main findings of the present work and contribute to the active field of heavy fermion systems.

![\[fig:ansatz\] The external electromagnetic field $\vec{A}$ may couple to conduction electron ($c$-electron), auxiliary fermion ($f$-electron) and more directly the heavy fermion quasi-particle (large tadpole), only the last one is found to be responsible for realistic superfluid response in heavy fermion superconductors.](ansatz.eps){width="0.6\columnwidth"}

As a crucial application of the derived superfluid response formula, we revisit the undoped CeCoIn$_{5}$ and Yb-doped Ce$_{1-x}$Yb$_{x}$CoIn$_{5}$. For the former one, the agreement between theory and experiment is rather good, thus confirms the present theoretical formalism and underlies the dominating heavy fermion excitations. Furthermore, when applied to the Yb-doped latter one, we successfully explains the doping evolution of pairing symmetry in Ce$_{1-x}$Yb$_{x}$CoIn$_{5}$ as a simple doping effect by inspecting its pairing strength. The calculated temperature-dependent superfluid density in both nodal-d wave and nodeless-s wave states is well consistent with available measurement,[@Kim2015] which is a nontrivial check on our theory. In addition, we have derived related formulas for general nonmagnetic impurity and non-local electrodynamics effect, which may be important to realistic applications, e.g. La and Nd substituted CeCoIn$_{5}$.[@Kim2015]

Having succeed in explaining prototypical $115$-series heavy fermion superconductors, we believe that the proposed formalism 