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Massless Propagators, $R(s)$ and Multiloop QCD

P. A. Baikov, K. G. Chetyrkin, J. H. Kühn

TL;DR

This review surveys state-of-the-art massless propagator techniques in QCD, highlighting IRR and $R^*$-based renormalization group methods plus large-$D$ and master integral strategies to reduce and evaluate L-loop p-integrals. It compiles five-loop RG-function results (ghost, ghost–gluon, quark fields, and quark mass) and applies them to phenomenology: vector and scalar correlators, $R(s)$, Higgs decays to quarks, and DIS Bjorken sums, including four-loop coefficient functions and Crewther-related constraints. The work demonstrates how high-order perturbative calculations refine precision tests of the SM, informs Higgs phenomenology, and provides essential inputs for lattice QCD via RG-invariant quantities. Overall, the paper emphasizes methodological advances enabling reliable, high-precision multiloop predictions in QCD and their phenomenological consequences.

Abstract

This is a short review of recent developments in calculation of higher order corrections to various two-point correlators and related quantities in (massless) QCD.

Massless Propagators, $R(s)$ and Multiloop QCD

TL;DR

This review surveys state-of-the-art massless propagator techniques in QCD, highlighting IRR and -based renormalization group methods plus large- and master integral strategies to reduce and evaluate L-loop p-integrals. It compiles five-loop RG-function results (ghost, ghost–gluon, quark fields, and quark mass) and applies them to phenomenology: vector and scalar correlators, , Higgs decays to quarks, and DIS Bjorken sums, including four-loop coefficient functions and Crewther-related constraints. The work demonstrates how high-order perturbative calculations refine precision tests of the SM, informs Higgs phenomenology, and provides essential inputs for lattice QCD via RG-invariant quantities. Overall, the paper emphasizes methodological advances enabling reliable, high-precision multiloop predictions in QCD and their phenomenological consequences.

Abstract

This is a short review of recent developments in calculation of higher order corrections to various two-point correlators and related quantities in (massless) QCD.

Paper Structure

This paper contains 24 sections, 74 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Massless Propagators and Physics
  3. RG functions and IR reduction
  4. Two-point correlators
  5. OPE and DIS
  6. Calculational Methods
  7. A: Reduction via $1/D$ expansion
  8. B: Master p-integrals and their evaluation
  9. Computer Algebra & FORM
  10. Scalar Correlator & $\Gamma(H \to \overline{q}q)$
  11. Vector Correlator & $R(s)$
  12. QCD RG-functions
  13. Five-loop running of the ghost field
  14. Five-loop running of the ghost-ghost-gluon vertex
  15. Five-loop running of the quark field
  16. ...and 9 more sections

Figures (5)

  • Figure 1: Non-trivial three-loop master p-integrals.
  • Figure 2: Lowest order non-singlet (a) and singlet (b) diagrams contributing to the polarization operator.
  • Figure 3: Examples of diagrams contributing to the coefficient function $C^{Bjp}_{NS}$ at three and four loops.
  • Figure 4: Examples of diagrams contributing to the coefficient function $C^{Bjp}_{SI}$ at three and four loops.
  • Figure 5: Perturbative part of the Bjorken sum rule (\ref{['gBSR']}) as a function of the momentum transfer squared $Q^2$ in different orders against the combined set of the Jefferson Lab (taken from V.L. Khandramai, R.S. Pasechnik, D.V. Shirkov, O.P. Solovtsova, O.V. Teryaev, Four-loop QCD analysis of the Bjorken sum rule vs data, Phys.Lett.B706:340-344,2012).