  We present an observational search for the possible correlation between
cosmic microwave background (CMB) polarization map and soft X-ray background
(SXRB) based on the ROSAT All-sky Survey (RASS) archive and WMAP five-year
observations. This is motivated by the fact that some of the CMB polarization
may arise from the scattering of CMB photons due to the free electrons
generated by X-ray heating sources in the epoch of reionization. Detection of
such a correlation allows one to study the role of X-ray heating in the process
of reionization. However, the cross angular power spectrum of the CMB
polarization and SXRB maps constructed from ROSAT RASS and WMAP five-year maps
is consistent with no correlation. We attribute this negative detection to both
the extremely weak signals and large instrumental noises. While a future search
is needed with high sensitivity instruments for both CMB polarization and soft
X-ray photons, our current results can still be used as a useful constraint on
the effect of X-ray heating in the epoch of reionization.
