The three-loop QCD β-function and anomalous dimensions

Abstract

The analytic calculation of the three-loop QCD β-function and anomalous dimensions within the minimal subtraction scheme in an arbitrary covariant guage is presented. The result for the β-function coincides with the previous calculation [1].

Jet mass spectra in Higgs boson plus one jet at next-to-next-to-leading logarithmic order

“…Up to three loops, the coefficients of the beta function [91,92] and cusp anomalous dimension [66,67] in MS are…”

Correlator of the quark scalar currents and Γtot(H → hadrons) at O(αs3) in pQCD

“…Thus, one needs only to know Π S to order a 2 s and the anomalous dimension γ SS q (a s ) to order a 3 s to find all Q-dependent terms in Π S at O(a 3 s ), since the beta function and the quark mass anomalous dimension γ m are reliably known to order a 3 s from Refs. [17][18][19][20]. As we shall see later both problems are eventually reduceable to calculation of a specific class of diagrams representing some massless Feynman integrals (FI) depending on only one external momentum (to be named p-integrals below) and with the number of loops not exceeding three.…”

Adler function and Bjorken polarized sum rule: Perturbation expansions in powers of theSU(Nc)conformal anomaly and studies of the conformal symmetry limit

“…of (4) and (5) are known in terms of powers of C F , C A and T F n f . The β 0 -term was evaluated in [18,19], β 1 in [20][21][22], β 2 in MS in [23,24]. To determine the coefficients (6) and (7) the l.h.s.…”