  Neutrino emission in cold neutron stars is dominated by the modified urca
(murca) process and nucleon-nucleon bremsstrahlung. The standard emission rates
were provided by Friman and Maxwell in 1979, effectively based on a chiral
Lagrangian framework with pion and rho meson exchange, supplemented by Landau
parameters to describe short-range interactions. We reevaluate these rates
within the same framework, correcting several errors and removing unnecessary
simplifications, notably the triangular approximation -- Fermi momenta of
protons and leptons negligible compared to the neutrons one -- in MURCA, and
quantify their importance. The impact of rho meson exchange, previously argued
to cancel with interference effects, is actually quite relevant. Altogether,
the cooling rates are reduced by as much as a factor 2. We provide
comprehensive analytical formulas encompassing all contributions, designed for
straightforward numerical implementation. Our results are particularly relevant
for astrophysical studies of neutron stars evolution and for studies of physics
beyond the standard model, where the emission of new particles -- such as
axions -- is typically computed within the same framework we adopt here.
