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 program to compute the result up to any mass dimension.