Four-loop QCD propagators and vertices with one vanishing external momentum

Abstract

We have computed the self-energies and a set of three-particle vertex functions for massless QCD at the four-loop level in the MSbar renormalization scheme. The vertex functions are evaluated at points where one of the momenta vanishes. Analytical results are obtained for a generic gauge group and with the full gauge dependence, which was made possible by extensive use of the Forcer program for massless four-loop propagator integrals. The bare results in dimensional regularization are provided in terms of master integrals and rational coefficients; the latter are exact in any space-time dimension. Our results can be used for further precision investigations of the perturbative behaviour of the theory in schemes other than MSbar. As an example, we derive the five-loop beta function in a relatively common alternative, the minimal momentum subtraction (MiniMOM) scheme.

50 pages, 4 figures, 15 ancillary files available with the source; v2: minor changes, version accepted by JHEP

References in corpus (15)

• The five-loop beta function of Yang-Mills theory with fermions
• Five-loop quark mass and field anomalous dimensions for a general gauge group
• Complete renormalization of QCD at five loops
• Towards the five-loop Beta function for a general gauge group
• Five-loop fermion anomalous dimension for a general gauge group from four-loop massless propagators
• The Form Factors of the Gauge-Invariant Three-Gluon Vertex
• Nearly perturbative lattice-motivated QCD coupling with zero IR limit
• The R*-operation for Feynman graphs with generic numerators
• Forcer, a FORM program for the parametric reduction of four-loop massless propagator diagrams
• Off-shell two loop QCD vertices
• Combinatorics of $\mathbf{R}$-, ${\mathbf{R}}^{-1}$-, and ${\mathbf{R}}^{\ast }$-operations and asymptotic expansions of feynman integrals in the limit of large momenta and masses
• The diamond rule for multi-loop Feynman diagrams
• Momentum subtraction and the R-ratio
• Forcer: a FORM program for 4-loop massless propagators
• FORM, Diagrams and Topologies

Cited by in corpus (32)

• Minimally subtracted six loop renormalization of $O(n)$-symmetric ${\varphi }^4$ theory and critical exponents
• Recola2: REcursive Computation of One-Loop Amplitudes 2
• Four-Loop Non-Singlet Splitting Functions in the Planar Limit and Beyond
• Collider Physics at the Precision Frontier
• Five-loop renormalisation of QCD in covariant gauges
• On Higgs decays to hadrons and the R-ratio at N^4LO
• Five-loop contributions to low-N non-singlet anomalous dimensions in QCD
• Infrared Singularities of Scattering Amplitudes and N${}^3$LL Resummation for $n$-Jet Processes
• Forcer, a FORM program for the parametric reduction of four-loop massless propagator diagrams
• Four-loop cusp anomalous dimension in QED
• The structure of generic anomalous dimensions and no-$\pi$ theorem for massless propagators
• Nonperturbative Renormalization in Lattice QCD with three Flavors of Clover Fermions: Using Periodic and Open Boundary Conditions
• Renormalization scheme and gauge (in)dependence of the generalized Crewther relation: what are the real grounds of the $\beta$-factorization property?
• Gauge-invariant Renormalization Scheme in QCD: Application to fermion bilinears and the energy-momentum tensor
• Reanalysis of the Higgs-boson decay $H\to gg$ up to ${\alpha }_s^6$-order level using the principle of maximum conformality
• Spectral Functions of Gauge Theories with Banks-Zaks Fixed Points
• Gauge dependence of the perturbative QCD predictions under the momentum space subtraction scheme
• QCD calculations for the LHC: status and prospects
• Five loop minimal MOM scheme field and quark mass anomalous dimensions in QCD
• QCD cusp anomalous dimension: current status
• Rings: an efficient Java/Scala library for polynomial rings
• Two-loop renormalization and mixing of gluon and quark energy-momentum tensor operators
• Four-loop singularities of the massless fermion propagator in quenched three-dimensional QED
• Five loop anomalous dimension of non-singlet quark currents in the RI' scheme
• The analytical $\mathcal{O}(a_s^4)$ expression for the polarized Bjorken sum rule in the miniMOM scheme and the consequences for the generalized Crewther relation
• R*-operation and five-loop calculations
• Renormalization-group improved Higgs to two gluons decay rate
• Numerically Computing QCD Laplace Sum-Rules Using pySecDec
• Total decay width of $H\to gg$ using the infinite-order scale-setting approach based on the intrinsic conformality
• Structure-dependent radiative corrections to $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\gamma$ in the GVMD approach
• Three-loop QCD Mass Relation between the $\overline{\mathrm{MS}}$ and Symmetric-momentum Subtraction Scheme Away from the Chiral Limit
• On the gauge dependence of Quantum Electrodynamics