  Context: Constraints on the internal rotation of red giants are now available
thanks to asteroseismic observations. Preliminary comparisons with rotating
stellar models indicate that an undetermined additional process for the
internal transport of angular momentum is required in addition to purely
hydrodynamic processes. Aims: We investigate how asteroseismic measurements of
red giants can help us characterize the additional transport mechanism.
Methods: We first determine the efficiency of the missing transport mechanism
for the low-mass red giant KIC 7341231 by computing rotating models that
include an additional viscosity corresponding to this process. We then discuss
the change in the efficiency of this transport of angular momentum with the
mass, metallicity and evolutionary stage. Results: In the case of the low-mass
red giant KIC 7341231, we find that the viscosity corresponding to the
additional mechanism is constrained to the range 1 x 10^3 - 1.3 x 10^4 cm^2/s.
This constraint on the efficiency of the unknown additional transport mechanism
during the post-main sequence is obtained independently of any specific
assumption about the modelling of rotational effects during the pre-main
sequence and the main sequence (in particular, the braking of the surface by
magnetized winds and the efficiency of the internal transport of angular
momentum before the post-main-sequence phase). When we assume that the
additional transport mechanism is at work during the whole evolution of the
star together with a solar-calibrated braking of the surface by magnetized
winds, the range of nu_add is reduced to 1 - 4 x 10^3 cm^2/s. In addition to
being sensitive to the evolutionary stage of the star, we show that the
efficiency of the unknown process for internal transport of angular momentum
increases with the stellar mass.
