  We combine constraints on the galaxy-dark matter connection with structural
and dynamical scaling relations to investigate the angular momentum content of
disc galaxies. For haloes with masses in the interval 10^{11.3} < M_vir/M_sun <
10^{12.7} we find that the galaxy spin parameters are independent of halo mass
with <\lambda'_gal> = (J_gal/M_gal) / (\sqrt{2} R_vir V_vir) =
0.019^{+0.004}_{-0.003} (1sigma). This is significantly lower than for relaxed
LCDM haloes, which have an average spin parameter <\lambda'_halo> = 0.031. The
average ratio between the specific angular momentum of disk galaxies and their
host dark matter haloes is therefore R_j = \lambda'_gal/\lambda'_halo =
0.61^{+0.13}_{-0.10}. This calls into question a standard assumption made in
the majority of all (semi-analytical) models for (disc) galaxy formation,
namely that R_j=1. Using simple disc formation models we show that it is
particularly challenging to understand why R_j is independent of halo mass,
while the galaxy formation efficiency (\epsilon_GF, proportional to the ratio
of galaxy mass to halo mass) reveals a strong halo mass dependence. We argue
that the empirical scaling relations between \epsilon_GF, R_j and halo mass
require both feedback (i.e., galactic outflows) and angular momentum transfer
from the baryons to the dark matter (i.e., dynamical friction). The efficiency
of angular momentum loss need to decrease with increasing halo mass. Such a
mass dependence may reflect a bias against forming stable discs in high mass,
low spin haloes or a transition from cold-mode accretion in low mass haloes to
hot-mode accretion at the massive end. However, current hydrodynamical
simulations of galaxy formation, which should include these processes, seem
unable to reproduce the empirical relation between \epsilon_GF and R_j. We
conclude that the angular momentum build-up of galactic discs remains poorly
understood.
