A valid prediction for a physical observable from quantum field theory should be independent of the choice of renormalization scheme -- this is the primary requirement of renormalization group invariance (RGI). Satisfying scheme invariance is a chall
enging problem for perturbative QCD (pQCD), since a truncated perturbation series does not automatically satisfy the requirements of the renormalization group. Two distinct approaches for satisfying the RGI principle have been suggested in the literature. One is the Principle of Maximum Conformality (PMC) in which the terms associated with the $beta$-function are absorbed into the scale of the running coupling at each perturbative order; its predictions are scheme and scale independent at every finite order. The other approach is the Principle of Minimum Sensitivity (PMS), which is based on local RGI; the PMS approach determines the optimal renormalization scale by requiring the slope of the approximant of an observable to vanish. In this paper, we present a detailed comparison of the PMC and PMS procedures by analyzing two physical observables $R_{e+e-}$ and $Gamma(Hto bbar{b})$ up to four-loop order in pQCD. At the four-loop level, the PMC and PMS predictions for both observables agree within small errors with those of conventional scale setting assuming a physically-motivated scale, and each prediction shows small scale dependences. However, the convergence of the pQCD series at high orders, behaves quite differently: The PMC displays the best pQCD convergence since it eliminates divergent renormalon terms; in contrast, the convergence of the PMS prediction is questionable, often even worse than the conventional prediction based on an arbitrary guess for the renormalization scale. ......
We report the synthesis and characterization of bulk form diluted magnetic semiconductors I-II-V Li1.1(Zn1-xCrx)As (x = 0.03, 0.05, 0.10, 0.15)with a cubic crystal structure identical to that of III-V GaAs and II-VI zinc-blende ZnSe. With p-type carr
iers created by excess Li, 10% Cr substitution for Zn results in a ferromagnetic ordering below TC ~ 218 K. Li(Zn,Cr)As represents another magnetic semiconducting system with the advantage of decoupling carriers and spins, where carriers are created by adding extra Li and spins are introduced by Cr substitution for Zn.
