The long-duration gamma-ray burst (GRB) 030329, associated with supernova
(SN) 2003dh, occurred inside a star-forming dwarf galaxy at redshift
z=0.1685. The low redshift, and a rich set of archival Hubble Space Telescope
(HST) images, makes this GRB well-suited for a detailed study of the stellar
population in the immediate vicinity of the explosion. Since the lifetime of a
star is directly tied to its mass, the age of the stellar population can be
used to put constraints on the GRB and SN progenitor mass. From the HST images
we extract the colours of the precise site from which the GRB originated, and
find that the colours are significantly different from those of the overall
host galaxy and the surrounding starburst environment. We have used spectral
evolutionary models, including nebular emission, to carefully constrain the age
of the stellar population, and hence the progenitor, at the very explosion
site. For instantaneous burst models we find that a population age of 5 Myr
best matches the data, suggesting a very massive (M > 50 M_sun) star as the
progenitor, with an upper limit of 8 Myr (M > 25 M_sun). For more extended star
formation scenarios, the inferred progenitor age is in most cases still very
young (age 25 M_sun), with an upper limit of 20 Myr (M >
12 M_sun). These age estimates are an order of magnitude lower than the ages
inferred from the overall host galaxy colours, indicating that progenitor mass
estimates based on data for spatially unresolved GRB host galaxies will in
general be of limited use. Our results are consistent with the collapsar
scenario.Comment: Accepted to MNRA