Simplified D=11 Pure Spinor b Ghost

A $b$-ghost was constructed for the $D=11$ non-minimal pure spinor superparticle by requiring that $\{Q,b\}=T$ where $Q = \Lambda^{\alpha}D_{\alpha} + R^{\alpha}\bar{W}_{\alpha}$ is the usual non-minimal pure spinor BRST operator. As was done for the $D=10$ $b$-ghost, we will show that the $D=11$ $b$-ghost can be simplified by introducing an $SO(10,1)$ fermionic vector ${\bar{\mathrm{\Sigma }}}^i$ constructed out of the fermionic spinor $D_{\alpha }$ and pure spinor variables. This simplified version will be shown to satisfy $\{Q,b\}=T$ and $\{b,b\}=$ BRST - trivial.