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 challenging problem for perturbative QCD (pQCD), since a truncated perturbation series does not automatically satisfy the requirements of the renormalization group. In a previous review, we provided a general introduction to the various scale setting approaches suggested in the literature. As a step forward, in the present review, we present a discussion in depth of two well-established scale-setting methods based on RGI. One is the 'principle of maximum conformality' (PMC) in which the terms associated with the β-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 [Formula: see text] 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. PMC predictions also have the property that any residual dependence on the choice of initial scale is highly suppressed even for low-order predictions. Thus the PMC, based on the standard RGI, has a rigorous foundation; it eliminates an unnecessary systematic error for high precision pQCD predictions and can be widely applied to virtually all high-energy hadronic processes, including multi-scale problems.

We observe a narrow enhancement near 2m(p) in the invariant mass spectrum of pp pairs from radiative J/psi-->gammapp decays. No similar structure is seen in J/psi-->pi(0)pp decays. The results are based on an analysis of a 58 x 10(6) event sample of J/psi decays accumulated with the BESII detector at the Beijing electron-positron collider. The enhancement can be fit with either an S- or P-wave Breit-Wigner resonance function. In the case of the S-wave fit, the peak mass is below 2m(p) at M=1859(+3)(-10) (stat)+5-25(syst) MeV/c(2) and the total width is Gamma<30 MeV/c(2) at the 90% confidence level. These mass and width values are not consistent with the properties of any known particle.

We report values of R = sigma(e(+)e(-)-->hadrons)/sigma(e(+)e(-)-->mu(+)mu(-)) for 85 center-of-mass energies between 2 and 5 GeV measured with the upgraded Beijing Spectrometer at the Beijing Electron-Positron Collider.

We study the pion leading-twist distribution amplitude (DA) within the framework of SVZ sum rules under the background field theory. To improve the accuracy of the sum rules, we expand both the quark propagator and the vertex (z · ↔ D)n of the correlator up to dimension-six operators in the background field theory. The sum rules for the pion DA moments are obtained, in which all condensates up to dimension-six have been taken into consideration. Using the sum rules, we obtain ξ 2 |1 GeV = 0.338 ± 0.032, ξ 4 |1 GeV = 0.211 ± 0.030 and ξ 6 |1 GeV = 0.163 ± 0.030. It is shown that the dimension-six condensates shall provide sizable contributions to the pion DA moments. We show that the first Gegenbauer moment of the pion leading-twist DA is a π 2 |1 GeV = 0.403 ± 0.093, which is consistent with those obtained in the literature within errors but prefers a larger central value as indicated by lattice QCD predictions.

No abstract