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Linking supernovae to their progenitors is a powerful method for furtheringour understanding of the physical origin of their observed differences, whileat the same time testing stellar evolution theory. In this second study of aseries of three papers where we characterise SNe II to understand theirdiversity, we derive progenitor properties (initial and ejecta masses, andradius), explosion energy, $^{56}$Ni mass, and its degree of mixing within theejecta for a large sample of SNe II. This dataset was obtained by the CarnegieSupernova Project-I and is characterised by a high cadence of their optical andNIR light curves and optical spectra that were homogeneously observed andprocessed. A large grid of hydrodynamical models and a fitting procedure basedon MCMC methods were used to fit the bolometric light curve and the evolutionof the photospheric velocity of 53 SNe II. We infer ejecta masses between 7.9and 14.8 $M_{\odot}$, explosion energies between 0.15 and 1.40 foe, and$^{56}$Ni masses between 0.006 and 0.069 $M_{\odot}$. We define a subset of24~SNe (the `gold sample') with well-sampled bolometric light curves andexpansion velocities for which we consider the results more robust. Most SNe~IIin the gold sample ($\sim$88%) are found with ejecta masses in the range of$\sim$8-10 $M_{\odot}$, coming from low zero-age main-sequence masses (9-12$M_{\odot}$). The modelling of the initial-mass distribution of the gold samplegives an upper mass limit of 21.3$^{+3.8}_{-0.4}$ $M_{\odot}$ and a muchsteeper distribution than that for a Salpeter massive-star IMF. This IMFincompatibility is due to the large number of low-mass progenitors found --when assuming standard stellar evolution. This may imply that high-massprogenitors lose more mass during their lives than predicted. However, a deeperanalysis of all stellar evolution assumptions is required to test thishypothesis.

Type II supernovae from the Carnegie Supernova Project-I. II. Physical parameter distributions from hydrodynamical modelling