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Modelling the anisotropies in the CIB on all the scales is a challenging taskdue to the complex nature of the galaxy evolution and thus often requires toomany parameters in order to fit the observational data. In this paper, wepresent a new halo model for the anisotropies of the CIB using only fourparameters. Our model connects the mass accretion on the dark matter halos tothe star formation rate. Using this model, we find that the halo mass with themaximum efficiency for converting the accreted baryons into stars is$\log_{10}M_\mathrm{max} = {12.94}^{+0.02}_{-0.02} \: M_\odot$, consistent withother studies. Accounting for the mass loss through stellar evolution, we find,for an intermediate age galaxy, that the star formation efficiency defined as$M_\star(z)/M_b(z)$ is equal to 0.19 and 0.21 at redshift 0.1 and 2respectively, in good agreement with the values obtained by previous studies.It is the first time that a CIB model is used to fit Planck and Herschel CIBpower spectra simultaneously. However we find that the large angular scalePlanck and Herschel data are not fully compatible with the small scale Herscheldata (for $\ell>3000$). The CIB is expected to be correlated with the tSZsignal of the galaxy clusters. Using this halo model for the CIB, and a halomodel for the tSZ with a single parameter, we also provide a consistentframework to calculate this cross-correlation, which requires no extraparameter. The CIB$\times$tSZ correlation is found to be higher when inferredwith a combination of two widely spaced frequency channels (e.g. 143x857 GHz).The CIB, tSZ, and CIB$\times$tSZ act as foregrounds while measuring the kSZpower spectrum from the CMB power spectrum and need to be removed. Due to itssimplistic nature and low number of parameters, the halo model formalismpresented here is quite useful for such an analysis to measure the kSZ powerspectrum accurately.

Simple halo model formalism for the cosmic infrared background and its correlation with the thermal Sunyaev Zel'dovich effect