Gluon Condensates and m_{c,b} from QCD-Moments and their ratios to Order alpha_s^3 and <G^4>

TL;DR

This paper refines the extraction of gluon condensates and quark masses from QCD moments by including higher-order corrections and analyzing stability, leading to more accurate and reliable determinations of these fundamental parameters.

Contribution

It introduces an improved method for extracting gluon condensates and quark masses using higher moments and ratios, incorporating alpha_s^3 corrections and <G^4> terms, with stability analysis.

Findings

Gluon condensate <alpha_s G^2> = (7.0 ± 1.3)×10^{-2} GeV^4

Charm quark mass m_c(m_c) = 1261(16) MeV

Bottom quark mass m_b(m_b) = 4171(14) MeV

Abstract

We reconsider the extraction of the gluon condensates <alpha_s G^2>, <g^3f_{abc} G^3> and the MS running quark masses m_{c,b} from different M_n(Q^2) Moments and their Ratios by including PT corrections to order alpha_s^3, NPT terms up to <G^4> 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 M_1(0) depends strongly (as expected) on its high-energy (continuum) contribution, which is minimized for M_{n> 3-4}(0). Using higher moments and the correlations of <alpha_s G^2> with <g^3f_{abc} G^3> and < G^4>, we obtain <alpha_s G^2>=(7.0+- 1.3)10^{-2} GeV^4 and <g^3f_{abc} G^3>=(8.8+- 5.5) GeV^2 <alpha_s G^2>, while our analysis favours a modified factorisation for <G^4>. Using the previous results, we re-determine m_c(m_c) and find that the commonly used M_1(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 M_1(0) may have been underestimated. Optimal results from different high-n moments converge to the accurate (artithmetic) mean values: m_c(m_c)=1261(16) MeV and m_b(m_b)=4171(14) MeV, in excellent agreement with results obtained in [1] using some judicious choices of ratios of moments.