H0LiCOW XII. Lens mass model of WFI2033-4723 and blind measurement of its time-delay distance and $H_0$

We present the lens mass model of the quadruply-imaged gravitationally lensed quasar WFI2033-4723, and perform a blind cosmographical analysis based on this system. Our analysis combines (1) time-delay measurements from 14 years of data obtained by the COSmological MOnitoring of GRAvItational Lenses (COSMOGRAIL) collaboration, (2) high-resolution $\mathit{\text{Hubble}}\mathit{\text{Space}}\mathit{\text{Telescope}}$ imaging, (3) a measurement of the velocity dispersion of the lens galaxy based on ESO-MUSE data, and (4) multi-band, wide-field imaging and spectroscopy characterizing the lens environment. We account for all known sources of systematics, including the influence of nearby perturbers and complex line-of-sight structure, as well as the parametrization of the light and mass profiles of the lensing galaxy. After unblinding, we determine the effective time-delay distance to be $4784_{-248}^{+399}\mathrm{M}\mathrm{p}\mathrm{c}$, an average precision of $6.6\mathrm{\%}$. This translates to a Hubble constant $H_{0} = 71.6_{-4.9}^{+3.8}~$\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}\mathrm{M}\mathrm{p}{\mathrm{c}}^{-1}$$,assumingaflat$\Lambda$CDM cosmology with a uniform prior on ${\mathrm{\Omega }}_{\mathrm{m}}$ in the range [0.05, 0.5]. This work is part of the $H_0$ Lenses in COSMOGRAIL’s Wellspring (H0LiCOW) collaboration, and the full time-delay cosmography results from a total of six strongly lensed systems are presented in a companion paper (H0LiCOW XIII).