Abstract
We identify the independent dimension 6 twist 4 gluon operators and calculate their renormalization in the pure gauge theory. By constructing the renormalization group invariant combinations, we find the scale invariant condensates that can be estimated in nonperturbative calculations and used in QCD sum rules for heavy quark systems in medium.
Highlights
Understanding the changes of the matrix elements of the gluon operators near the critical temperature in QCD offers a useful picture on the nature of the QCD phase transition[1]
In the pure gauge theory, the lowest dimensional operators are the scalar gluon condensate and the twist 2 gluon operator. These dimension 4 operators can be reexpressed in terms of the electric condensate and the magnetic condensate
The gauge invariant dimension 6 operators are obtained by combining the covariant derivative Dμ and the field strength tensor Gμν
Summary
Understanding the changes of the matrix elements of the gluon operators near the critical temperature in QCD offers a useful picture on the nature of the QCD phase transition[1]. These can be used in QCD sum rule analysis to understand the changes and melting of heavy quark system at finite temperature[2,3,4]. To further understand the phase transition in terms of local operators and to expand the findings for the charmonium system by using QCD sum rule to dimension 6 level, we will identify the dimension 6 and twist 4 gluon operators and calculate their renormalization in the pure gauge theory.
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