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We provide the first combined cosmological analysis of South Pole Telescope(SPT) and Planck cluster catalogs. The aim is to provide an independentcalibration for Planck scaling relations, exploiting the cosmologicalconstraining power of the SPT-SZ cluster catalog and its dedicated weak lensing(WL) and X-ray follow-up observations. We build a new version of the Planckcluster likelihood. In the $\nu \Lambda$CDM scenario, focusing on the massslope and mass bias of Planck scaling relations, we find $\alpha_{\text{SZ}} =1.49_{-0.10}^{+0.07}$ and $(1-b)_{\text{SZ}} = 0.69_{-0.14}^{+0.07}$respectively. The results for the mass slope show a $\sim 4 \, \sigma$departure from the self-similar evolution, $\alpha_{\text{SZ}} \sim 1.8$. Thisshift is mainly driven by the matter density value preferred by SPT data,$\Omega_m = 0.30 \pm 0.03$, lower than the one obtained by Planck data alone,$\Omega_m = 0.37_{-0.06}^{+0.02}$. The mass bias constraints are consistentboth with outcomes of hydrodynamical simulations and external WL calibrations,$(1-b) \sim 0.8$, and with results required by the Planck cosmic microwavebackground cosmology, $(1-b) \sim 0.6$. From this analysis, we obtain a newcatalog of Planck cluster masses $M_{500}$. We estimate the ratio between thepublished Planck $M_{\text{SZ}}$ masses and our derived masses $M_{500}$, as a"measured mass bias", $(1-b)_M$. We analyse the mass, redshift and detectionnoise dependence of $(1-b)_M$, finding an increasing trend towards highredshift and low mass. These results mimic the effect of departure fromself-similarity in cluster evolution, showing different dependencies for thelow-mass high-mass, low-z high-z regimes.

Combining Planck and SPT cluster catalogs: cosmological analysis and impact on Planck scaling relation calibration