Generalized Crewther relation and a novel demonstration of the scheme independence of commensurate scale relations up to all orders

In this study,we investigate in detail the generalized Crewther Relation(GCR)between the Adler function(D)and the Gross-Llewellyn Smith sum rules coefficient(C^(GLS))using the newly proposed single-scale approach of the principle of maximum conformality(PMC).The resultant GCR is scheme-independent,with the residual scale dependence due to unknown higher-order terms highly suppressed.Thus,a precise test of QCD theory without renormalization schemes and scale ambiguities can be achieved by comparing with data.Moreover,a demonstration of the scheme independence of the commensurate scale relation up to all orders is presented.Additionally,for the first time,the Pade approximation approach has been adopted for estimating the unknown 5th-loop contributions from the known four-loop perturbative series.

Renormalizability of leading order covariant chiral nucleon-nucleon interaction

In this work,we study the renormalization group invariance of the recently proposed covariant power counting in the case of nucleon-nucleon scattering[Chin.Phys.C 42(2018)014103]at leading order.We show that unlike the Weinberg scheme,renormalizaion group invariance is satisfied in the^(3)P0 channel.Another interesting feature is that the^(1)S0 and^(3)P1 channels are correlated.Fixing the relevant low energy constants by ftting to the^(1)S0 phase shiftsat T_(lab)=10 and 25 MeV with cutoff values∧=400-650 MeV,one can describe the 3 P1 phase shifts relatively well.In the limit of∧→∞,the^(1)S0 phase shifts become cutoff-independent,whereas the 3P1 phase shifts do not.This is consistent with the Wigner bound and previous observations that the 3P1 channel is best treated perturbatively.As for the^(2)P1 and^(3)S1-^(3)D1 channels,renormalization group invariance is satisfied.