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tokens: of the new fitting functions are shown in the second and fourth columns of Fig. 4 . In this case, the measurements of P θ θ are reproduced with a maximum systematic error of 3% on all scales below k = 0.7 h Mpc −1 , and for all redshifts and neutrino masses considered. We therefore use a total of only five free parameters k δ , b , a 1 , a 2 and a 3 to mimic, with a 3% level accuracy at k 0.7 h Mpc −1 , the nonlinear effects on both the auto- and cross-spectra P θ θ and P δ θ . Let us now focus on the sensitivity of these parameters to cosmology and specifically to the overall amplitude of the matter power spectrum. From our set of four simulations at four different redshifts we are able to span a large range of possible values of σ 8 , which we use as a proxy for the amount of nonlinearities. Regarding neutrino cosmologies it is necessary to choose whether we use the σ 8 defined for cold dark matter only, σ 8, c , or the one defined for the total matter, σ 8, m . It has been shown ( Castorina et al. 2015 ) that regarding the bias or the nonlinear effects on the density power spectrum P δ δ , what matters is the amplitude of the cold dark matter clustering and not the total one. We have analyzed the dependency of the fitted parameters with respect to both amplitudes σ 8, c and σ 8, m and we found that one should use the total matter σ 8, m parameter in order to assess the correct values of k δ , b , a 1 , a 2 and a 3 ; at least, this choice is the one that lowers the residual dependency with respect to the neutrino mass. Figure 5 shows that the cosmological dependance of the fitting parameters can be mostly encapsulated into the σ 8, m parameter evaluated at the corresponding redshift. The most relevant example is the good match at redshift 1.5 of the ΛCDM simulation with the M ν = 0.53eV simulation at redshift 1; these simulations share almost the same value of the total matter σ 8, m , while differing significantly in the power spectrum shape. For the two cases, we obtain the same values for the fitted parameters k δ and k θ . Fig. 5. Top panel : dependence of the fitting parameters k δ , b , k θ , a 1 , a 2 and a 3 on the total matter clustering amplitude σ 8,m at each redshift, in the corresponding simulation (symbols). Lines are showing the fit of the dependance. Bottom panel : residual between the fitted σ 8,m dependance and the measured one. On the contrary, when using the cold dark matter σ 8,c parameter (see Table 1 ) the residuals are increasing because of spurious neutrino mass dependence when going from one cosmology to another. This effect can be explained by the fact that if massive neutrinos have a weak effect on the dark matter clustering in the nonlinear regime, they add, instead, a relevant contribution to the velocity field which is felt by dark matter particles. As a result, it seems that the preferred dependence on the total matter σ 8,m comes from the fact that nonlinearities in the velocity field are generated by the