  Accurate physical parameters of exoplanet systems are essential for further
exploration of planetary internal structure, atmospheres, and formation
history. We aim to use simultaneous multicolour transit photometry to improve
the estimation of transit parameters, to search for transit timing variations
(TTVs), and to establish which of our targets should be prioritised for
follow-up transmission spectroscopy. We performed time series photometric
observations of 12 transits for the hot Jupiters HAT-P-19b, HAT-P-51b,
HAT-P-55b, and HAT-P-65b using the simultaneous four-colour camera MuSCAT2 on
the Telescopio Carlos S\'anchez. We collected 56 additional transit light
curves from TESS photometry. To derive transit parameters, we modelled the
MuSCAT2 light curves with Gaussian processes to account for correlated noise.
To derive physical parameters, we performed EXOFASTv2 global fits to the
available transit and radial velocity data sets, together with the Gaia DR3
parallax, isochrones, and spectral energy distributions. To assess the
potential for atmospheric characterisation, we compared the multicolour transit
depths with a flat line and a clear atmosphere model. We consistently refined
the transit and physical parameters. We improved the orbital period and
ephemeris estimates, and found no evidence for TTVs or orbital decay. The
MuSCAT2 broadband transmission spectra of HAT-P-19b and HAT-P-65b are
consistent with previously published low-resolution transmission spectra. We
also found that, except for HAT-P-65b, the assumption of a planetary atmosphere
can improve the fit to the MuSCAT2 data. In particular, we identified HAT-P-55b
as a priority target among these four planets for further atmospheric studies
using transmission spectroscopy.
