Testing the Landau gauge operator product expansion on the lattice with a〈A2〉condensate

Using the operator product expansion we show that the ${O(1/p}^2)$ correction to the perturbative expressions for the gluon propagator and the strong coupling constant resulting from lattice simulations in the Landau gauge are due to a nonvanishing vacuum expectation value of the operator $A^{\mu }{A}_{\mu }.$ This is done using the recently published Wilson coefficients of the identity operator computed to third order, and the subdominant Wilson coefficient computed in this paper to the leading logarithm. As a test of the applicability of OPE we compare the $〈A^{\mu }{A}_{\mu }〉$ estimated from the gluon propagator and the one from the coupling constant in the flavorless case. Both agree within the statistical uncertainty $\sqrt{〈A^{\mu }{A}_{\mu }〉}\simeq 1.64\left(15\right)\mathrm{}\hspace{0.5em}\mathrm{GeV}.$ Simultaneously we fit ${\Lambda }_{\overline{\mathrm{MS}}}=233\mathrm{}\left(28\right)\mathrm{}\hspace{0.5em}\mathrm{MeV},$ in perfect agreement with previous lattice estimates. When the leading coefficients are only expanded to two loops, the two estimates of the condensate differ drastically. As a consequence we insist that the OPE can be applied in predicting physical quantities only if the Wilson coefficients are computed to a high enough perturbative order.