Gluon Condensates and precise mc,b\overline{m}_{c,b} from QCD-Moments and their ratios to Order αs3\alpha_s^3 and < G4^4 >

May, 2011
11 pages
Published in:
  • Phys.Lett.B 706 (2012) 412-422
  • Published: Jan 5, 2012
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Abstract: (Elsevier)
We reconsider the extraction of the gluon condensates 〈αsG2〉 , 〈g3fabcG3〉 and the MS¯ running quark masses m¯c,b from different Mn(Q2) moments and their ratios by including PT corrections to order αs3 , NPT terms up to 〈G4〉 and using stability criteria of the results versus the degree n (number of Q2 -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 〈αsG2〉 with 〈g3fabcG3〉 and 〈G4〉 , we obtain 〈αsG2〉=(7.0±1.3)×10−2 GeV4 and 〈g3fabcG3〉=(8.8±5.5) GeV2×〈αsG2〉 , while our analysis favours a modified precise factorisation for 〈G4〉 . Using the previous results, we re-determine m¯c(m¯c) 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 m¯c(m¯c) versus the variations of n and the continuum models are reached. These features can indicate that the quoted errors of m¯c,b from M1(0) may have been underestimated. Our best results from different high- n moments and their ratios are: m¯c(m¯c)=1261(16) MeV and m¯b(m¯b)=4171(14) MeV , in excellent agreement with results obtained in Narison (2010) [1] using some judicious choices of ratios of moments.
Note:
  • 11 pages, 9 figures, 5 tables. Improved version to appear in Phys. Lett. B including a reevaluation of the different sources of the errors
  • QCD spectral sum rules
  • Gluon condensates
  • Heavy quark masses
  • gluon: condensation
  • charm: mass
  • bottom: mass
  • stability
  • moment: higher-order
  • factorization
  • quantum chromodynamics