  The cosmic infrared background (CIB) anisotropies and cosmic microwave
background (CMB) lensing are powerful measurements for exploring the
cosmological and astrophysical problems. In this work, we measure the
auto-correlation power spectrum of the CIB anisotropies in the Herschel-SPIRE
HerMES Large Mode Survey (HeLMS) field, and the cross power spectrum with the
CMB lensing measurements from the Planck satellite. The HeLMS field covers more
than 270 deg^2, which is much larger than the previous analysis. We use the
Herschel Level 1 time stream data to merge the CIB maps at 250, 350, and 500 um
bands, and mask the areas where the flux is greater than 3-sigma (~50 mJy/beam)
or no measured data. We obtain the final CIB power spectra at 100<ell<20000 by
considering several effects, such as beam function, mode coupling, transfer
function, and so on. We also calculate the theoretical CIB auto- and
cross-power spectra of CIB and CMB lensing by assuming that the CIB emissivity
follows Gaussian distribution in redshift. We find that, for the CIB auto power
spectra, we obtain the signal to noise ratio (SNR) of 15.9, 15.7, and 15.3 at
250, 350, and 500 um, and for the CIBxCMB lensing power spectra, SNR of 7.5,
7.0, and 6.2 at 250, 350, and 500 um, respectively. Comparing to previous
works, the constraints on the relevant CIB parameters are improved by factors
of 2~5 in this study.
