Renormalizability of leading order covariant chiral nucleon-nucleon interaction

Abstract

In this work, we study the renormalization group invariance (RGI) of the recently proposed covariant power counting (PC) scheme in the case of nucleon-nucleon scattering [Chin.Phys. C42 (2018) 014103] at leading order (LO). We show that unlike the LO Weinberg case, RGI is satisfied in the ${}^3{P}_0$ channel, because a term of $p{p}^{\prime }$ appears naturally in the covariant PC scheme at LO. Another interesting feature is that the ${}^1{S}_0$ and ${}^3{P}_1$ channels are correlated. Fixing the two relevant low energy constants by fitting to the ${}^1{S}_0$ phase shifts at $T_{lab.}=10$ and $25$ MeV with a cutoff $\Lambda$ of $400-650$ MeV, the ${}^3{P}_1$ phase shifts can be described relatively well. In the limit of $\Lambda \to \infty$, the ${}^1{S}_0$ channel becomes cutoff independent, while RGI is lost in the ${}^3{P}_1$ channel, consistent with the Wigner bound and the previous observation that the ${}^3{P}_1$ channel better be treated perturbatively. As for the ${}^1{P}_1$ and ${}^3{S}_1$-${}^3{D}_1$ channels, RGI is satisfied, similar to the Weinberg approach.

Comments: 15 pages, 7 figures