Brownian loop-soup cluster expansion conjecture in fractional occupation fields

Fix $c\in(0,1)$. Let $\mathcal L_D^c$ be a Brownian loop soup of central charge $c$, let $\mathcal C$ be one of its clusters, and let $:\mathtt h_c\Theta_{\mathcal L_D^c}^{n-1}:$ denote the hypothetical renormalized signed fractional occupation-field power. Brownian loop-soup cluster expansion conjecture. The $\varepsilon$-neighborhood of $\mathcal C$, for both Euclidean distance and conformal radius, should admit an $L^2$ asymptotic expansion in the powers

$$\lvert\log\varepsilon\rvert^{-(n-c/2)},\qquad n\geq1,$$

whose coefficient of $\lvert\log\varepsilon\rvert^{-(n-c/2)}$ is a linear combination of the restricted fields $\sigma(\mathcal C):\mathtt h_c\Theta_{\mathcal L_D^c}^{k-1}:_{\vert\overline{\mathcal C}}$ for $k\in\{1,\dots,n\}$. The renormalized intersection local times $:\Theta_{\mathcal L_D^c}^{n}:$ should not appear, and the Euclidean and conformal-radius expansions should be related through MKS loop-measure moments.