Gluon Condensates and m_b(m_b) from QCD-Exponential Moments at Higher Orders

TL;DR

This paper refines the determination of gluon condensates and the bottom quark mass using QCD exponential moments, including higher-order perturbative and non-perturbative corrections, and compares results from charmonium and bottomonium systems.

Contribution

It introduces an analysis of QCD exponential moments with corrections up to ^3 and D=8 condensates, providing a more precise correlation between gluon condensates and bottom quark mass.

Findings

Determined ^3 corrections improve convergence of sum rules.

Established a correlation between ^2 and ^3 gluon condensates.

Estimated bottom quark mass as 4177(11) MeV from sum rules.

Abstract

We test the convergence of the QCD exponential moments by including PT corrections to order \alpha_s^3 and the NP contributions up to D=8 <G^4> condensates. Then, using the ratio of exponential sum rules where the QCD PT series is more convergent, we study the correlation between the gluon condensates <\alpha_s G^2> and < g^3f_{abc} G^3>. From charmonium systems and using the charm quark mass as input, we deduce:< g^3f_{abc} G^3> =(8.2+-1.0)GeV^2 <\alpha_s G^2> corresponding to < \alpha_s G^2>=(7.5+- 2.0) 10^{-2} GeV^4. Using these results for the bottomium systems, we obtain: m_b(m_b)= 4212(32) MeV, which is slightly higher but consistent within the errrors with the ones from Q^2-moments and their ratios: m_b(m_b)= 4172(12) MeV. We are tempted to consider as a final result from the sum rules approaches, the average m_b(m_b)= 4177(11) MeV of the two previous determinations.