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We use the full-mission Planck PR4 data to measure the CMB lensingconvergence ($\kappa$)--thermal Sunyaev-Zel'dovich (tSZ, $y$)cross-correlation, $C_\ell^{y\kappa}$. This is only the second measurement todate of this signal, following Hill \& Spergel (2014). We perform themeasurement using foreground-cleaned tSZ maps built from the PR4 frequency mapsvia a tailored needlet internal linear combination (NILC) code in our companionpaper, in combination with the Planck PR4 $\kappa$ maps and varioussystematic-mitigated PR3 $\kappa$ maps. A serious systematic is the residualcosmic infrared background (CIB) in the tSZ map, as the high CIB--$\kappa$correlation can significantly bias the inferred tSZ--$\kappa$cross-correlation. We mitigate this by deprojecting the CIB in our NILC, usinga moment-deprojection approach to avoid leakage due to incorrect modelling ofthe CIB frequency dependence. We validate our method on mm-sky simulations. Wefit a theoretical halo model to our measurement, finding a best-fit amplitudeof $A=0.82\pm0.21$ (for the highest signal-to-noise PR4 $\kappa$ map) or$A=0.56\pm0.24$ (for a PR3 $\kappa$ map built from a tSZ-deprojected CMB map),indicating that the data are consistent with our model within $\sim1$-$2\sigma$. Although our error bars are similar to those of the 2014measurement, our method is significantly more robust to CIB contamination. Ourmoment-deprojection approach lays the foundation for future measurements ofthis signal with higher signal-to-noise maps from ground-based telescopes,which will precisely probe the astrophysics of the intracluster medium ofgalaxy groups and clusters in the intermediate-mass ($M\sim 10^{13} -10^{14}h^{-1} M_\odot$), high-$z$ ($z<\sim1.5$, c.f. $z<\sim0.8$ for the tSZauto-power signal) regime, as well as CIB-decontaminated measurements of tSZcross-correlations with other large-scale structure probes.

Cross-correlation of the thermal Sunyaev--Zel'dovich and CMB lensing signals in Planck PR4 data with robust CIB decontamination