Landau pole screening in the Gross-Neveu model: 1N versus operator product expansion

In asymptotically free theories, Landau poles at low energy scales limit the range of validity of perturbative predictions. Taking into account non-perturbative corrections in an operator product expansion (OPE) does not alleviate this problem, however, non-vanishing condensates are believed to prevent the singularities from producing unphysical (tachyonic) poles in Greenʹs functions. We illustrate the mechanism of Landau pole screening by dynamically generated condensates in the Gross-Neveu model, in which a dynamical fermion mass and a scalar boundstate are formed. In the large N limit the pertinent Greenʹs function is an entirely smooth function of the Euclidean momentum transfer. We demonstrate that its asymptotic behaviour nevertheless resembles the renormalisation group improved perturbative result accompanied by OPE corrections for momenta well above the Landau pole. The 1N expansion is suited to account for non-trivial ground state correlations beyond the range of validity of OPE predictions.