Hyperasymptotic approximation to the plaquette and determination of the gluon condensate

We give the hyperasymptotic expansion of the plaquette with a precision that includes the terminant associated to the leading renormalon. Subleading effects are also considered. The perturbative series is regulated using the principal value prescription for its Borel integral. We use this analysis to give a determination of the gluon condensate in SU(3) pure gluodynamics that is independent of the scale and renormalization scheme used for the coupling constant: $$ {\left\langle {G}^2\right\rangle}_{\mathrm{PV}}\left({n}_f=0\right)=3.15(18){r}_0^{-4} $$ G 2 PV n f = 0 = 3.15 18 r 0 − 4 .