Simplified Pure Spinor b Ghost in a Curved Heterotic Superstring   Background
  Using the RNS-like fermionic vector variables introduced in arXiv:1305.0693, the pure spinor $b$ ghost in a curved heterotic superstring background is easily constructed. This construction simplifies and completes the $b$ ghost construction in a curved background of arXiv:1311.7012. 
Nathan Berkovits and Osvaldo Chandia
hep-th