Gluon condensates and precise mc,b from QCD-moments and their ratios to order αs3 and {left double angle bracket;G~4{right double angle bracket}

摘要

We reconsider the extraction of the gluon condensates {left double angle bracket;α_sG~2{right double angle bracket}, {left double angle bracket;g~3f_(ab))G~3{right double angle bracket} and the MS running quark masses mc,b from different Mn(Q2) moments and their ratios by including PT corrections to order αs3, NPT terms up to {left double angle bracket;G~4{right double angle bracket} and using stability criteria of the results versus the degree n (number of Q~2-derivative). We explicitly show that the spectral part of the lowest moment M1(0) depends strongly (as expected) on its high-energy (continuum) contribution, which is minimized for Mn≥3-4(0). Using higher moments and the correlations of {left double angle bracket;α_sG~2{right double angle bracket} with {left double angle bracket;g~3f_(abc)G~3{right double angle bracket} and {left double angle bracket;G~4{right double angle bracket}, we obtain {left double angle bracket;α_sG~2{right double angle bracket}=(7.0±1.3)×10~(-2)GeV~4 and {left double angle bracket;g~3f_(abc)G~3{right double angle bracket}=(8.8±5.5)GeV~2×{left double angle bracket;α_sG~2{right double angle bracket}, while our analysis favours a modified precise factorisation for {left double angle bracket;G~4{right double angle bracket}. Using the previous results, we re-determine mc(mc) and find that the commonly used M1(0) lowest moment tends to overestimate its value compared to the ones from higher moments where stable values of mc(mc) versus the variations of n and the continuum models are reached. These features can indicate that the quoted errors of mc,b from M1(0) may have been underestimated. Our best results from different high-n moments and their ratios are: mc(mc)=1261(16)MeV and mb(mb)=4171(14)MeV, in excellent agreement with results obtained in Narison (2010) [1] using some judicious choices of ratios of moments.