{\rm d}r \frac{r~\xi(r)}{\sqrt{r^2-r_p^2}} \;,$$ where the comoving distance ($r$) has been decomposed into components parallel ($r_{||}$) and perpendicular ($r_p$) to the line of sight. The integration is truncated at $45$ Mpc. Due to the finite size of the simulation box ($L_{\rm box}=100$ Mpc) the model correlation function is not reliable beyond scales of $r\sim0.1~L_{\rm box}\sim10$ Mpc.

In order to fit the model to the observations we use Powell’s directions set method in multidimensions (e.g. Press et al. 1992) to find the values of $M_1$, $(m/M)_0$, $\beta$ and $\gamma$ that minimize either $$\chi_r^2 = \chi_r^2 (\Phi)= \frac{\chi^2(\Phi)}{N_{\Phi}}$$ (mass function fit) or $$\chi_r^2 = \chi_r^2 (\Phi)+\chi_r^2 (w_p) = \frac{\chi^2(\Phi)}{N_{\Phi}} +
\frac{\chi^2(w_p)}{N_r\;N_m}$$ (mass function and projected CF fit) with $N_{\Phi}$ and $N_{r}$ the number of data points for the SMF and projected CFs, respectively, and $N_{m}$ the number of mass bins for the projected CFs.

In this context $\chi^2(\Phi)$ and $\chi^2(w_p)$ are defined as: $$\begin{aligned}
\chi^2(\Phi) &=& \sum_{i=1}^{N_{\Phi}} \left[ \frac{\Phi_{\rm mod}(m_i)-\Phi_{\rm obs}(m_i)}{\sigma_{\Phi_{\rm obs}(m_i)}} \right]^2\notag\\
\chi^2(w_p) &=& \sum_{i=1}^{N_m} \sum_{j=1}^{N_r} \left[ \frac{w_{p,\rm mod}(r_{p,j},m_i)-w_{p,\rm obs}(r_{p,j},m_i)}{\sigma_{w_{p,\rm obs}(r_{p,j},m_i)}} \right]^2\notag\;,\end{aligned}$$ with $\sigma_{\Phi_{\rm obs}}$ and $\sigma_{w_{p,\rm obs}}$ the errors for the SMF and projected CFs, respectively. Note that for the simultaneous fit, by adding the reduced $\chi_r^2$, we give the 