  We investigate the link between the bar rotation rate and dark matter content
in barred galaxies by concentrating on the cases of the lenticular galaxies
NGC4264 and NGC4277. These two gas-poor galaxies have similar morphologies,
sizes, and luminosities. But, NGC4264 hosts a fast bar, which extends to nearly
the corotation, while the bar embedded in NGC4277 is slow and falls short of
corotation. We derive the fraction of dark matter $f_{\rm DM, bar}$ within the
bar region from Jeans axisymmetric dynamical models by matching the stellar
kinematics obtained with the MUSE integral-field spectrograph and using SDSS
images to recover the stellar mass distribution. We build mass-follows-light
models as well as mass models with a spherical halo of dark matter, which is
not tied to the stars. We find that the inner regions of NGC4277 host a larger
fraction of dark matter ($f_{\rm DM, bar} = 0.53 \pm 0.02$) with respect to
NGC4264 ($f_{\rm DM, bar} = 0.33 \pm 0.04$) in agreement with the predictions
of theoretical works and the findings of numerical simulations, which have
found that fast bars live in baryon-dominated discs, whereas slow bars
experienced a strong drag from the dynamical friction due to a dense DM halo.
This is the first time that the bar rotation rate is coupled to $f_{\rm DM,
bar}$ derived from dynamical modelling.
