On mass dependences of the one-loop effective action in simple backgrounds

If background fields are soft on the scale set by mass of the particle involved, a reliable approximation to the field-theoretic one-loop effective action is obtained by a systematic large mass expansion involving higher-order Seeley-DeWitt coefficients. Moreover, if the small mass limit of the effective action in a particular background has been found by some other means, the two informations may be used to infer the corresponding result for {\em arbitrary} mass values. This method is used to estimate the one-loop contribution to the QCD vacuum tunneling amplitude by quarks of arbitrary mass.