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We characterize the Cosmic Infrared Background (CIB)-lensing bispectrum whichis one of the contributions to the three-point functions of Cosmic MicrowaveBackground (CMB) maps in harmonic space. We show that the CIB-lensingbispectrum has a considerable strength and that it can be detected with highsignificance in the Planck high-frequency maps. We also present forecasts ofthe contamination on different shapes of the primordial non-Gaussianity$f_{nl}$ parameter produced by the CIB-lensing bispectrum and by theextragalactic point sources bispectrum in the Planck high-resolution CMBanisotropy maps. The local, equilateral and orthogonal shapes are consideredfor 'raw' single-frequency (i.e., without applying any component separationtechnique) and foreground-reduced Planck temperature maps. The CIB-lensingcorrelation seems to mainly affect orthogonal shapes of the bispectrum - with{\Delta}$f_{nl}$ = -21 and -88 for the 143 and 217 GHz bands respectively -while point sources mostly impact equilateral shapes, with {\Delta}$f_{nl}$ =160, 54 and 60 at 100, 143 and 217 GHz. However, the results indicate thatthese contaminants do not induce any relevant bias on Planck $f_{nl}$ estimateswhen foreground-reduced maps are considered: using SEVEM for the componentseparation we obtain {\Delta}$f_{nl}$ = 10.5 due to the CIB-lensing and{\Delta}$f_{nl}$ = 30.4 due to point sources, corresponding to 0.30{\sigma} and0.45{\sigma} in terms of the Planck 2013 $f_{nl}$ uncertainty. The componentseparation technique is, in fact, able to partially clean the extragalacticsource contamination and the bias is reduced for all the shapes. We havefurther developed single- and multiple-frequency estimators based on theKomatsu, Spergel & Wandelt (2005) formalism that can be implemented toefficiently detect this signal.

The CIB-lensing bispectrum: impact on primordial non-Gaussianity and detectability for the Planck mission