to the underlying density field. Following [@Matsubara:2008wx; @2013MNRAS.429.1674C], we employ a model of a local in matter density Lagrangian bias in which the positions of biased tracers are purely specified by a distribution of the underlying CDM density field $\delta(\bold{q},t=0)\equiv\delta(\bold{q})$, encoded through a function $F\left[\delta_R(\bold{q})\right]$, as $$\label{biasF}
\rho_{X}(\bold{q}) =\bar{\rho}_{X} F\left[\delta_R(\bold{q})\right],$$ where, consistent with the literature, we use the subscript $X$ to indicate biased tracers. $\delta_R(\bold{q})$ denotes the primordial density field smoothed over some scale $R$, while $\bar{\rho}_{X}$ is the mean density of tracers. Density conservation provides the equivalent of equation (\[delJac\]) for tracers, $$\label{delJacX}
\delta_X(\bold{x},t) = \int d^3q F\left[\delta_R(\bold{q})\right]\delta_{D}\left[\bold{x}-\bold{q}-\bold{\Psi}(\bold{q},t)\right] -1.$$ This model of local Lagrangian bias, which corresponds to a non-local bias in the Eulerian space, can be extended to include a biasing scheme that is non-local in the Lagrangian space [@PhysRevD.83.083518]. Combining (\[delJacX\]) and (\[xi\]) and after some transformations one gets the general expression for the 2-point correlation function for biased tracers in LPT, $$\label{xiX}
1+\xi_{X}(r) = \int d^3q\int \frac{d^3k}{\left(2 \pi\right)^3}e^{i\bold{k}\cdot(\bold{q}-\bold{r})} \int \frac{d\lambda_1}{\left(2 \pi\right)}\frac{d\lambda_2}{\left(2 \pi\right)} L(\bold{q},\bold{k},\lambda_1,\lambda_2),$$ with $$\label{LX}
L(\bold{q},\bold{k},\lambda_1,\lambda_2)=\tilde{F}_1 \tilde{F}_2\underbrace{\langle e^{i\left[\lambda_1 \delta_1+\lambda_2 \delta_2+\bold{k}\cdot(\bold{\Delta}))\right]} \rangle}_\text{$K(\bold{q},\bold{k},\lambda_1,\lambda_2)$},$$ where $\tilde{F}_1$, $\tilde{F}_2$ are the Fourier space representations of $F$, with corresponding wavemodes $\lambda_1$ and $\lambda_2$ and $\bold{\Delta}=\bold{\Psi}_2-\bold{\Psi}_1$. The notation $\delta(\bold{q}_1)\equiv \delta_1$ has been adopted 