The static quark self-energy at large orders from NSPT

Abstract

Using Numerical Stochastic Perturbation Theory (NSPT), we calculate the static self-energy of SU(3) gauge theory up to order α 20. Simulations on a large set of different lattice volumes allow for a careful treatment of finite size effects. The resulting infinite volume perturbative series of the static self-energy is in remarkable agreement with the predicted asymptotic behaviour of high order expansions, namely with a factorial growth of perturbative coefficients known as renormalon.

Estimation of the large order behavior of the plaquette

“…This may suggest the renormalon behavior would set in at orders around i ∼ 40. Recently, the renormalon behavior in heavy-quark pole mass was confirmed in numerical simulation of the coefficients to order α 20 s [14,15]. Our estimate of the large order behavior of the plaquette suggests a numerical evidence of renormalon in plaquette would require much higher order computations.…”

“…For instance this yields a rapidly converging series for the static interquark potential or the heavy quark pole mass, rendering the normalization to be evaluated accurately with the first few orders of perturbation [12,13]. Recently, the estimation of the normalization was confirmed by numerical simulation [14,15]. Numerically, the series for the normalization for the plaquette does not converge well at the orders known so far and so it cannot be obtained through the scheme.…”