A small cosmological constant due to non-perturbative quantum effects

Abstract

We propose that the expectation value of the stress energy tensor of the Standard Model should be given by $< T_{μν} > = ρ_\vac η_{μν}$, with a vacuum energy $ρ_\vac$ 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 $ρ_\vac ~ Λ^4 \e^{-O(1)/g^2}$, where $Λ$ is an energy scale such as $Λ= M_{H}$, and $g$ is a gauge coupling such as $g^2/4π= α_{EW}$. The exponentially small factor due to non-perturbative effects could explain the "unnatural" smallness of this quantity.