One-loop effective action up to any mass-dimension for non-degenerate scalars and fermions including light–heavy mixing

We propose a heat-kernel-based method to compute one-loop effective action up to any mass-dimension with arbitrary numbers of non-degenerate scalars and fermions. We demonstrate our prescription by computing the dimension six effective action for arbitrary numbers of non-degenerate scalars, which are consistent with degenerate results presented in prior studies. We have further shown that the effective action for any partially degenerate mass-spectrum can be easily derived from that for the non-degenerate case by employing suitable limits for masses. Our prescription allows us to express the effective action in terms of local operators for the scenarios that involve light–heavy mixing as well, simply by employing an infrared regulator in the non-degenerate action. Along with the formalism, we have also provided the algorithm and outlined the Mathematica programme to compute the result up to any mass dimension.