Study Of Scale-Fixed Prediction For η_c+γ In Electron-positron Collisions At NNLO In Perturbative QCD

Processes involving the production of heavy quarkonium are important for testing Quantum Chromodynamics(QCD)as well as the effective theory of Nonrelativistic QCD(NQRCD).In the present paper,based on the NRQCD theory,we presented the precise theoretical predictions for γ+ηc production in electron-positron collisions up to next-to-next-to-leading order(NNLO)accuracy without renormalization scale ambiguities using the principle of maximum conformality(PMC).The NNLO total cross section for e++e-→γ+ηc using the conventional scale-setting approach had large renormalization scale ambiguities,usually estimated by choosing the renormalization scale to be the e++e-center-of-mass collision energy(?)and varying within[(?)].According to PMC,such artificially introduced ambiguities can be eliminated.PMC determines the effective strong coupling constant free of renormalization scale dependence by summing the nonconformal {βi} terms.Then the virtuality of the underlying process is achieved.Removing the nonconformal terms enables the PMC series to be independent of renormalization scheme and scale,leading to precise pQCD predictions.Furthermore,PMC can achieve better convergence of pQCD series due to the elimination of divergent renolmalons.After applying the PMC,we did obtain a renormalization scale-and-scheme independent prediction σPMCNNLO=41.18 fb for(?)GeV.The discussion of other main errors from charm quark mass and factorization scale was also involved.We obeserved the poor convergence of the pQCD series even though renormalons were removed.This observation reinforced the importance of uncalculated NNNLO and higher-order terms.Using the PMC scale-and-scheme independent conformal series and the Páde approximation approach,we predicted σPMC+PádeNNNLO=18.99 fb,which wasconsistent with the recent BELLE measurement σobs=16.58-9.93+10.51 fb at(?)GeV.This procedure also provided a first estimate of the NNNLO contribution for this process.