Five-loop fermion anomalous dimension for a general gauge group from four-loop massless propagators

Abstract

Abstract:We extend the O(α 5 s ) result of the analytic calculation of the quark mass anomalous dimension in pQCD [1] to the case of a generic gauge group. We present explicit formulas which express the relevant renormalization constants in terms of fourloop massless propagators. We also use our result to shed new light on the old puzzle of the absence of even zetas in results of perturbative calculations for a class of physical observables.

QCD vacuum energy in 5 loops

“…The result completes recent series of works [1][2][3][4][5][6][7] devoted to the renormalization of QCD at the five-loop level.…”

“…Last year saw a remarkable development in the program of renormalization of the QCD Lagrangian: the β -function, the quark anomalous dimension as well as anomalous dimensions of all relevant quantum fields had been computed at the five-loop level [2][3][4][5][6][7] for the case of a generic gauge group. Essentially every result has been successfully cross-checked by (at least) two independent calculations!…”

Scheme-independent calculations of anomalous dimensions of baryon operators in conformal field theories

“…However, beyond the lowest orders, the result is schemedependent, because of scheme dependence in both the higher-order b l and the c O;l coefficients. The calculations of γψ ψ;IR to four-loop order in [8,9] and to five-loop order in [15] used the four-loop and five-loop coefficients cψ ψ;4 [26] and cψ ψ;5 [27], respectively, calculated in the MS scheme. This scheme dependence of higher-order perturbative calculations is, of course, not limited to these quantities, but is a generic property of higher-order calculations.…”

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.…”