dimensionless $\lambda^{\ast}$ measures the overlap of pairing function $\gamma_{k}$ on normal-state Fermi surface. Obviously, less (more) overlap between nodal point/line (maximized gap zone) and Fermi surface is helpful to lower ground-state energy and the corresponding pairing strength is larger. In other words, pairing symmetry with larger $\lambda^{\ast}$ will ultimately become the true superconducting pairing instability. For the Fermi surface shown in Fig. \[fig:pairingstrength\], although the nodal line of $d_{x^{2}-y^{2}}$-wave has much overlap over Fermi surface, its high gap zone also has large overlap, thus the whole effect is to promote $d_{x^{2}-y^{2}}$-wave over than the nodeless extended-s wave, (The nodal line of extended-s wave indeed exists but it does not contact with the present Fermi surface, thus it behaves like a nodeless pairing.) which is consistent with the calculated value $\lambda_{d}^{\ast}=0.957>\lambda_{s}^{\ast}=0.875$ and as well agrees with the observed dominated nodal d-wave feature in CeCoIn$_{5}$.

When considering the doping case, we plot the pairing strength $\lambda^{\ast}$ and effective mass ratio $m^{\ast}/m$ in Fig. \[fig:20\]. (We use $t=-1$, $t'=0.14t$, $J_{K}=1.92$, $J_{H}=0.6$, $\chi=0.2222$ and $T=0.01$. $V$, $\mu$ and $\lambda$ are self-consistently solved through mean-field equations.)

![\[fig:20\] Doping evolution of pairing strength $\lambda^{\ast}$ (a) and effective mass ratio $m^{\ast}/m$ (b).](222.eps){width="1.0\columnwidth"}

It is found that when 