Borel representation of τ hadronic spectral function moments in contour-improved perturbation theory

Borel–Laplace sum rules with τ decay data, using OPE with improved anomalous dimensions

“…in the integrand (in the D = 0 sum rule contour integral) numerically, with a(σ m e i f ) running along the contour according to the (five-loop MS) renormalisation group equation (RGE). However, as argued in [37] (see also [38,39]), the (truncated) CI approach is inconsistent with the standard treatment of the OPE. Furthermore, the CI approach does not respect the renormalon structure of the considered sum rules when truncated [1,37,40,41].…”

“…However, as argued in [37] (see also [38,39]), the (truncated) CI approach is inconsistent with the standard treatment of the OPE. Furthermore, the CI approach does not respect the renormalon structure of the considered sum rules when truncated [1,37,40,41]. It is expected to give numerically extracted results significantly different from those of the methods FO and PV.…”

“…are given in equations(37), by replacing there p a − p. The leading UV renormalon has −p = − 1. In the large-β 0 (LB) approximation the power indices are63,64].…”

Quantum Field Theory

“…In the realm of non-abelian gauge theory (or Yang-Mills theory), there is promise in understanding emergent phenomena (e.g., the dynamical breaking of chiral symmetries [14][15][16][17][18]), triggered by topologically stabilised, extended gauge-field configurations, to alleviate or even solve the mathematical problems of perturbatively spirited approaches with spontaneous gauge-symmetry breaking in spite of the latters' many successes. These problems concern uncertainties in the convergence properties of small-coupling expansions [19], a shaky conceptual justification of the heuristically successful renormalisation programme [20], the probably oversimplistic, yet successful notion of elementary particles as pointlike quantum objects, and an embarassingly poor modelling of the vacuum state [21,22]. Thus, a prime field of activity should be to improve our understanding of the emergence and implications of nonperturbative ground states in pure Yang-Mills theories, which differ strongly from their perturbative counterparts [23].…”