Complete renormalization of QCD at five loops

Abstract

We present new analytical five-loop Feynman-gauge results for the anomalous dimensions of ghost field and -vertex, generalizing the known values for SU(3) to a general gauge group. Together with previously published results on the quark mass and -field anomalous dimensions and the Beta function, this completes the 5-loop renormalization program of gauge theories in that gauge.

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.…”

“…In the spatial directions L-periodic boundary conditions are imposed on all fields. At the time boundaries the fermionic fields satisfy [24] 5) with the projectors P ± = 1 2 (1 ± γ 0 ). For the gauge field one has…”

“…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.…”

“…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.…”

The method of global R* and its applications

“…In this respect, a central role is played by the renormalisation of QCD, which has a long history, starting with the one-loop calculation and the groundbreaking discovery of asymptotic freedom [1][2][3][4]. Impressive progress in this field pushed state-of-the-art calculations to five-loop level [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. One of the main difficulties in the calculation of high order corrections is the dramatic growth of the number and of the complexity of Feynman diagrams, that can be tackled only with the use of highly efficient computational methods.…”