Asymptotic expansion of Feynman integrals near threshold

Abstract

We present general prescriptions for the asymptotic expansion of massive multi-loop Feynman integrals near threshold. As in the case of previously known prescriptions for various limits of momenta and masses, the terms of the threshold expansion are associated with subgraphs of a given graph and are explicitly written through Taylor expansions of the corresponding integrands in certain sets of parameters. They are manifestly homogeneous in the threshold expansion parameter, so that the calculation of the given Feynman integral near the threshold reduces to the calculation of integrals of a much simpler type. The general method is illustrated by two-loop two-point and three-point diagrams. We discuss the use of the threshold expansion for problems of physical interest, such as the next-to-next-to-leading order heavy quark production cross sections close to threshold and matching calculations and power counting in non-relativistic effective theories.

24 pages, LaTeX, 4 figures included via epsf.sty

References in corpus (1)

• Two-loop Correction to the Leptonic Decay of Quarkonium

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• Infrared properties of five-point massive amplitudes in N=4 SYM on the Coulomb branch
• Effective Lagrangians in bound state calculations
• On the contribution of the electromagnetic dipole operator ${\mathcal{O}}_7$ to the ${\bar{B}}_s\to {\mu }^{+}{\mu }^{-}$ decay amplitude
• Finite Volume Corrections to the Electromagnetic Mass of Composite Particles
• Dissecting polytopes: Landau singularities and asymptotic expansions in $2\to 2$ scattering
• Can $B->X_c\ell \nu$ help us extract |V_{ub}| ?
• Threshold expansion for heavy-light systems and flavor off-diagonal current-current correlators
• Quark and gluon two-loop beam functions for leading-jet $p_T$ and slicing at NNLO
• Parity-Violating Møller Scattering at NNLO: Closed Fermion Loops
• Regge behavior in effective field theory
• NLO fragmentation functions for a quark into a spin-singlet quarkonium: Same flavor case
• Evaluating four-loop conformal Feynman integrals by D-dimensional differential equations
• A Finite $S$-Matrix
• Two-Loop integrals for CP-even heavy quarkonium production and decays
• ${\chi }_{QJ}\to {\ell }^{+}{\ell }^{-}$ within and beyond the Standard Model
• Effective Field Theory Islands from Perturbative and Nonperturbative Four-Graviton Amplitudes
• Effective Field Theory with Dibaryon Fields: Nucleon-Nucleon amplitudes at NNLO
• Recent Progress in Perturbative Quantum Field Theory
• The Sommerfeld Enhancement in the Scotogenic Model with Large Electroweak Scalar Multiplets
• Diboson production in the SMEFT from gluon fusion
• Structure Function Sum rules for Systems with Large Scattering Lengths
• Total Born cross section of $e^{+}{e}^{-}$-pair production in relativistic ion collisions from differential equations
• Resummation methods for Master Integrals
• One-loop matching of $CP$-odd four-quark operators to the gradient-flow scheme
• Chiral Perturbation Theory in a Nuclear Background
• Three-loop banana integrals with four unequal masses
• Covariant calculation of a two-loop test of nonrelativistic QCD factorization
• Asymptotic analysis of Feynman diagrams and their maximal cuts
• A factorization theorem connecting the light-cone distribution amplitudes of heavy-flavor mesons in QCD and HQET
• The NNLO soft function for N-jettiness in hadronic collisions
• Subtracting IR Renormalons from Wilson Coefficients: Uniqueness and power dependences on ${\Lambda }_{\mathrm{QCD}}$
• Calculations of binding energies and masses of heavy quarkonia using renormalon cancellation
• One-loop effective potential in the non-local supersymmetric gauge theory
• Top quark production near threshold
• Renormalization group improved pQCD prediction for ${\rm Y}(1S)$ leptonic decay
• 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
• A factorization approach to next-to-leading-power threshold logarithms
• Details on the $\mathcal{O}(m_e{\alpha }^6)$ Positronium Hyperfine Splitting due to Single Photon Annihilation
• Two-loop QCD corrections to the $V\to q\bar{q}g$ helicity amplitudes with axial-vector couplings
• Gapped Goldstones at the cut-off scale: a non-relativistic EFT
• Lepton pair production at NNLO in QED with EW effects
• Special case of sunset: reduction and epsilon-expansion
• Two-loop splitting in double parton distributions: the colour non-singlet case
• On supersymmetric gauge theories with higher derivatives and nonlocal terms in the matter sector
• Factorization of low-energy gluons in exclusive processes
• Threshold singularities, dispersion relations and fixed-order perturbative calculations
• Two-loop corrections to false vacuum decay in scalar field theory
• Radiative corrections and Monte Carlo tools for low-energy hadronic cross sections in $e^{+}{e}^{-}$ collisions
• Subleading Effects in Soft-Gluon Emission at One-Loop in Massless QCD
• $Z$ boson radiative decays to a $P$-wave quarkonium at NNLO and LL accuracy
• Natural Boundaries for Scattering Amplitudes
• Heavy meson semileptonic differential decay rate in two dimensions in the large Nc
• One-loop matching of the $CP$-odd three-gluon operator to the gradient flow
• New Covariant Feynman Rules for Effective Field Theories
• Recoil corrections to the energy levels of hydrogenic atoms
• $Z$ boson radiative decays to a $S$-wave quarkonium at NNLO and NLL accuracy
• Theory for quarkonium: from NRQCD factorization to soft gluon factorization
• Resummation of double logarithms in loop-induced processes with effective field theory
• Massive two-loop four-point Feynman integrals at high energies with AsyInt
• Exploring slicing variables for jet processes
• Non-factorizable virtual corrections to Higgs boson production in weak boson fusion beyond the eikonal approximation
• $p$-Forms on the Celestial Sphere
• One-loop Matching of Scotogenic Model onto Standard Model Effective Field Theory up to Dimension 7
• Invariant-mass distribution of top-quark pairs and top-quark mass determination
• The leading twist light-cone distribution amplitudes for the S-wave and P-wave Bc mesons
• Complex-mass renormalization in hadronic EFT: applicability at two-loop order
• QCD radiative corrections to the soft spectator contribution in the wide angle Compton scattering
• $P$-wave quarkonium wavefunctions at the origin in the $\overline{\mathrm{MS}}$ scheme
• Matching the heavy-quark fields in QCD and HQET at four loops
• XEFT, the challenging path up the hill: dim = 6 and dim = 8
• Higher order hadronic and leptonic contributions to the muon $g-2$
• Next-to-leading order QCD corrections to the production of $B_c$ and $B_c^{\ast }$ through $W^{+}$-boson decays
• Evaluating double and triple (?) boxes
• The Higgs-gluon form factor at three loops in QCD with three mass scales
• Multiple soft-photon emission at next-to-leading power to all orders
• Expansion by regions meets angular integrals
• Some recent results on evaluating Feynman integrals
• New proofs for the two Barnes lemmas and an additional lemma
• Reconciling the nonrelativistic QCD prediction and the $J/\psi \to 3\gamma$ data
• Complete One-loop Structure of the Type-(I+II) Seesaw Effective Field Theory
• On the one-loop effective potential in nonlocal supersymmetric theories
• Three-loop non-singlet matching coefficients for heavy quark currents
• $\mathcal{O}({\alpha }_s^2)$ corrections to $J/\psi +{\chi }_{c0,1,2}$ production at $B$ factories
• Factorizing the hard and soft spectator scattering contributions for the nucleon form factor F_1 at large Q^2
• General Relativity from Intersection Theory
• Relativistic corrections to the static energy in terms of Wilson loops at weak coupling
• On renormalons of static QCD potential at $u=1/2$ and $3/2$
• Probing heavy meson lightcone distribution amplitudes with heavy quark spin symmetry
• Learning Feynman integrals from differential equations with neural networks
• Master integrals for bipartite cuts of three-loop photon self energy
• Once more on the Higgs decay into two photons
• Manifestly Soft Gauge Invariant Formulation of vNRQCD
• Renormalon-free definition of the gluon condensate within the large-${\beta }_0$ approximation
• Post-Newtonian Dynamics of Spinning Black Hole Binaries in Einstein-Scalar-Gauss-Bonnet Gravity
• Double-Real-Virtual and Double-Virtual-Real Corrections to the Three-Loop Thrust Soft Function
• Next-to-leading-order QCD corrections to a vector bottomonium radiative decay into a charmonium
• One-loop corrections to the double-real emission contribution to the zero-jettiness soft function at N3LO in QCD
• Chiral Perturbation Theory Reflections on Effective Theories of the Standard Model
• Heavy Quarkonium Physics beyond the Next-to-Next-to-Leading Order of NRQCD
• Decay constant of $B_c^{\ast }$ accurate up to $\mathcal{O}({\alpha }_s^3)$
• Expansion by regions with pySecDec
• OPITeR: A program for tensor reduction of multi-loop Feynman Integrals
• Tensor Reduction for Feynman Integrals with Lorentz and Spinor Indices
• Soft-Collinear Supersymmetry
• The method of expansion of Feynman integrals
• Removing phase-space restrictions in factorized cross sections
• Small-angle scattering and quasiclassical approximation beyond leading order
• $\mathcal{O}({\alpha }_s{v}^2)$ corrections to hadronic decay of vector quarkonia
• The Sky Remembers everything: Celestial amplitude, Shadow and OPE in quadratic EFT of gravity
• Towards pair production near threshold with unstable particle effective theory
• Top quark mass definition and top quark pair production near threshold at the NLC
• Charm-quark mass effects in NRQCD matching coefficients and the leptonic decay of the ${\rm Y}(1S)$ meson
• Machine Learning Post-Minkowskian Integrals
• Structure-dependent QED effects in exclusive $B$-meson decays
• UV contribution and power dependence on ${\Lambda }_{\mathrm{QCD}}$ of Adler function
• QCD one-loop correction to Higgs boson decay into quarkonium-pair
• Angular distribution of thrust axis with power-suppressed contribution in e+e- annihilation
• Heavy Quarkonium and Nonrelativistic Effective Field Theories
• Specific three-loop contributions to $b\to s\gamma$ associated with the current-current operators
• The SCET_II and factorization
• Observation prospects of leptonic and Dalitz decays of pseudoscalar quarkonia
• $(Z\alpha {)}^4$ order of the polarization operator in Coulomb field at low energy
• Generalized eikonal identities for charged currents
• Region analysis of $H\to \gamma \gamma$ via a bottom quark loop
• NNNLO correction to the toponium and bottomonium wave-functions at the origin
• Analytical evaluation of certain on-shell two-loop three-point diagrams
• Evaluating the last missing ingredient for the three-loop quark static potential by differential equations
• NNLO electron structure functions (PDFs) from SCET
• The $q_{\mathrm{T}}$ and $\Delta {\varphi }_{t\bar{t}}$ spectra in top-antitop hadroproduction at NNLL+NNLO: the interplay of soft-collinear resummation and Coulomb singularities
• New Physics Search in Flavour Physics
• A Study of Power Suppressed Contributions in $J/\psi \to p\bar{p}$ Decay
• Disperon QED
• Five-loop massless propagator integrals
• SM single-top production at hadron colliders
• Mass Dependence of Higgs Production at Large Transverse Momentum
• Renormalon Subtraction in OPE by Dual Space Approach: Nonlinear Sigma Model and QCD
• An Elliptic One-Loop Amplitude in Anti-de-Sitter Space
• Energy and decay width of the pi-K atom
• Supersymmetric structure of electroweak Sudakov corrections
• Resummation of terms enhanced by trilinear squark-Higgs couplings in the MSSM
• Inclusive production of heavy quarkonium ${\eta }_Q$ via $Z$ boson decays within the framework of nonrelativistic QCD
• Classical gravitational scattering from a gauge-invariant double copy
• Two-loop corrections to Lamb shift and hyperfine splitting in hydrogen via multi-loop methods
• Mass Dependence of Higgs Production at Large Transverse Momentum through a Bottom Quark Loop
• Decoupling heavy particles simultaneously
• Photon pair production in gluon fusion: Top quark effects at NLO with threshold matching
• Dark origin of quark flavor hierarchy and mixing
• Two-Loop QCD-EW Master Integrals for Z Plus Jet Production at Large Transverse Momentum
• Soft-Collinear Factorization and Sudakov Resummation of Heavy Meson Decay Amplitudes with Effective Field Theories
• Running couplings for the simultaneous decoupling of heavy quarks
• Two-loop mixed QCD-electroweak amplitudes for $Z+$jet production at the LHC: bosonic corrections
• Three-Loop OPE Wilson Coefficients of Dimension-Four Operators for (Axial-)Vector and (Pseudo-)Scalar Current Correlators
• Color-octet contributions for $J/\psi$ inclusive production at B factories in soft gluon factorization
• Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes
• Non-relativistic high-energy physics: top production and dark matter annihilation
• Threshold corrections to the gamma t anti-t vertex at O(alpha alpha(s))
• The HiggsTools Handbook: Concepts and observables for deciphering the Nature of the Higgs Sector
• $B_c\to {\eta }_c$ form factors at large recoil: Interplay of soft-quark and soft-gluon dynamics
• The method of direct expansions of Feynman integrals
• The High-Temperature Expansion of the Thermal Sunset
• Analytic Result of Higgs Boson Decay to Gluons with Full Quark Mass Dependence
• NLO QCD Corrections to Inclusive Charmonium and $B_c$ Meson Production in $W^{+}$ Decays
• Improved analysis of double $J/\psi$ production in $Z$-boson decay
• Next-to-leading order QCD corrections to $Z\to {\eta }_Q+Q+\bar{Q}$
• Matching the Standard Model to Heavy-Quark Effective Theory and Nonrelativistic QCD
• Two loop QCD corrections to $e^{+}{e}^{-}\to J/\psi +{\eta }_c$ in asymptotic expansion
• Sudakov Logarithms in Four-Fermion Electroweak Processes at High Energy
• An improved calculation of the $D_{(s)}^{\ast }{D}_{(s)}V$ and $B_{(s)}^{\ast }{B}_{(s)}V$ couplings from light-cone sum rules
• The hierarchical three-body problem at $\mathcal{O}(G^2)$
• Radiative distortion of kinematic edges in cascade decays
• Radiative decays ${\chi }_{cJ}\to V\gamma$ within the QCD factorisation framework
• Unregulated Divergences of Feynman Integrals
• Short-range force between two Higgs bosons
• Correction to the energy spectrum of ${}^1{S}_0$ heavy quarkonia due to two-gluon annihilation effect
• Threshold Resummation for Dark-Matter Production at the LHC
• On multi-propagator angular integrals
• Automated One-loop Computation in Quarkonium Process within NRQCD Framework
• A new method for finding more symmetry relations of Feynman integrals
• One-loop corrections of order (Z alpha)^6m_1/m_2, (Z alpha)^7 to the muonium fine structure
• Unstable-particle effective field theory
• Renormalization group analysis of electromagnetic properties of the deuteron
• Evaluating Feynman Integrals through differential equations and series expansions
• Symmetry Restoration in the SMEFT: Finite Counterterms for a Non-Anticommuting ${\gamma }_5$
• Analytic auxiliary mass flow to compute master integrals in singular kinematics
• Evaluating master integrals in non-factorizable corrections to $t$-channel single-top production at NNLO QCD
• Singlet and non-singlet three-loop massive form factors
• Universal structure of radiative QED amplitudes at one loop
• The soft-energy region in the radiative decay of bound states
• NRQCD, Effective Field Theories and Potential Models
• From Models to SMEFT and Back?
• Next-to-leading power two-loop soft functions for the Drell-Yan process at threshold
• Scattering Amplitudes for Binary Systems beyond GR
• One Formula To Match Them All: The Bispinor Universal One-Loop Effective Action
• Role of Resonances in Heavy Meson Processes within Standard Model and Beyond
• Applications of QCD
• Heavy Quarkonium at finite temperature and chemical potential
• NNLO corrections to false vacuum decay rate in thin-wall approximation
• Gauge dependence and matching procedure of a nonrelativistic QED/QCD boundstate formalism
• Exclusive decays ${\chi }_{cJ}\to K^{\ast }(892)K$ within the effective field theory framework
• Scattering Amplitudes in Gauge Theories
• Nonrelativistic effective field theory of unstable top
• An Effective Field Theory Look at Deep Inelastic Scattering
• A theoretical update on t \bar{t} production near threshold
• Effective Field Theories for the LHC
• QCD corrections of $e^{+}{e}^{-}\to J/\psi +c+\bar{c}$ using the principle of maximum conformality
• $\mathcal{O}({\alpha }_s)$ corrections to $e^{+}{e}^{-}\to J/\psi +{\eta }_{c2}({\chi }_{c1}^{\prime })$ at $B$ factories
• Higher-Order Corrections to Higgs Boson Amplitudes with Full Quark Mass Dependence in Quantum Chromodynamics
• Impact on the decay rate of $B_s\to {\mu }^{+}{\mu }^{-}$ from the dispersive two-photon transition
• Dark Matter Recoupling
• Higgs boson decay to massive bottom quarks at order ${\alpha }_s^4$ induced by top-quark Yukawa couplings
• A coordinate description of partonic processes
• One-loop matching of the LEFT to the QCD gradient flow
• Large mass expansion in two-loop QCD corrections of para-charmonium decay
• The Soft Régime and βFunction of NRQCD
• Quantum dynamics of perfect fluids
• Effective string theory for vortex lines in fluids and superfluids
• Three-loop vertex corrections
• $\sigma (e^{+}{e}^{-}\to hadrons)$ and the Heavy Quark Masses
• NLO electroweak potentials for minimal dark matter and beyond
• Some recent progress in understanding exclusive double charmonium production at $B$ factories
• CoLoRFulNNLO for hadron collisions: integrating the iterated single unresolved subtraction terms
• A stroll through the loop-tree duality
• QCD Beyond Leading Power
• Effective Angular Momentum Operators in NRQED and Matching at One-Loop Order
• The analytic two-loop soft function for leading-jet $p_T$
• Soft Integrals and Soft Anomalous Dimensions at N${}^3$LO and Beyond
• Photon pair production in gluon fusion: Top quark effects around threshold
• Mixed QCD-EW corrections to $W$-pair production at electron-positron colliders
• QCD calculations of radiative heavy meson decays with subleading power corrections
• Potential Nonrelativistic QCD and Heavy Quarkonium Spectrum in Next-to-Next-to-Next-to-Leading Order
• Subleading Effects in Soft-Gluon Emission at One-Loop in Massive QCD
• An Effective Field Theory of Magneto-Elasticity
• Anomalous Ward identities for on-shell amplitudes at the conformal fixed point