Acceleration conjecture for asymptotically free QFTs

Let $G(\Lambda,a)$ be the formal series for the two-point function of an asymptotically free quantum field theory, where $\Lambda$ is the kinematical parameter. Suppose its $\beta$-function satisfies

$$\beta(a)=-\beta_0+\mathcal{O}(a^3).$$

An acceleratrix is the change of variable used in accelero-summation; here it is $F(y)=\frac{1}{\sigma_\Lambda}\log(y)$. Acceleration conjecture. For each value of $\Lambda$, there exists a number $\sigma_\Lambda\geq\frac{1}{2\beta_0}$ such that $G(\Lambda,a)$ is accelero-summable with acceleratrix

$$F(y)=\frac{1}{\sigma_\Lambda}\log(y).$$

This conjecture aims to extend Borel–Écalle resummation to asymptotically free theories and is motivated by the analyticity domain obtained through Écalle acceleration; it remains open in the source.