# Gluon condensate and c-quark mass in pseudoscalar sum rules at 3-loop order

Source: [Gluon condensate and c-quark mass in pseudoscalar sum rules at 3-loop order](<https://www.sota2.com/research/paper/68fa25db2c2a3760193b4711>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T11:00:39.335Z

Authors: K. Zyablyuk

Published: 2002-10-07T14:40:59.000Z

## Abstract

Charmonium sum rules for pseudoscalar 0^{-+} state eta\_c(1S) are analyzed within perturbative QCD and Operator Product Expansion. The perturbative part of the pseudoscalar correlator is considered at alpha\_s^2 order and the contribution of the gluon condensate \<G^2\> is taken into account with alpha\_s correction. The OPE series includes the operators of dimension D=6,8 computed both in the instanton and factorization model. The method of moments in MS-bar scheme allows to establish acceptable values of the charm quark mass and gluon condensate, using the experimental mass of eta\_c. In result of the analisys the charm quark mass is found to be m\_c(m\_c)=1.26+-0.02 GeV independently of the condensate value. The sensitivity of the results to various approximations for the massive 3-loop pseudoscalar correlator is discussed.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/hep-ph/0210103>)

[PDF](<https://arxiv.org/pdf/hep-ph/0210103.pdf>)