  We apply the hierarchical probabilistic SED model BayeSN to analyse a sample
of 475 SNe Ia (0.015 < z < 0.4) from Foundation, DES3YR and PS1MD to
investigate the properties of dust in their host galaxies. We jointly infer the
dust law $R_V$ population distributions at the SED level in high- and low-mass
galaxies simultaneously with dust-independent, intrinsic differences. We find
an intrinsic mass step of $-0.049\pm0.016$ mag, at a significance of
3.1$\sigma$, when allowing for a constant intrinsic, achromatic magnitude
offset. We additionally apply a model allowing for time- and
wavelength-dependent intrinsic differences between SNe Ia in different mass
bins, finding $\sim$2$\sigma$ differences in magnitude and colour around peak
and 4.5$\sigma$ differences at later times. These intrinsic differences are
inferred simultaneously with a difference in population mean $R_V$ of
$\sim$2$\sigma$ significance, demonstrating that both intrinsic and extrinsic
differences may play a role in causing the host galaxy mass step. We also
consider a model which allows the mean of the $R_V$ distribution to linearly
evolve with redshift but find no evidence for any evolution - we infer the
gradient of this relation $\eta_R = -0.38\pm0.70$. In addition, we discuss in
brief a new, GPU-accelerated Python implementation of BayeSN suitable for
application to large surveys which is publicly available and can be used for
future cosmological analyses; this code can be found here:
https://github.com/bayesn/bayesn.
