Five-loop renormalisation of QCD in covariant gauges

Abstract

We present the complete set of vertex, wave function and charge renormalisation constants in QCD in a general simple gauge group and with the complete dependence on the covariant gauge parameter ξ in the minimal subtraction scheme of conventional dimensional regularisation. Our results confirm all already known results, which were obtained in the Feynman gauge, and allow the extraction of other useful gauges such as the Landau gauge. We use these results to extract the Landau gauge five-loop anomalous dimensions of the composite operator A 2 as well as the Landau gauge scheme independent gluon, ghost and fermion propagators at five loops.

A non-perturbative exploration of the high energy regime in $$N_{\mathrm{f}}=3$$ N f = 3 QCD

“…Namely, we have converted our non-perturbative observable, an SF ν -coupling with some choice for ν and L, to the MS-coupling where we allowed for a relative scale factor s in this perturbative conversion. Given the coupling in the MS-scheme the full machinery with up to 5-loops for the β-function [3][4][5][6][7] is available to extract the -parameter. However, as in phenomenological applications, the limiting factor is the perturbative order in the conversion to the MS-scheme.…”

“…The 3-loop coefficient has been obtained by matching the coupling at the 2-loop level to the MS-scheme, where the β-function is now even known to 5-loop order (b 3 and b 4 in our notation) [3][4][5][6][7]. For later use we collect the numerical values for N f = 3 QCD in Table 1, together with the SF ν scheme results for the 3 choices of the parameter, ν = −0.5, 0, 0.3, which we selected for more detailed analysis in Sect.…”

“…At large flow times we selected the gauge field configurations in the Q = 0 sector. 3 Apart from the background field, Eq. (2.17), we have indeed found a single further local minimum.…”

“…The gauge function ω(x) is thus non-constant in the x 3 -direction, which induces the shift by ±2π in 2 of the angles 3 In practice we defined this to mean gauge configurations for which |Q| < 0.5, with Q defined as in Ref. [28].…”

“…For processes involving the strong interactions the precision is usually less impressive, due to our limited ability to extract quantitative information from QCD. One of the main tools is perturbation theory (PT) in the strong coupling, α s , and there has been significant progress in high order perturbative QCD calculations, with renormalization group functions now available up to 5-loop order in the MS-scheme [3][4][5][6][7]. However, before a perturbative result can be confronted with experimental observables, the transition from quarks and gluons to hadronic degrees of freedom needs to be modelled in some way.…”