Four-loop non-singlet QCD splitting functions are verified for consistency and used to finalize analytical forms for the gluon virtual anomalous dimension and N^4LL threshold resummation coefficients, revealing a new small-x logarithmic structure.
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The four-loop beta-function in Quantum Chromodynamics
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abstract
We present the analytical calculation of the four-loop QCD beta-function within the minimal subtraction scheme.
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New high-precision MS-bar masses m_b(m_b, n_f=5)=4.1923(63) GeV, m_c(3 GeV, n_f=4)=0.9813(34) GeV, and m_s(3 GeV, n_f=4)=83.39(26) MeV from HISQ lattice QCD correlators including quenched QED.
A self-consistent heavy-quark transport model using a lattice-constrained potential with Yukawa and string contributions predicts 2πT Ds ≈ 0.5-1.7 near the QCD crossover, matching lattice QCD results.
Combined fits of KEDR and BESIII R(s) data yield alpha_s(M_Z) = 0.1179, 0.1221, and 0.1312 at NLO, NNLO, and NNNLO, demonstrating strong dependence on perturbative truncation order.
Asymptotic Padé approximants validated on five-loop QCD data now yield six-loop QCD beta-function and quark-mass anomalous-dimension predictions plus eight-loop results in scalar theory.
A mass-dependent renormalization scheme from dimensional regularization yields smooth threshold transitions in QCD and implements the Appelquist-Carazzone theorem by reducing to minimal subtraction at high energies.
The FLAG 2024 review provides updated averages of lattice QCD determinations for quark masses, decay constants, form factors, mixing parameters, and nucleon matrix elements.
An introductory review of renormalisation procedures, the renormalisation group, and scale-setting optimisation in gauge theories such as QCD.
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Perturbative QCD fitting of KEDR and BESIII $e^+e^-$ data for R(s) and $\alpha_s$ determination
Combined fits of KEDR and BESIII R(s) data yield alpha_s(M_Z) = 0.1179, 0.1221, and 0.1312 at NLO, NNLO, and NNNLO, demonstrating strong dependence on perturbative truncation order.