ACT-DR5 Sunyaev-Zel'dovich Clusters: weak lensing mass calibration with KiDS

We present weak gravitational lensing measurements of a sample of 157 clusters within the Kilo Degree Survey (KiDS), detected with a $>5\sigma$ thermal Sunyaev-Zel'dovich (SZ) signal by the Atacama Cosmology Telescope (ACT). Using a halo-model approach we constrain the average total cluster mass, $M_{\rm WL}$, accounting for the ACT cluster selection function of the full sample. We find that the SZ cluster mass estimate $M_{\rm SZ}$, which was calibrated using X-ray observations, is biased with $M_{\rm SZ}/M_{\rm WL} = (1-b_{\rm SZ}) = 0.65\pm 0.05$. Separating the sample into six mass bins, we find no evidence of a strong mass-dependency for the mass bias, $(1-b_{\rm SZ})$. Adopting this ACT-KiDS SZ mass-calibration would bring the Planck SZ cluster count into agreement with the counts expected from the {\it Planck} cosmic microwave background $\Lambda$CDM cosmological model, although it should be noted that the cluster sample considered in this work has a lower average mass $M_{\rm SZ, uncor} = 3.64 \times 10^{14} M_{\odot}$ compared to the Planck cluster sample which has an average mass in the range $M_{\rm SZ, uncor} = (5.5-8.5) \times 10^{14} M_{\odot}$, depending on the sub-sample used.