  The charge and spin correlations in La$_{1.875}$Ba$_{0.125}$CuO$_4$ (LBCO
1/8) are studied using Cu $L_3$ edge resonant inelastic x-ray scattering
(RIXS). The static charge order (CO) is observed at a wavevector of $(0.24,0)$
and its charge nature confirmed by measuring the dependence of this peak on the
incident x-ray polarization. The paramagnon excitation in LBCO 1/8 is then
measured as it disperses through the CO wavevector. Within the experimental
uncertainty no changes are observed in the paramagnon due to the static CO, and
the paramagnon seems to be similar to that measured in other cuprates, which
have no static CO. Given that the stripe correlation modulates both the charge
and spin degrees of freedom, it is likely that subtle changes do occur in the
paramagnon due to CO. Consequently, we propose that future RIXS measurements,
realized with higher energy resolution and sensitivity, should be performed to
test for these effects.
