Evidence for an Obstruction to Perturbative Renormalization Group in Stochastic Turbulence

We examine whether the perturbative renormalization group (RG) regime of stochastic turbulence can be continued from small $\epsilon$ to the physical value ${\epsilon }_{\mathrm{p}\mathrm{h}\mathrm{y}\mathrm{s}}=2$, corresponding to large-scale forcing. Exploiting the simplifications of the large-$d$ limit, we calculate the correction exponent $\omega$ to five-loop order and find a simple structure suggesting a closed analytic form. This form implies that the fixed point stable near $\epsilon =0$ ceases to be simultaneously real and infrared stable before reaching ${\epsilon }_{\mathrm{p}\mathrm{h}\mathrm{y}\mathrm{s}}=2$, pointing to a possible change of infrared regime rather than a controlled perturbative RG extrapolation.