  We propose that the expectation value of the stress energy tensor of the
Standard Model should be given by $< T_{\mu \nu} > = \rho_\vac \eta_{\mu\nu}$,
with a vacuum energy $\rho_\vac$ that differs from the usual "dimensional
analysis" result by an exponentially small factor associated with
non-perturbative effects. We substantiate our proposal by a rigorous analysis
of a toy model, namely the 2-dimensional Gross-Neveu model. In particular, we
address, within this model, the key question of the renormalization ambiguities
affecting the calculation. The stress energy operator is constructed concretely
via the operator-product-expansion. The non-perturbative factor in the vacuum
energy is seen as a consequence of the facts that a) the OPE-coefficients have
an analytic dependence on $g$, b) the vacuum correlations have a non-analytic
(=non-perturbative) dependence on $g$, which we propose to be a generic feature
of QFT. Extrapolating our result from the Gross-Neveu model to the Standard
Model, one would expect to find $\rho_\vac ~ \Lambda^4 \e^{-O(1)/g^2}$, where
$\Lambda$ is an energy scale such as $\Lambda = M_{H}$, and $g$ is a gauge
coupling such as $g^2/4\pi = \alpha_{EW}$. The exponentially small factor due
to non-perturbative effects could explain the "unnatural" smallness of this
quantity.
