Algorithm FIRE -- Feynman Integral REduction

Abstract

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.

Comparison with AIR updated

Cited by in corpus (334)

• Multiloop integrals in dimensional regularization made simple
• LiteRed 1.4: a powerful tool for the reduction of the multiloop integrals
• Cold Quark Matter
• FIRE5: a C++ implementation of Feynman Integral REduction
• Kira - A Feynman Integral Reduction Program
• Reduze - Feynman Integral Reduction in C++
• FIRE6: Feynman Integral REduction with Modular Arithmetic
• Calculation of the quark and gluon form factors to three loops in QCD
• A novel approach to integration by parts reduction
• Quark and gluon form factors to three loops
• Scattering Amplitudes and Conservative Binary Dynamics at $\mathcal{O}(G^4)$
• Bootstrapping rapidity anomalous dimension for transverse-momentum resummation
• Towards a Basis for Planar Two-Loop Integrals
• Three-loop static potential
• Scattering Amplitudes, the Tail Effect, and Conservative Binary Dynamics at $O(G^4)$
• Next-to-Next-to-Leading-Order Charm-Quark Contribution to the CP Violation Parameter epsilon_K and Delta M_K
• The Eikonal Approach to Gravitational Scattering and Radiation at $\mathcal{O}(G^3)$
• Integration-by-parts reductions from unitarity cuts and algebraic geometry
• Reconstructing Rational Functions with $\text{FireFly}$
• FIRE4, LiteRed and accompanying tools to solve integration by parts relations
• Feynman Integrals and Intersection Theory
• Four Loop Massless Propagators: an Algebraic Evaluation of All Master Integrals
• Analytic form of the two-loop planar five-gluon all-plus-helicity amplitude in QCD
• The Ultraviolet Properties of N=4 Supergravity at Four Loops
• Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
• On the Higgs boson pair production at the LHC
• Two-loop virtual corrections to Higgs pair production
• Gravitational Effective Field Theory Islands, Low-Spin Dominance, and the Four-Graviton Amplitude
• Two-loop planar master integrals for Higgs$\to 3$ partons with full heavy-quark mass dependence
• Pentagon functions for massless planar scattering amplitudes
• Fuchsia: a tool for reducing differential equations for Feynman master integrals to epsilon form
• Antenna subtraction at NNLO with hadronic initial states: double real initial-initial configurations
• Perturbative Thermal QCD: Formalism and Applications
• Leading singularities and off-shell conformal integrals
• Collider Physics at the Precision Frontier
• Absence of Three-Loop Four-Point Divergences in N=4 Supergravity
• Critical points and number of master integrals
• Hepta-Cuts of Two-Loop Scattering Amplitudes
• All master integrals for three-jet production at NNLO
• Iterative structure of finite loop integrals
• Master Integrals for Four-Loop Massless Propagators up to Transcendentality Weight Twelve
• Planar Two-Loop Five-Gluon Amplitudes from Numerical Unitarity
• $\overline{\mathrm{MS}}$-on-shell quark mass relation up to four loops in QCD and a general SU$(N)$ gauge group
• Antenna subtraction at NNLO with hadronic initial states: double real radiation for initial-initial configurations with two quark flavours
• $Apart: A Generalized Mathematica Apart Function
• Maximal Unitarity at Two Loops
• The 3-Loop Non-Singlet Heavy Flavor Contributions and Anomalous Dimensions for the Structure Function $F_2(x,Q^2)$ and Transversity
• A New Algorithm For The Generation Of Unitarity-Compatible Integration By Parts Relations
• Virtual three-loop corrections to Higgs boson production in gluon fusion for finite top quark mass
• Interpolation of Dense and Sparse Rational Functions and other Improvements in $\text{FireFly}$
• The three-loop cusp anomalous dimension in QCD
• Integrand-Level Reduction of Loop Amplitudes by Computational Algebraic Geometry Methods
• The gluon jet function at two-loop order
• Evaluating single-scale and/or non-planar diagrams by differential equations
• The Energy-Energy Correlation at Next-to-Leading Order in QCD, Analytically
• Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers
• Leading Nonlinear Tidal Effects and Scattering Amplitudes
• Analytic Results for Massless Three-Loop Form Factors
• Single soft gluon emission at two loops
• Two-Loop Four-Gluon Amplitudes with the Numerical Unitarity Method
• The three-loop cusp anomalous dimension in QCD and its supersymmetric extensions
• On the Generalized Harmonic Polylogarithms of One Complex Variable
• Low energy moments of heavy quark current correlators at four loops
• Three Loop Analysis of the Critical $O(N)$ Models in $6-\epsilon$ Dimensions
• The Ultraviolet Structure of Half-Maximal Supergravity with Matter Multiplets at Two and Three Loops
• Loop amplitudes in gauge theories: modern analytic approaches
• Binary Dynamics Through the Fifth Power of Spin at $\mathcal{O}(G^2)$
• The Sub-Leading Scattering Waveform from Amplitudes
• Four-loop photon quark form factor and cusp anomalous dimension in the large-$N_c$ limit of QCD
• The Four-Loop Konishi in N=4 SYM
• $t{t}^{\ast }$ equations, localization and exact chiral rings in 4d N=2 SCFTs
• Azurite: An algebraic geometry based package for finding bases of loop integrals
• Solving differential equations for Feynman integrals by expansions near singular points
• Fragmentation in Jets at NNLO
• Matter dependence of the four-loop cusp anomalous dimension
• Ultraviolet Cancellations in Half-Maximal Supergravity as a Consequence of the Double-Copy Structure
• Complete integration-by-parts reductions of the non-planar hexagon-box via module intersections
• Dimension-six matrix elements for meson mixing and lifetimes from sum rules
• Feynman integral relations from parametric annihilators
• Complete sets of logarithmic vector fields for integration-by-parts identities of Feynman integrals
• Leading-Color Two-Loop Amplitudes for Four Partons and a W Boson in QCD
• Structure of two-loop SMEFT anomalous dimensions via on-shell methods
• Analytic results for two-loop master integrals for Bhabha scattering I
• Antenna subtraction for the production of heavy particles at hadron colliders
• The last of the simple remainders
• Two-Loop Leading Color Corrections to Heavy-Quark Pair Production in the Gluon Fusion Channel
• Nine-Propagator Master Integrals for Massless Three-Loop Form Factors
• Geometric IR subtraction for real radiation
• Maximal Cuts in Arbitrary Dimension
• Two-body non-leptonic heavy-to-heavy decays at NNLO in QCD factorization
• Non-planar master integrals for the production of two off-shell vector bosons in collisions of massless partons
• Two-Loop Master Integrals for the mixed EW-QCD virtual corrections to Drell-Yan scattering
• Analytic results for planar three-loop four-point integrals from a Knizhnik-Zamolodchikov equation
• NLO Antenna Subtraction with Massive Fermions
• Anomalous magnetic moment with heavy virtual leptons
• Five-loop Konishi in N=4 SYM
• Four-loop quark form factor with quartic fundamental colour factor
• The $n_f^2$ contributions to fermionic four-loop form factors
• Next-to-Leading Order QCD Corrections to the Decay Width $H\to Z\gamma$
• Analytic Epsilon Expansions of Master Integrals Corresponding to Massless Three-Loop Form Factors and Three-Loop g-2 up to Four-Loop Transcendentality Weight
• The Sudakov form factor at four loops in maximal super Yang-Mills theory
• Baikov representations, intersection theory, and canonical Feynman integrals
• Two-Loop Maximal Unitarity with External Masses
• Bananas of equal mass: any loop, any order in the dimensional regularisation parameter
• Integration-by-parts reductions of Feynman integrals using Singular and GPI-Space
• Complete reduction of integrals in two-loop five-light-parton scattering amplitudes
• The two-loop five-particle amplitude in $\mathcal{N}=8$ supergravity
• The $Hb\bar{b}$ form factor to three loops in QCD
• Direct Solution of Integration-by-Parts Systems
• Simplified differential equations approach for Master Integrals
• Top-Yukawa effects on the $\beta$-function of the strong coupling in the SM at four-loop level
• Simultaneous decoupling of bottom and charm quarks
• Multi-loop techniques for massless Feynman diagram calculations
• Two-loop $gg\to Hg$ amplitude mediated by a nearly massless quark
• Two-Loop Master Integrals for the Planar QCD Massive Corrections to Di-photon and Di-jet Hadro-production
• Towards the exact Bremsstrahlung function of ABJM theory
• Comparison of post-Minkowskian and self-force expansions: Scattering in a scalar charge toy model
• Gluon-fusion Higgs production in the Standard Model Effective Field Theory
• Four-loop corrections with two closed fermion loops to fermion self energies and the lepton anomalous magnetic moment
• Two-loop helicity amplitudes for the production of two off-shell electroweak bosons in quark-antiquark collisions
• Les Houches 2021: Physics at TeV Colliders: Report on the Standard Model Precision Wishlist
• Leading QCD-induced four-loop contributions to the $\beta$-function of the Higgs self-coupling in the SM and vacuum stability
• Double-real corrections at O(alpha alpha_s) to single gauge boson production
• Master integrals for the four-loop Sudakov form factor
• Precise MS-bar light-quark masses from lattice QCD in the RI/SMOM scheme
• Pseudo-scalar Form Factors at Three Loops in QCD
• Analytic Computing Methods for Precision Calculations in Quantum Field Theory
• Double collinear splitting amplitudes at next-to-leading order
• Evaluating `elliptic' master integrals at special kinematic values: using differential equations and their solutions via expansions near singular points
• Towards a new approximation for pair-production and associated-production of the Higgs boson
• Evaluating two-loop non-planar master integrals for Higgs + jet production with full heavy-quark mass dependence
• Massive three-loop form factor in the planar limit
• Antenna subtraction with massive fermions at NNLO: Double real initial-final configurations
• The R*-operation for Feynman graphs with generic numerators
• The Dimensional Recurrence and Analyticity Method for Multicomponent Master Integrals: Using Unitarity Cuts to Construct Homogeneous Solutions
• An Integrand Reconstruction Method for Three-Loop Amplitudes
• Two-loop five-point massless QCD amplitudes within the IBP approach
• Gluon Regge trajectory at two loops from Lipatov's high energy effective action
• Moments of heavy quark correlators with two masses: exact mass dependence to three loops
• Calabi-Yau meets Gravity: A Calabi-Yau three-fold at fifth post-Minkowskian order
• The NLO fragmentation functions of heavy quarks into heavy quarkonia
• $O({\alpha }_s{v}^2)$ correction to $e^{+}{e}^{-}\to J/\psi +{\eta }_c$ at $B$ factories
• The real radiation antenna function for $S\to Q\bar{Q}q\bar{q}$ at NNLO QCD
• Massive planar and non-planar double box integrals for light Nf contributions to gg->tt
• The QCD NLO fragmentation functions for $c$ or $\bar{b}$ quark to $B_c$ or $B_c^{\ast }$ meson and their application
• Large $N_f$ quantum field theory
• Curvature-Squared Multiplets, Evanescent Effects and the U(1) Anomaly in N = 4 Supergravity
• Two-loop Master Integrals with the Simplified Differential Equations approach
• Four-loop wave function renormalization in QCD and QED
• Differential equations on unitarity cut surfaces
• Towards next-to-next-to-leading-log accuracy for the width difference in the $B_s-{\bar{B}}_s$ system: fermionic contributions to order $(m_c/m_b{)}^0$ and $(m_c/m_b{)}^1$
• Adequate bases of phase space master integrals for $gg\to h$ at NNLO and beyond
• Two-Loop Master Integrals for $q\bar{q}\to VV$: the Planar Topologies
• IBP reduction coefficients made simple
• The ghost-antighost-gluon vertex from the Curci-Ferrari model: Two-loop corrections
• Differential equations for loop integrals in Baikov representation
• Two-loop amplitudes for $qg\to Hq$ and $q\bar{q}\to Hg$ mediated by a nearly massless quark
• P-wave contribution to third-order top-quark pair production near threshold
• Two-loop massless QCD corrections to the $g+g\to H+H$ four-point amplitude
• A Numerical Routine for the Crossed Vertex Diagram with a Massive-Particle Loop
• RI'/SMOM scheme amplitudes for quark currents at two loops
• Finding Linear Dependencies in Integration-By-Parts Equations: A Monte Carlo Approach
• On Epsilon Factorized Differential Equations for Elliptic Feynman Integrals
• Locally finite two-loop amplitudes for off-shell multi-photon production in electron-positron annihilation
• Analytic results for planar three-loop integrals for massive form factors
• Leading transcedental contribution to the four-loop universal anomalous dimension in N=4 SYM
• Next-to-Next-to-Leading-Order QCD Prediction for the Photon-Pion Form Factor
• Non-planar form factors of generic local operators via on-shell unitarity and color-kinematics duality
• Reduction to master integrals via intersection numbers and polynomial expansions
• Subleading Regge limit from a soft anomalous dimension
• Counting master integrals: integration by parts vs. differential reduction
• Two-loop amplitudes for processes $gg\to Hg,qg\to Hq$ and $q\bar{q}\to Hg$ at large Higgs transverse momentum
• The non-planar contribution to the four-loop universal anomalous dimension in N=4 Supersymmetric Yang-Mills theory
• Two-loop QCD Corrections to $B_c$ Meson Leptonic Decays
• Maximal Unitarity for the Four-Mass Double Box
• Large-m_c Asymptotic Behaviour of O(alpha_s^2) Corrections to B -> X_s gamma
• Numerical multi-loop integrals and applications
• Analytic Computation of Three-point Energy Correlator in QCD
• Building Bases of Loop Integrands
• On the ABJM four-point amplitude at three loops and BDS exponentiation
• Next-to-leading order QCD corrections to paired $B_c$ production in $e^{+}{e}^{-}$ annihilation
• Electroweak corrections to double Higgs production at the LHC
• On the computation of finite bottom-quark mass effects in Higgs boson production
• Konishi Form Factor at Three Loop in $\mathcal{N}=4$ SYM
• Two-loop non-leptonic penguin amplitude in QCD factorization
• Calculation of two-loop QCD corrections for hadronic single top-quark production in the t channel
• Master Integrals for two-loop QCD corrections to Quasi PDFs
• Spontaneous chiral symmetry breaking in the massive Landau gauge: realistic running coupling
• Dimensional recurrence relations: an easy way to evaluate higher orders of expansion in $\epsilon$
• The QCD NLO Corrections to Inclusive $B_c^{\ast }$ Production in $Z^0$ Decays
• Master Integrals for the two-loop, non-planar QCD corrections to top-quark pair production in the quark-annihilation channel
• Form Factors of Chiral Primary Operators at Two Loops in ABJ(M)
• Two-loop Sudakov Form Factor in ABJM
• Four-loop QCD $\beta$-function with different fermion representations of the gauge group
• IBP methods at finite temperature
• Phase space analysis for three and four massive particles in final states
• Non-planarity through unitarity in ABJM
• Radiative-nonrecoil corrections of order alpha^2 (Z alpha)^5 to the Lamb shift
• Two-loop corrections to the triple Higgs boson production cross section
• Two-Loop integrals for CP-even heavy quarkonium production and decays: Elliptic Sectors
• Corrections of Order $\alpha {\alpha }_s$ to W Boson Decays
• The Bremsstrahlung function of $\mathcal{N}=2$ SCQCD
• Two-Loop anomalous dimensions of QCD operators up to dimension-sixteen and Higgs EFT amplitudes
• On phase-space integrals with Heaviside functions
• $O({\alpha }_s)$ corrections to $J/\psi +{\chi }_{cJ}$ production at $B$ factories
• TripleK: A Mathematica package for evaluating triple-K integrals and conformal correlation functions
• One-loop hexagon integral to higher orders in the dimensional regulator
• Two-loop master integrals for non-leptonic heavy-to-heavy decays
• The diamond rule for multi-loop Feynman diagrams
• Scattering Amplitudes and N-Body Post-Minkowskian Hamiltonians in General Relativity and Beyond
• On Epsilon Expansions of Four-loop Non-planar Massless Propagator Diagrams
• Two-loop planar master integrals for the production of off-shell vector bosons in hadron collisions
• Computation of $H\to gg$ in FDH and DRED: renormalization, operator mixing, and explicit two-loop results
• Global Poles of the Two-Loop Six-Point N=4 SYM integrand
• Two loop QCD corrections for the process Pseudo-scalar Higgs $\to 3$ partons
• Open problems in hot QCD
• One-loop Feynman Integral Reduction by Differential Operators
• Resummation of Goldstone Infrared Divergences: A Proof to All Orders
• A massive momentum-subtraction scheme
• Colour octet potential to three loops
• NLO fragmentation functions for a quark into a spin-singlet quarkonium: Same flavor case
• PV-Reduction of Sunset Topology with Auxiliary Vector
• ABJ(M) Chiral Primary Three-Point Function at Two-loops
• Master integrals for splitting functions from differential equations in QCD
• HepLib: A C++ Library for High Energy Physics
• Two-Loop integrals for CP-even heavy quarkonium production and decays
• Reduction of General One-loop Integrals Using Auxiliary Vector
• Evaluating four-loop conformal Feynman integrals by D-dimensional differential equations
• Exclusive decay of ${\rm Y}$ into $J/\psi +{\chi }_{c0,1,2}$
• Reduction of Feynman Integrals in the Parametric Representation II: Reduction of Tensor Integrals
• Effective Field Theory Islands from Perturbative and Nonperturbative Four-Graviton Amplitudes
• Three loop form factors of a massive spin-2 particle with nonuniversal coupling
• NLO QCD corrections to $B_c$-pair production in photon-photon collision
• On three-point functions in ABJM and the latitude Wilson loop
• Two-Loop QCD Correction to massive spin-2 resonance $\to$ 3 gluons
• The Exclusive Decay of Upsilon into $h_c$, the $X(3940)$ and $X(4160)$
• Two loop QCD amplitudes for di-pseudo scalar production in gluon fusion
• FaRe: a Mathematica package for tensor reduction of Feynman integrals
• Calculating four-loop massless propagators with Forcer
• On structure constants with two spinning twist-two operators
• Four-point amplitudes in $\mathcal{N}=2$ SCQCD
• On the scattering of gluons in the GKP string
• Next-to-leading order QCD corrections for the charmonium production via the channel $e^{+}{e}^{-}\to H(|c\bar{c}⟩)+\gamma$ round the $Z^0$ peak
• Feynman Integrals from Positivity Constraints
• One-loop unquenched three-gluon and ghost-gluon vertex in the Curci-Ferrari model
• The real-virtual antenna functions for $S\to Q\bar{Q}X$ at NNLO QCD
• Two-Loop master integrals for heavy-to-light form factors of two different massive fermions
• On canonical differential equations for Calabi-Yau multi-scale Feynman integrals
• ABJM $\theta$-Bremsstrahlung at four loops and beyond
• ABJM $\theta$-Bremsstrahlung at four loops and beyond: non-planar corrections
• Radiative-nonrecoil corrections of order alpha^2 (Z alpha) E_F to the hyperfine splitting of muonium
• Two-loop Integral Reduction from Elliptic and Hyperelliptic Curves
• Independently Parameterised Momenta Variables and Monte Carlo IR Subtraction
• NLO QCD Corrections for $J/\psi +c+\bar{c}$ Production in Photon-Photon Collision
• Twisted Riemann bilinear relations and Feynman integrals
• Next-to-leading order QCD corrections to the production of $B_c$ and $B_c^{\ast }$ through $W^{+}$-boson decays
• Feynman integral reduction using Gröbner bases
• Universal Treatment of Reduction for One-Loop Integrals in Projective Space
• Is the colour-octet mechanism consistent with the double $J/\psi$ production measurement at B-factories?
• Next-to-leading-order study of $J/\psi$ angular distributions in $e^{+}{e}^{-}\to J/\psi +{\eta }_c,{\chi }_{cJ}$ at $\sqrt{s}\approx 10.6$ GeV
• Four-loop renormalization of QCD with a reducible fermion representation of the gauge group: anomalous dimensions and renormalization constants
• Reconciling the nonrelativistic QCD prediction and the $J/\psi \to 3\gamma$ data
• Master integrals for $\mathcal{O}(\alpha {\alpha }_s)$ corrections to $H\to Z{Z}^{\ast }$
• Heavy quark and gluino potentials to two loops
• Rings: an efficient Java/Scala library for polynomial rings
• The gravitational Compton amplitude from flat and curved spacetimes at second post-Minkowskian order
• NLL QCD contribution of the Electromagnetic Dipole operator to B-> X_s gamma gamma
• Les Houches 2023 -- Physics at TeV Colliders: Report on the Standard Model Precision Wishlist
• The static quark potential to three loops in perturbation theory
• Analysis of double-$J/\psi$ production in $Z$ decay at next-to-leading-order QCD accuracy
• One-loop corrections to the processes $e^{+}{e}^{-}\to \gamma ,Z\to J/\psi {\eta }_c$ and $e^{+}{e}^{-}\to Z\to J/\psi J/\psi$
• Renormalized $\epsilon$-finite master integrals and their virtues: the three-loop self energy case
• Bottomonium production associated with a photon at a high luminosity $e^{+}{e}^{-}$ collider with next-to-leading order QCD corrections
• Associated charmonium-bottomonium production in a single boson $e^{+}{e}^{-}$ annihilation
• Spin-2 Form Factors at Three Loop in QCD
• A note on three-point functions of unprotected operators
• NLO corrections to ${\chi }_{bJ}$ to two-$J/\psi$ exclusive decay processes
• Relativistic corrections to ${\rm Y}$ exclusive decay into double $S-$wave charmonia
• From perturbative calculations of the QCD static potential towards four-loop pole-running heavy quarks masses relation
• Three twist-two, two spins, two loops
• $J/\psi$ associated production with a bottom quark pair from the Higgs boson decay in next-to-leading order QCD
• Comprehensive studies of ${\rm Y}$ inclusive production in $Z$ boson decay
• Evaluating the last missing ingredient for the three-loop quark static potential by differential equations
• QCD one-loop correction to Higgs boson decay into quarkonium-pair
• HQET sum rules for matrix elements of dimension-six four-quark operators for meson lifetimes within and beyond the Standard Model
• NLO QCD Corrections to ${\eta }_c+h_c(1P)/{\psi }_{1,2}(1D)$ Production at B-factories
• Dimensional schemes for cross sections at NNLO
• Reduction to master integrals and transverse integration identities
• Three-loop master integrals for the Higgs boson self-energy with internal top-quarks and W-bosons
• Heavy quark mass expansion of vector and tensor currents and intrinsic charm in nucleon form factors
• Classical gravitational scattering from a gauge-invariant double copy
• Observables and Unconstrained Spin Tensor Dynamics in General Relativity from Scattering Amplitudes
• Inclusive production of heavy quarkonium ${\eta }_Q$ via $Z$ boson decays within the framework of nonrelativistic QCD
• NNLO QED contribution to the $\mu e\to \mu e$ elastic scattering
• Reduction of Feynman Integrals in the Parametric Representation
• Phi4tools: Compilation of Feynman diagrams for Landau-Ginzburg-Wilson theories
• NLO QCD Corrections for ${\chi }_{cJ}$ Inclusive Production at $B$ Factories
• Non-relativistic high-energy physics: top production and dark matter annihilation
• Evaluation of three-loop self-energy master integrals with four or five propagators
• Next-to-leading order QCD corrections to $Z\to {\eta }_Q+Q+\bar{Q}$
• Track 3: Computations in theoretical physics -- techniques and methods
• Improved analysis of double $J/\psi$ production in $Z$-boson decay
• Unitarity methods for Mellin moments of Drell-Yan cross sections
• Automated One-loop Computation in Quarkonium Process within NRQCD Framework
• A new method for finding more symmetry relations of Feynman integrals
• Master Integrals for double real radiation emission in heavy-to-light quark decay
• Impact of $Z\to {\eta }_{c,b}+g+g$ on the inclusive ${\eta }_{c,b}$ meson yield in $Z$-boson decay
• Multi-loop calculations: numerical methods and applications
• NLO QCD Corrections to Inclusive Charmonium and $B_c$ Meson Production in $W^{+}$ Decays
• The real photon structure functions in massive parton model in NLO
• The polarized photon structure function $g_1^{\gamma }(x,Q^2)$ in massive parton model in NLO
• Inclusive $J/\psi$ and ${\eta }_c$ production in ${\rm Y}$ decay at $\mathcal{O}({\alpha }_s^5)$ in nonrelativistic QCD factorization
• Extended Projection Method for Massive Fermion
• $\mathcal{O}({\alpha }_s)$ corrections to $e^{+}{e}^{-}\to J/\psi +{\eta }_{c2}({\chi }_{c1}^{\prime })$ at $B$ factories
• QCD corrections of $e^{+}{e}^{-}\to J/\psi +c+\bar{c}$ using the principle of maximum conformality
• Top-Quark Decay at Next-to-Next-to-Next-to-Leading Order in QCD
• Two-loop form factors for $P$-wave quarkonium production and decay
• Evaluating Feynman Integrals through differential equations and series expansions
• Evaluating master integrals in non-factorizable corrections to $t$-channel single-top production at NNLO QCD
• A Recursive Method to Calculate UV-divergent Parts at One-Loop Level in Dimensional Regularization
• The Radial Action from Probe Amplitudes to All Orders
• Two-loop amplitude for mixed QCD-EW corrections to $gg\to Hg$
• Revisit prompt $J/\psi$ production in associated with Higgs Boson via gluon fusion at the LHC
• Magnetic moment of a bound electron
• Inclusive ${\chi }_{cJ}$ production in ${\rm Y}$ decay at $\mathcal{O}({\alpha }_s^5)$ in NRQCD factorization
• IBP reduction via Gröbner bases in a rational double-shift algebra
• Transversity and heavy quark production on hadron colliders
• Reduction of planar double-box diagram for single-top production via auxiliary mass flow
• Transition Form-Factor for ${\eta }_Q$ at NNLO in the strong coupling ${\alpha }_s$ and with all-order $v^2$ resummation
• A Feynman integral depending on two elliptic curves
• $X(3860)$ production in association with $J/\psi$ via $e^{+}{e}^{-}$ annihilation at Belle
• The Stratification of Rigidity
• Next-to-leading order analysis of $J/\psi +\gamma$ production in photon-photon collisions at CEPC
• Higgs probes of top quark contact interactions and their interplay with the Higgs self-coupling