Regularization Ambiguity Problem for the Chern-Simons Shift
  We consider the Chern-Simons parameter shift with the hybrid regularization consisting of the higher covariant derivative (HCD) and the Pauli-Villars (PV) regulators. We show that the shift is closely related to the parity of the regulators and get the shift and no-shift results by a suitable choice of the PV regulators. A naive treatment of the HCD term leads incorrect value of the shift. 
K. Nittoh and T. Ebihara