Impact of radio sources and cosmic infrared background on thermal
  Sunyaev-Zel'dovich - gravitational lensing cross correlation
  Cross correlation with thermal Sunyaev-Zel'dovich (tSZ) effect in cosmic
microwave background observation and weak gravitational lensing effect in
galaxy imaging survey opens a new window on constraining matter contents in the
Universe at redshift less than 1. In this paper, we study the impact of radio
sources and cosmic infrared background (CIB) on observed tSZ-lensing
correlation. Assuming the best-fit model of CIB by the Planck satellite, we
estimate that the residual correlation of CIB with large-scale structures will
be of an order of $2\%$ of expected tSZ-lensing correlation from intracluster
medium in current lensing surveys. On the other hand, despite large model
uncertainties, we find that correlation of lensing and radio sources can induce
a negative correction for the observed tSZ-lensing correlation with a
$\sim10-30\%$ level. This is originated from positive cross correlation with
radio sources and lensing at $\sim100\, {\rm GHz}$ frequency, whereas
tSZ-lensing correlation should show a negative value in temperature
fluctuations at that frequency. We also show that the negative correction by
radio-lensing correlation can solve the tension between recent measurements of
tSZ-lensing correlation and an expected signal from "universal" gas pressure
profile of nearby galaxy clusters, when the radio sources with flat-spectral
index are assumed to populate massive cluster-sized dark matte halos. Our
results indicate that minor source population in radio bands can play an
important role in determining observed tSZ-lensing correlation at $<10$ arcmin.
