Consistent extinction model for type Ia supernovae in Cepheid-based calibration galaxies and its impact on $H_{0}$

The most recent SH0ES measurement of the Hubble constant employs corrections of type Ia supernova magnitudes due to extinction in their host galaxies. These corrections are estimated using a probabilistic model which is trained on Hubble flow (z>0.03) supernovae and extrapolated to the calibration galaxies (those with observed Cepheids), despite the fact that the latter are selected based on criteria favouring disky and dust-rich systems. We show that this standard approach underestimates the brightness of reddened supernovae in the high stellar-mass ($M_{\star}>10^{10}M_{\odot}$) calibration galaxies. This can be traced back to the fact that for these galaxies, a low total-to-selective extinction coefficient (R_B~3) is assumed, while for the low stellar-mass analogues a more standard R_ B~4 is adopted. We propose a minimalistic modification of the extinction model in the calibration galaxies in order to alleviate this systematic effect. The modification is twofold and it involves: (i) the same, Milky Way-like distribution of R_B (with mean R_B of 4.3 -- consistent with the extinction curve used for colour corrections of the Cepheids -- and scatter 0.4) and (ii) a modified shape of the E(B-V) reddening distribution while keeping the same effective slope of the supernova peak magnitude-colour relation and the same mean E(B-V) reddening as measured for supernovae in the Hubble flow. We show that this new approach yields a significantly better fit ($\Delta BIC=-11$) to the calibration data and results in a lower value of $H_{0}$. Our result is $H_{0}=70.5\pm1$ km/s/Mpc implying a reduction of the Hubble constant tension from $5.2\sigma$ to $2.8\sigma$.