Explicit solutions of the 3--loop vacuum integral recurrence relations

Abstract

Explicit formulas for the solutions of the recurrence relations for 3--loop vacuum integrals are suggested. This formulas can be used for direct calculations and demonstrate a high efficiency. They also produce a new type of recurrence relations over the space--time dimension.

5 pages, misprint in the intermediate formula corrected

References in corpus (5)

• $O(\alpha {\alpha }_s^2)$ correction to the electroweak $\rho$ parameter
• Corrections of order ${\cal O}(G_F M_t^2 \as^2)$ to the $\rho$ parameter
• QCD Corrections from Top Quark to Relations between Electroweak Parameters to Order ${\alpha }_s^2$
• Two-Loop Gluon-Condensate Contributions To Heavy-Quark Current Correlators: Exact Results And Approximations
• Analytical on-shell QED results: 3-loop vacuum polarization, 4-loop beta-function and the muon anomaly

Cited by in corpus (115)

• Five-Loop Running of the QCD coupling constant
• Hadronic Z- and tau-Decays in Order alpha_s^4
• Black Hole Binary Dynamics from the Double Copy and Effective Theory
• Quark and gluon form factors to three loops
• Three-Loop Polarization Function and $\mathcal{O}({\alpha }_s^2)$ Corrections to the Production of Heavy Quarks
• Scalar Correlator at O(alpha_s^4), Higgs Decay into b-quarks and Bounds on the Light Quark Masses
• Generalized Recurrence Relations for Two-loop Propagator Integrals with Arbitrary Masses
• Integration-by-parts reductions from unitarity cuts and algebraic geometry
• New results for the epsilon-expansion of certain one-, two- and three-loop Feynman diagrams
• Explicit solutions of the multi-loop integral recurrence relations and its application
• Four Loop Massless Propagators: an Algebraic Evaluation of All Master Integrals
• Quark Mass and Field Anomalous Dimensions to $\mathcal{O}({\alpha }_s^5)$
• Ultraviolet Properties of N = 8 Supergravity at Five Loops
• Cuts of Feynman Integrals in Baikov representation
• Maximal cuts and differential equations for Feynman integrals. An application to the three-loop massive banana graph
• All master integrals for three-jet production at NNLO
• Adler Function, Sum Rules and Crewther Relation of Order O(alpha_s^4): the Singlet Case
• Vector Correlator in Massless QCD at Order O(alpha_s^4) and the QED beta-function at five loop
• On the Precise Determination of the Fermi Coupling Constant from the Muon Lifetime
• The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
• Five-loop quark mass and field anomalous dimensions for a general gauge group
• FeynHelpers: Connecting FeynCalc to FIRE and Package-X
• Two-Loop Four-Gluon Amplitudes with the Numerical Unitarity Method
• Complete QCD Corrections to Hadronic $Z$--Decays in Order ${\alpha }_s^4$
• Feynman Integrals in Dimensional Regularization and Extensions of Calabi-Yau Motives
• Azurite: An algebraic geometry based package for finding bases of loop integrals
• Complete integration-by-parts reductions of the non-planar hexagon-box via module intersections
• Five-loop fermion anomalous dimension for a general gauge group from four-loop massless propagators
• Automatic Computation of Feynman Diagrams
• Complete sets of logarithmic vector fields for integration-by-parts identities of Feynman integrals
• Feynman integral relations from parametric annihilators
• The two-loop five-point amplitude in $\mathcal{N}=8$ supergravity
• A practical criterion of irreducibility of multi--loop Feynman integrals
• On the evaluation of a certain class of Feynman diagrams in x-space: Sunrise-type topologies at any loop order
• Differential equations from unitarity cuts: nonplanar hexa-box integrals
• ep-Finite Basis of Master Integrals for the Integration-By-Parts Method
• Strange Quark Mass from Tau Lepton Decays with O(alpha_s^3) Accuracy
• Maximal Cuts in Arbitrary Dimension
• Integration by parts: An introduction
• On a procedure to derive $\epsilon$-factorised differential equations beyond polylogarithms
• Isolated photon production in association with a jet pair through next-to-next-to-leading order in QCD
• Applying Groebner Bases to Solve Reduction Problems for Feynman Integrals
• Integration-by-parts reductions of Feynman integrals using Singular and GPI-Space
• Two-Loop Static QCD Potential for General Colour State
• Multi-loop techniques for massless Feynman diagram calculations
• $M(B_c^{\ast })-M(B_c)$ Splitting from Nonrelativistic Renormalization Group
• Massless correlators of vector, scalar and tensor currents in position space at orders alpha_s^3 and alpha_s^4: explicit analytical results
• The Cross Section of e^+ e^- Annihilation into Hadrons of Order alpha_s^4 n_f^2 in Perturbative QCD
• Solving Recurrence Relations for Multi-Loop Feynman Integrals
• The ice cone family and iterated integrals for Calabi-Yau varieties
• The FORM project
• Analytic Computing Methods for Precision Calculations in Quantum Field Theory
• Scattering Amplitudes in Quantum Field Theory
• The Dimensional Recurrence and Analyticity Method for Multicomponent Master Integrals: Using Unitarity Cuts to Construct Homogeneous Solutions
• Mathematical properties of nested residues and their application to multi-loop scattering amplitudes
• Two-loop helicity amplitudes for $gg\to ZZ$ with full top-quark mass effects
• The relation between the QED charge renormalized in MSbar and on-shell schemes at four loops, the QED on-shell beta-function at five loops and asymptotic contributions to the muon anomaly at five and six loops
• Forcer, a FORM program for the parametric reduction of four-loop massless propagator diagrams
• Towards Order alpha_s^4 Accuracy in tau-decays
• Two-Loop Vertices in Quantum Field Theory: Infrared Convergent Scalar Configurations
• Leading singularities in Baikov representation and Feynman integrals with uniform transcendental weight
• Differential equations on unitarity cut surfaces
• Differential equations for loop integrals in Baikov representation
• Fermionic Corrections to the Three-Loop Matching Coefficient of the Vector Current
• Numerical multi-loop integrals and applications
• Three-loop mixed QCD-electroweak corrections to Higgs boson gluon fusion
• An Algorithm to Construct Groebner Bases for Solving Integration by Parts Relations
• A study of Feynman integrals with uniform transcendental weights and the symbology from dual conformal symmetry
• Three-Loop Radiative Corrections to Lamb Shift and Hyperfine Splitting
• Hypergeometric representation of a four-loop vacuum bubble
• Evaluating multiloop Feynman integrals by Mellin-Barnes representation
• Massless Propagators, $R(s)$ and Multiloop QCD
• Pentagon integrals to arbitrary order in the dimensional regulator
• S-bases as a tool to solve reduction problems for Feynman integrals
• Beam functions for $N$-jettiness at N${}^3$LO in perturbative QCD
• New Polarization Operator Contributions to Lamb Shift and Hyperfine Splitting
• New Results in Four and Five Loop QED calculations
• Laurent series expansion of sunrise-type diagrams using configuration space techniques
• Forcer: a FORM program for 4-loop massless propagators
• ParFORM: recent development
• Two-loop Feynman integrals for leading colour $t\bar{t}W$ production at hadron colliders
• Three-loop vacuum integrals in FORM and REDUCE
• On the reduction of Feynman integrals to master integrals
• Five-loop vacuum polarization in pQCD: O(m_q^2α_s^4 n_f^2) contribution
• Calculating four-loop massless propagators with Forcer
• Classical 3-loop 2-body diagrams
• Field theoretic study of electron-electron interaction effects in Dirac liquids
• Two-Loop Vacuum Diagrams in Background Field and Heisenberg-Euler Effective Action
• Syzygies Probing Scattering Amplitudes
• Maximal transcendental weight contribution of scattering amplitudes
• ParFORM: Parallel Version of the Symbolic Manipulation Program FORM
• Some recent results on evaluating Feynman integrals
• Symmetries of Feynman integrals and the Integration By Parts method
• Evaluating double and triple (?) boxes
• Two-Loop Diagrammatics in a Self-Dual Background
• "Background Field Integration-by-Parts" and the Connection Between One-Loop and Two-Loop Heisenberg-Euler Effective Actions
• Bubble diagram through the Symmetries of Feynman Integrals method
• A first computation of three-loop master integrals for the production of two off-shell vector bosons with different masses
• The algebraic locus of Feynman integrals
• A new reduction strategy for special negative sectors of planar two-loop integrals without Laporta algorithm
• Multiloop Calculations: towards R at Order alpha_s^4
• Towards QCD running in 5 loops: quark mass anomalous dimension
• On the two-loop amplitude for $gg\to ZZ$ production with full top-mass dependence
• Kite diagram through Symmetries of Feynman Integrals
• A new method for finding more symmetry relations of Feynman integrals
• pfd-parallel, a Singular/GPI-Space package for massively parallel multivariate partial fractioning
• Evaluating master integrals in non-factorizable corrections to $t$-channel single-top production at NNLO QCD
• Solving recurrence relations for multiloop integrals in the limit of large values of the dimensional regularization parameter
• Triangle diagram, Distance Geometry and Symmetries of Feynman Integrals
• Multi-Loop Results, Charm- and Bottom-Quark Masses and the Strong Coupling Constant
• Scalar one-loop 4-point integral with one massless vertex in loop regularization
• Three-loop vertex corrections
• A stroll through the loop-tree duality
• General One-loop Reduction in Generalized Feynman Parametrization Form
• The number of master integrals as Euler characteristic