REVIEW 76 cited by
High-precision calculation of multi-loop Feynman integrals by difference equations
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
read the original 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.
Forward citations
Showing 60 of 76 Pith papers that cite this
-
Recursive construction of scalar one-loop integrals in dimensional regularisation
A recursion based on hyperbolic simplex volumes expresses every epsilon-expansion coefficient of scalar one-loop Feynman integrals in terms of multiple polylogarithms.
-
Efficient AI-Inspired Reduction of Feynman Integrals via Tube Seeding
Machine learning discovers a tube-seeding strategy for IBP reduction of Feynman integrals that scales linearly with numerator power, demonstrated on rank-20 2-loop 5-point integrals.
-
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.
-
Analytic two-loop amplitudes for $q\bar{q}\to \gamma \gamma$ and $gg \to \gamma \gamma$ mediated by a heavy-quark loop
The two-loop amplitudes for q qbar -> gamma gamma and gg -> gamma gamma with a heavy-quark loop are computed analytically in terms of elliptic iterated integrals, with validated fast series expansions for numerical ev...
-
Numerical evaluation of two-loop QCD helicity amplitudes for $gg\to t \bar{t} g$ at leading colour
The two-loop finite remainders for gg to ttbar g at leading colour are evaluated numerically at one benchmark point, with elliptic functions confined to the finite part.
-
Full-colour double-virtual amplitudes for associated production of a Higgs boson with a bottom-quark pair at the LHC
First analytic full-color two-loop five-particle amplitudes for associated Higgs-plus-bottom-quark-pair production at the LHC, with public C++ implementation.
-
RI-(S)MOM to $\overline{\rm MS}$ conversion for $B_K$ at two-loop order
A two-loop scheme-conversion calculation shifts and tightens the world average of the kaon bag parameter to 0.7627(60), updating the Standard Model prediction for epsilon_K.
-
Emergence of Calabi-Yau manifolds in high-precision black hole scattering
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.
-
Black Hole Binary Dynamics from the Double Copy and Effective Theory
The authors derive the complete conservative two-body Hamiltonian for spinless black holes at third post-Minkowskian order using scattering amplitudes and effective field theory.
-
Two-loop QCD amplitudes for $t\bar{t}W$ production at the LHC in the leading-colour approximation
First two-loop QCD hard functions for ttW production with exact top and W masses in leading colour, evaluated on a 224,640-point grid and cross-checked by an independent calculation.
-
Two-loop amplitude for $t\bar{t}W$ production at hadron colliders in the leading colour approximation
The leading-colour two-loop QCD amplitude for ttbar-W production is evaluated numerically at phase-space points using differential equations and finite-field rational reconstruction.
-
Scattering Amplitudes as Programs: Self-Evolving Search for Theory and Event Generation
Self-evolving program search over scattering amplitudes discovers known and hybrid evaluation structures, cutting counted arithmetic ~48x and reaching within ~14x of optimized MadGraph at n=6 while beating the tested ...
-
Compact Syzygies for Feynman Integrals from Landau Singularities
Syzygy solutions for IBP reduction are systematically constructed as maximal minors of certificate matrices derived from the leading Landau singularities of Feynman diagrams.
-
NNLO QCD predictions for $t\bar{t}W$ production at the LHC
NNLO QCD predictions for ttW production with two-loop amplitudes evaluated explicitly in the generalised leading-colour limit.
-
Landau's Leviathans
New algorithm identifies complete Landau singularities of Feynman integrals via Euler characteristic drops over finite fields, applied to non-planar two-loop six-point and massive three-loop graphs.
-
Gravitational Compton scattering at the fourth post-Minkowskian order
Derives gravitational Compton amplitude at O(G^4) and N-matrix element for scattering phase shift, verified by agreement with black-hole perturbation theory.
-
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.
-
Analytic results for heavy-quark contributions to charged-current DIS at NNLO
Analytic NNLO partonic coefficient functions for F2, FL, F3 in charged-current DIS with exact charm mass, expressed via Goncharov polylogarithms and Chen iterated integrals.
-
NNLO QCD predictions for $t\bar t W$ production at hadron colliders
NNLO QCD predictions for ttW production at hadron colliders using direct two-loop amplitude computation in the generalised leading-colour limit.
-
Magic Relations and Critical Varieties of Feynman Integrals
Magic relations in Feynman integral families coincide with higher-dimensional critical varieties, enabling a practical test to detect and handle them.
-
Renormalization of three-quark operators with up to two derivatives at three loops
Three-loop renormalization constants and anomalous dimensions are derived analytically for three-quark operators with derivatives in QCD, confirming prior N=0 results and enabling lattice matching.
-
Learning to Unscramble: Simplifying Symbolic Expressions via Self-Supervised Oracle Trajectories
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 ...
-
Resumming Scattering Amplitudes for Waveforms
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: from generating functions to spin-resummed post-Minkowskian dynamics
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.
-
Double virtual QCD corrections to $t\bar{t}+$jet production at the LHC
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.
-
Analytical two-loop amplitudes of $e^{+} e^{-} \longrightarrow \boldsymbol{J} / \boldsymbol{\psi}+\boldsymbol{\eta}_c$ at $B$ factories
The authors present the first analytical two-loop NRQCD amplitude for e+e- to J/psi+eta_c as an expansion in m_c^2/s, with cross-section predictions consistent (within uncertainties) with B-factory data.
-
Anomalous dimensions and critical exponents for the Gross-Neveu-Yukawa model at five loops
First five-loop renormalization group functions for the O(N) Gross-Neveu-Yukawa model, yielding refined, resummed critical exponent estimates for N=1, 2, and 5.
-
Dihadron Angular Correlations in the $e^+e^-$ Collision
The paper derives the first complete O(alpha_s^2) analytic QCD corrections to the dihadron angular separation distribution in e+e- annihilation, with verified cancellation of infrared poles.
-
Gravitational Bremsstrahlung in Black-Hole Scattering at $\mathcal{O}(G^3)$: Quadratic-in-Spin Effects
First computation of the O(G^3 S^2) momentum-space gravitational waveform for two scattering spinning black holes, plus the leading three-body spinning waveform.
-
First Look at Quartic-in-Spin Binary Dynamics at Third Post-Minkowskian Order
The O(G^3) conservative and radiation-reaction classical observables for spinning black-hole scattering are extended to quartic order in spin, with all-order-in-spin radiation reaction beyond the aligned-spin limit.
-
Two-loop helicity amplitudes for diphoton production with massive quark loop
Two-loop helicity amplitudes for diphoton production with a massive top quark loop are computed, providing new analytic results for gluon fusion and benchmark numbers for both channels.
-
Tame multi-leg Feynman integrals beyond one loop
A 'branch' reformulation of Feynman integrals claims to reduce multi-loop integrals to one-loop-like low-dimensional integrals, but the advertised parameter bound is wrong and the numerical validation is not shown.
-
HQET sum rules for matrix elements of dimension-six four-quark operators for meson lifetimes within and beyond the Standard Model
HQET sum rules yield the first four-quark bag parameters for B-meson lifetimes with beyond-standard-model operators, plus updated standard-model results.
-
Spinning bodies in general relativity from bosonic worldline oscillators
A bosonic-oscillator worldline action for spinning compact bodies in general relativity is constructed, and it reproduces known post-Minkowskian scattering results while remaining valid to all orders in spin.
-
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.
-
Higher-Order Corrections to Higgs Boson Amplitudes with Full Quark Mass Dependence in Quantum Chromodynamics
The thesis computes three-loop and two-loop QCD corrections to Higgs processes with full quark mass dependence, including a new analytic series-expansion treatment of elliptic two-loop master integrals for Higgs-plus-...
-
A numerical evaluation of planar two-loop helicity amplitudes for a W-boson plus four partons
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.
-
Analytic result of a three-loop integral family in the Higgs decay to four massive bottom quarks
Analytic master-integral results through O(ε²) are obtained for a three-loop family containing elliptic and K3 geometries by building and solving a mixed-sector ε-factorized differential equation.
-
Notes on the bootstrap of four-point conformal integrals
A leading-singularity bootstrap workflow yields new analytic expressions for four-loop conformal integrals, including previously intractable non-planar sectors.
-
First look at the evaluation of two-loop Feynman integrals for radiative return processes
Planar two-loop four-point master integrals for massive radiative-return QED, including elliptic and nested-root sectors, are reduced to polynomial-in-ε differential equations that evaluate stably in the physical region.
-
Chebyshev Approximations of Feynman Integrals for Collider Physics
Chebyshev polynomial approximations with adaptive sampling solve canonical differential equations for Feynman integrals, demonstrated to be stable and competitive for two-loop five-point cases in double precision.
-
LinApart3: efficient algorithm for multivariate partial fraction decomposition with linear denominators
LinApart3 performs multivariate partial fraction decomposition for linear-denominator rational functions using linear algebra and residue extraction on hyperplane arrangements, with guarantees on term structure, no sp...
-
Hard thermal contributions to phase transition observables at NNLO
Three-loop thermal masses and two-loop quartic couplings complete the O(g^6) high-temperature EFT of U(1) and SU(N) gauge-Higgs models, with a missing contribution identified in a known three-loop master integral.
-
All planar three-loop Feynman integrals for the production of two vector bosons at hadron colliders
All nine planar three-loop four-point integral families for two massive external legs are cast into canonical differential equations and evaluated numerically, completing the set needed for leading-colour N3LO diboson...
-
New algorithms for Feynman integral reduction and $\varepsilon$-factorised differential equations
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.
-
Tensor Reduction of Sunset by Generating Function
A complete set of recurrence relations is derived to reduce any tensor integral of the sunset diagram to seven master integrals, using generating functions supplemented by syzygy equations.
-
Angular phase-space integrals with four denominators through Mellin--Barnes
Four-denominator angular phase-space integrals are computed to O(epsilon^0) in dimensional regularization and expressed in GPLs for massless and massive momenta.
-
Fast evaluation of Feynman integrals for Monte Carlo generators
A new numerical integrator evaluates one- and two-loop five-point Feynman integrals with complex masses in milliseconds, using variable-by-variable integration and a new branch-cut prescription.
-
Differential Space of Feynman Integrals: Annihilators and $\mathcal{D}$-module
A Griffiths-Dwork based algorithm builds annihilators and D-modules for Feynman-like integrals, and in all tested cases the holonomic rank matches the twisted de Rham cohomology dimension.
-
Kira 3: integral reduction with efficient seeding and optimized equation selection
Kira 3 cuts Feynman-integral reduction cost by up to two orders of magnitude using smarter seeding and equation selection.
-
Explainable AI-assisted Optimization for Feynman Integral Reduction
FunSearch discovered a simple priority function for ordering IBP seeding integrals, reducing the number needed for multi-loop Feynman integral reductions by factors up to 3058.
-
Refining Integration-by-Parts Reduction of Feynman Integrals with Machine Learning
Machine learning program search rediscovers state-of-the-art integration-by-parts seeding heuristics and finds a modestly smaller seed set for a single two-loop benchmark integral.
-
Region analysis of $H\to \gamma \gamma $ via a bottom quark loop
A two-loop region analysis of H to gamma gamma via a bottom quark loop shows that with a Delta regulator and a transverse momentum cut, the leading and next-to-leading logarithms come entirely from the soft sector.
-
Efficient Computation of One-Loop Feynman Integrals and Fixed-Branch Integrals to High Orders in $\epsilon$
A dimension-changing transformation computes one-loop and fixed-branch Feynman integrals to high orders in the dimensional regulator by integrating auxiliary-mass integrals over the mass parameter, implemented in an o...
-
Triple real-emission contribution to the zero-jettiness soft function at N3LO in QCD
The paper provides the technical derivation and cross-checks of the triple-real-emission piece of the N3LO zero-jettiness soft function, confirming the result announced in arXiv:2409.11042.
-
Renormalization of effective field theories via on-shell methods: the case of axion-like particles
Complete one-loop anomalous dimension matrix for a CP-violating ALP effective field theory, derived via on-shell unitarity methods and extended to dimension-6 SMEFT operators.
-
One-Loop Observables to Higher Order in Spin
New one-loop formulas express the momentum impulse and spin kick of two scattered spinning bodies directly in terms of the eikonal phase, valid to all orders in spin and independent of the spin supplementary condition.
-
Quantum de Sitter Entropy and Sphere Partition Functions: A-Hypergeometric Approach to Higher Loop Corrections
Scalar and vector Feynman integrals on the sphere are mapped to A-hypergeometric (GKZ) systems via embedding space propagators, enabling algorithmic higher-loop computations.
-
Integration-by-parts reductions of Feynman integrals using Singular and GPI-Space
The authors build a parallelized Singular and GPI-Space pipeline for integration-by-parts reductions and use it to compute the two-loop nonplanar double-pentagon family analytically up to numerator degree 4.
-
Transverse Parton Distribution and Fragmentation Functions at NNLO: the Quark Case
The authors compute NNLO quark transverse momentum dependent PDFs and fragmentation functions with the exponential regulator, and extract the two-loop quark jet function needed for N3LL energy-energy correlator resummation.
Discussion (0). Continue with ORCID to comment.