for the identification of master integrals and the reduction of generic Feynman integrals to master integrals, and procedures for generating and solving systems of differential equations in masses and momenta for master integrals. We apply our method to the calculation of the master integrals of massive vacuum and self-energy diagrams up to three loops and of massive vertex and box diagrams up to two loops. Implementation in a computer program of our approach is described. Important features of the implementation are: the ability to deal with hundreds of master integrals and the ability to obtain very high precision results expanded at will in the number of dimensions.
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representative citing papers
At 5PM-1SF order, Calabi-Yau three-fold periods emerge in radiation-reacted observables for classical black hole scattering computed with worldline QFT and advanced IBP/DE methods.
Four-loop non-singlet splitting functions in QCD are computed analytically for the first time, with numerical representations provided.
A self-supervised transformer learns to unscramble Feynman integrals for online IBP reduction, delivering bounded memory use on complex two-loop topologies while matching Kira's speed on the hardest cases tested.
A permutation-equivariant transformer trained on self-supervised oracle trajectories from scrambled expressions achieves near-perfect simplification rates for dilogarithms and 100% success on 5-point gluon scattering amplitudes with over 200 terms.
A new projector-based formalism determines effective potentials from perturbative amplitudes and resums them to compute non-perturbative gravitational waveforms for generic two-body trajectories.
Twisted Feynman integrals are introduced with graded Symanzik polynomials, classified as exponential periods, and shown to have geometry not inferable from generalized Baikov leading singularities.
Leading-colour two-loop virtual amplitudes for ttbar+jet are extracted analytically via finite-field evaluations and differential equations, then packaged in a C++ library with new numerical integration techniques.
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.
First numerical evaluation of planar two-loop helicity amplitudes for W-boson plus four partons using finite-field reduction and sector decomposition on a subset of master integrals.
The heavy-quark condensate is computed at five-loop order in QCD with massive quarks, confirming the five-loop vacuum anomalous dimension.
SIRENA automates IBP reduction of sum-integrals in finite-temperature QFT, reproduces known results to 3 loops, supplies new 3-loop fermionic reductions, and derives an analytic factorization formula for arbitrary 2-loop fermionic sum-integrals.
First beyond-NLO tensor decomposition and higher-order analytic one-loop amplitudes for e+e- to pi+pi-gamma, paired with a fast numerical five-point integral evaluator.
OPE-based recursive renormalization for mixed composite operators gives five-loop anomalous dimensions in phi^4 and two-loop in phi^3 models.
Covariant differentiation on the dual vector space spanned by master integrals reduces a large class of Feynman integrals to masters, with connections reusable across mass configurations.
Branch representation reduces the variable count for intersection-theory-based Feynman integral reduction to at most 3L-3 for L-loop integrals regardless of leg number.
A geometric order relation in IBP reduction yields a master-integral basis with Laurent-polynomial differential equations on the maximal cut that are then ε-factorized.
The authors introduce static correlators in worldline QFT to compute angular momentum dissipation in black hole scattering, reproducing the known O(G^3) flux and extending the approach to electromagnetism at O(α^3).
Analytic expressions for the planar master integrals in two-loop NLO EW light-fermion contributions to gg → ZH are derived via canonical differential equations and expressed using Goncharov polylogarithms or one-fold integrals over them.
Analytic expressions for one-loop helicity amplitudes in ttj and ttγ production are derived to O(ε²) as linear combinations of pentagon functions with rational coefficients in momentum-twistor variables, obtained via differential equations solved numerically by generalized power series expansion.
Three-loop QCD corrections to electroweak radiative parameters Δρ, Δr, and Δκ are computed, yielding an updated W boson mass prediction relevant for FCC precision targets.
The report reviews progress since 2021 in fixed-order computations for LHC applications and identifies processes requiring missing higher-order corrections to match anticipated experimental precision.
Graphical functions, defined as massless three-point position-space integrals, serve as a powerful tool for evaluating multi-loop Feynman integrals, with extensions to conformal field theory and recent algorithmic computability.
citing papers explorer
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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.
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Heavy-Quark Condensate and Vacuum Energy Anomalous Dimension at Five Loops
The heavy-quark condensate is computed at five-loop order in QCD with massive quarks, confirming the five-loop vacuum anomalous dimension.
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SIRENA -- Sum-Integral REductioN Algorithm
SIRENA automates IBP reduction of sum-integrals in finite-temperature QFT, reproduces known results to 3 loops, supplies new 3-loop fermionic reductions, and derives an analytic factorization formula for arbitrary 2-loop fermionic sum-integrals.
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Tensor decomposition of $e^+e^-\to\pi^+\pi^-\gamma$ to higher orders in the dimensional regulator
First beyond-NLO tensor decomposition and higher-order analytic one-loop amplitudes for e+e- to pi+pi-gamma, paired with a fast numerical five-point integral evaluator.
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The OPE Approach to Renormalization: Operator Mixing
OPE-based recursive renormalization for mixed composite operators gives five-loop anomalous dimensions in phi^4 and two-loop in phi^3 models.
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Feynman integral reduction by covariant differentiation
Covariant differentiation on the dual vector space spanned by master integrals reduces a large class of Feynman integrals to masters, with connections reusable across mass configurations.
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Planar master integrals for two-loop NLO electroweak light-fermion contributions to $g g \rightarrow Z H$
Analytic expressions for the planar master integrals in two-loop NLO EW light-fermion contributions to gg → ZH are derived via canonical differential equations and expressed using Goncharov polylogarithms or one-fold integrals over them.
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Three loop QCD corrections to electroweak radiative parameters
Three-loop QCD corrections to electroweak radiative parameters Δρ, Δr, and Δκ are computed, yielding an updated W boson mass prediction relevant for FCC precision targets.
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Les Houches 2023 -- Physics at TeV Colliders: Report on the Standard Model Precision Wishlist
The report reviews progress since 2021 in fixed-order computations for LHC applications and identifies processes requiring missing higher-order corrections to match anticipated experimental precision.
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Graphical Functions by Examples
Graphical functions, defined as massless three-point position-space integrals, serve as a powerful tool for evaluating multi-loop Feynman integrals, with extensions to conformal field theory and recent algorithmic computability.
- Four-loop Anomalous Dimensions of Scalar-QED Theory from Operator Product Expansion