We study the impact of neutrino masses on the shape and height of the BAO peak of the matter correlation function , both in real and redshift space .
In order to describe the nonlinear evolution of the BAO peak we run N-body simulations and compare them with simple analytic formulae .
We show that the evolution with redshift of the correlation function and its dependence on the neutrino masses is well reproduced in a simplified version of the Zel ’ dovich approximation , in which the mode-coupling contribution to the power spectrum is neglected .
While in linear theory the BAO peak decreases for increasing neutrino masses , the effect of nonlinear structure formation goes in the opposite direction , since the peak broadening by large scale flows is less effective .
As a result of this combined effect , the peak decreases by \sim 0.6 % for \sum m _ { \nu } = 0.15 eV and increases by \sim 1.2 % for \sum m _ { \nu } = 0.3 eV , with respect to a massless neutrino cosmology with equal value of the other cosmological parameters .
We extend our analysis to redshift space and to halos , and confirm the agreement between simulations and the analytic formulae .
We argue that all analytical approaches having the Zel ’ dovich propagator in their lowest order approximation should give comparable performances , irrespectively to their formulation in Lagrangian or in Eulerian space .