  We investigate the impact of the star formation efficiency in cluster forming
cores on the evolution of the mass in star clusters over the age range
1-100Myr, when star clusters undergo their infant weight-loss/mortality phase.
Assuming a constant formation rate of gas-embedded clusters and a weak tidal
field, we show that the ratio between the total mass in stars bound to the
clusters over that age range and the total mass in stars initially formed in
gas-embedded clusters is a strongly increasing function of the averaged local
SFE, with little influence from any assumed core mass-radius relation. Our
results suggest that, for young starbursts with estimated tidal field strength
and known recent star formation history, observed cluster-to-star mass ratios,
once corrected for the undetected clusters, constitute promising probes of the
local SFE, without the need of resorting to gas mass estimates. Similarly, the
mass ratio of stars which remain in bound clusters at the end of the infant
mortality/weight-loss phase depends sensitively on the mean local SFE, although
the impacts of the width of the SFE distribution function and of the core
mass-radius relation require more careful assessment in this case. Following
the recent finding by Bastian (2008) that galaxies form, on the average, 8% of
their stars in bound clusters regardless of their star formation rate, we raise
the hypothesis that star formation in the present-day Universe is characterized
by a near-universal distribution for the local SFE. A related potential
application of our model consists in tracing the evolution of the local SFE
over cosmological lookback times by comparing the age distribution of the total
mass in star clusters to that in field stars. We describe model aspects which
are still to be worked out before achieving this goal.
