Renormalizability of leading order covariant chiral nucleon-nucleon interaction *

In this work, we study the renormalization group invariance (RGI) of recently proposed covariant power counting (PC) scheme in case nucleon-nucleon scattering [Chin.Phys. C42 (2018) 014103] at leading order (LO). We show that unlike LO Weinberg case, RGI is satisfied $^3P_{0}$ channel, because a term $pp'$ appears naturally PC LO. Another interesting feature $^1S_{0}$ and $^3P_{1}$ channels are correlated. Fixing two relevant low energy constants by fitting to phase shifts $T_\mathrm{lab.}=10$ $25$ MeV with cutoff $\Lambda$ $400-650$ MeV, can be described relatively well. limit $\Lambda\rightarrow \infty$, $^1S_0$ channel becomes independent, while lost consistent Wigner bound previous observation $^{3}P_1$ better treated perturbatively. As for $^1P_{1}$ $^3S_{1}$-$^3D_{1}$ channels, satisfied, similar approach.