  We report the results of a comprehensive study of the relationship between
galaxy size, stellar mass and specific star-formation rate (sSFR) at redshifts
1.3<z<1.5. Based on a mass complete (M_star >= 6x10^10 Msun), spectroscopic
sample from the UKIDSS Ultra-deep Survey (UDS), with accurate stellar-mass
measurements derived from spectro photometric fitting, we find that at z~1.4
the location of massive galaxies on the size-mass plane is determined primarily
by their sSFR. At this epoch we find that massive galaxies which are passive
(sSFR <= 0.1 Gyr^-1) follow a tight size-mass relation, with half-light radii a
factor f=2.4+/-0.2 smaller than their local counterparts. Moreover, amongst the
passive sub-sample we find no evidence that the off-set from the local
size-mass relation is a function of stellar population age. Based on a
sub-sample with dynamical mass estimates we also derive an independent estimate
of f=2.3+/-0.3 for the typical growth in half-light radius between z~1.4 and
the present day. Focusing on the passive sub-sample, we conclude that to
produce the necessary evolution predominantly via major mergers would require
an unfeasible number of merger events and over populate the high-mass end of
the local stellar mass function. In contrast, we find that a scenario in which
mass accretion is dominated by minor mergers can produce the necessary
evolution, whereby an increase in stellar mass by a factor of ~2, accompanied
by an increase in size by a factor of ~3.5, is sufficient to reconcile the
size-mass relation at z~1.4 with that observed locally. Finally, we note that a
significant fraction (44+/-12%) of the passive galaxies in our sample have a
disk-like morphology, providing additional evidence that separate physical
processes are responsible for the quenching of star-formation and the
morphological transformation of massive galaxies (abridged).
