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Abstract: Title: Implications of the dimension two gluon condensate on the deconfined phase of QCD

Abstract: In a series of recent papers it has been shown that the dimension two gluon
condensate can be used to construct a phenomenological model that explain quite well the non-perturbative
behaviour observed in lattice data for the heavy quark-antiquark free energy in the deconfined phase of
QCD [1] and more specifically in the renormalized Polyakov Loop [2,3]. It is considered in this
model a new piece in the gluon propagator driven by a positive mass dimension parameter.
This non-perturbative contribution is the responsible of power-like temperature corrections, in contrast to the flat temperature
dependence of the logarithmic running of the QCD coupling constant derived in perturbation theory. The model
predicts a interesting duality between the zero temperature potential as a function of the q-q separation,
on the one hand, and the quark self-energy as a function of the temperature, on the
other.
At finite temperature the trace of the energy momentum tensor is related not only to the
trace anomaly but also to the difference e - 3p, with e the energy density and
p the pressure [4]. Far from the conformal limit, e = 3p, it provides a measure
of the interaction. It has been shown recently that unmistakable traces of power temperature corrections also
appear in lattice data for the trace anomaly (and pressure) in the region slightly above the
phase transition [5,6]. In the present work we extend the previous phenomenological model to derive this
non-perturbative behaviour, which may be accomodated by the dimension two gluon condensate. We show under Renormalization
Group requeriments, explicit expressions of the thermal behaviour for several observables: pressure, energy density, free energy,
etc; which reproduces very well lattice data. The value for the gluon condensate predicted from these
observables agree quite well with previous works. The mass parameter in the mod!
el signals an explicit breaking of the scale invariance.
This remarkable result seems to imply an unified and coherent description of finite temperature observables in
the deconfined phase of QCD just above the phase transition in terms of the dimension two
gluon condensate.
[1] E.Megias, E. Ruiz Arriola, and L.L. Salcedo, Phys. Rev. D 75, 105019 (2007).
[2] E.Megias, E. Ruiz Arriola, and L.L. Salcedo, JHEP, 0601:073, (2006).
[3] E. Megias, E. Ruiz Arriola, and L.L. Salcedo, Eur. Phys. Journal A31, 553-556 (2007).
[4] N.P.Landsman, and C.G. van Weert, Phys. Rep. 145, 141 (1987).
[5] R.D.Pisarski, Phys. Rev. D 74, 121703 (2006).
[6] M.Cheng et al., Phys. Rev. D 77, 014511 (2008).