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 $< T_{\mu \nu} > = \rho_\vac \eta_{\mu\nu}$, 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.