  Future or ongoing galaxy redshift surveys can put stringent constraints on
neutrinos masses via the high-precision measurements of galaxy power spectrum,
when combined with cosmic microwave background (CMB) information. In this paper
we develop a method to model galaxy power spectrum in the weakly nonlinear
regime for a mixed dark matter (CDM plus finite-mass neutrinos) model, based on
perturbation theory (PT) whose validity is well tested by simulations for a CDM
model. In doing this we carefully study various aspects of the nonlinear
clustering and then arrive at a useful approximation allowing for a quick
computation of the nonlinear power spectrum as in the CDM case. The nonlinear
galaxy bias is also included in a self-consistent manner within the PT
framework. Thus the use of our PT model can give a more robust understanding of
the measured galaxy power spectrum as well as allow for higher sensitivity to
neutrino masses due to the gain of Fourier modes beyond the linear regime.
Based on the Fisher matrix formalism, we find that BOSS or Stage-III type
survey, when combined with Planck CMB information, gives a precision of total
neutrino mass constraint, sigma(m_nu,tot) 0.1eV, while Stage-IV type survey may
achieve sigma(m_nu,tot) 0.05eV, i.e. more than a 1-sigma detection of neutrino
masses. We also discuss possible systematic errors on dark energy parameters
caused by the neutrino mass uncertainty. The significant correlation between
neutrino mass and dark energy parameters is found, if the information on power
spectrum amplitude is included. More importantly, for Stage-IV type survey, a
best-fit dark energy model may be biased and falsely away from the underlying
true model by more than the 1-sigma statistical errors, if neutrino mass is
ignored in the model fitting.
