Three-Loop OPE Wilson Coefficients of Dimension-Four Operators for (Axial-)Vector and (Pseudo-)Scalar Current Correlators

Abstract

We calculate the three-loop Wilson coefficients of all physically relevant dimension-four operators, i.e. $G_{\mu \nu }^a{G}^{a,\mu \nu }$, $m_i{\bar{q}}_j{q}_j$ and $m_i{m}_j{m}_k^2$, in the short-distance expansion of the time-ordered product of a pair of gauge-singlet vector, axial-vector, scalar and pseudo-scalar currents. The results are given for a general non-Abelian gauge theory with arbitrary (compact semi-simple) gauge group and $n_f$ light fermion flavors (quarks) in a common arbitrary representation of the gauge group, which includes QCD as a special case. In particular, we allow for arbitrary flavor contents of each of the currents. For the axial-vector current the included contributions from so-called singlet diagrams are consistent with the one-loop axial anomaly.

34 pages, 2 figures, 2 appendices, 1 ancillary file; v2: journal version

References in corpus (31)

• Asymptotic expansion of Feynman integrals near threshold
• FLAG Review 2021
• LiteRed 1.4: a powerful tool for the reduction of the multiloop integrals
• FIRE6: Feynman Integral REduction with Modular Arithmetic
• Group theory factors for Feynman diagrams
• JaxoDraw: A graphical user interface for drawing Feynman diagrams. Version 2.0 release notes
• Flavour-symmetry breaking of the quark condensate and chiral corrections to the Gell-Mann-Oakes-Renner relation
• Vector Correlator in Massless QCD at Order O(alpha_s^4) and the QED beta-function at five loop
• Five-loop renormalisation of QCD in covariant gauges
• Recent Progress in QCD Condensate Evaluations and Sum Rules
• Determination of the QCD Coupling from ALEPH $\tau$ Decay Data
• Complete renormalization of QCD at five loops
• Strange Quark Mass Determination from Cabibbo-Suppressed Tau Decays
• The Three-loop Quark Jet Function
• The bottom-quark mass from non-relativistic sum rules at NNNLO
• Mass Corrections to the Vector Current Correlator
• The strong coupling from an improved $\tau$ vector isovector spectral function
• Higgs Decay to Top Quarks at O(α_s^2)
• QCD sum rule determination of the charm-quark mass
• Renormalization Group Improved Bottom Mass from Upsilon Sum Rules at NNLL Order
• Singlet Polarization Functions at O(α_s^2)
• Addendum to arXiv:0907.2110: "Charm and Bottom Quark Masses: An Update"
• O(α_s^2) Corrections to Top Quark Production at $e^{+}{e}^{-}$ Colliders
• Reconciling the Contour-Improved and Fixed-Order Approaches for $\tau$ Hadronic Spectral Moments I: Renormalon-Free Gluon Condensate Scheme
• Reconciling the Contour-Improved and Fixed-Order Approaches for $\tau$ Hadronic Spectral Moments II: Renormalon Norm and Application in ${\alpha }_s$ Determinations
• Borel-Laplace Sum Rules with $\tau$ decay data, using OPE with improved anomalous dimensions
• Renormalization of the flavor-singlet axial-vector current and its anomaly in dimensional regularization
• Charm Quark Mass with Calibrated Uncertainty
• Hadronic vacuum polarization using gradient flow
• Optimal renormalization and the extraction of the strange quark mass from moments of the $\tau$-decay spectral function
• Low- and High-Energy Expansion of Heavy-Quark Correlators at Next-To-Next-To-Leading Order

Cited by in corpus (2)

• FLAG Review 2024
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