STATIC QUARK ANTI-QUARK FREE AND INTERNAL ENERGY IN 2-FLAVOR QCD AND BOUND STATES IN THE QGP. Page: 4 of 8
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Static quark anti-quark free and internal energy in 2-flavor QCD
1000 . :' 1.5
500 0.90T - 1
o 0 0.96T ; -
' - 1.07Tc ~.5-!.
-500 r [fm] ,4.01TI --_ 0
0 0.5 1 1.5 2 2.5 3 0 1 2 3 T/Tc 4
Figure 1: (left) The colour singlet quark anti-quark free energies, Fl (r, T), at several temperatures as func-
tion of distance in physical units. Shown are results from lattice studies of 2-flavour QCD (from ). The
solid line represents the T = 0 heavy quark potential, V (r). The dashed error band corresponds to the string
breaking energy at zero temperature, V(rbreaking) ~ 1000 - 1200 MeV, based on the estimate of the string
breaking distance, breaking ~ 1.2- 1.4 fm . (right) The screening radius estimated from the inverse Debye
mass, rD = 1/m (Nf=0: open squares, Nf=2 filled squares), and the scale r,7ed (Nf=0: open circles, Nf=2:
filled circles, Nf=3: crosses) defined in (2.1) as function of T /TC. The horizontal lines give the mean squared
charge radii of some charmonium states, J/y, Xc and y/ (see also [3, 4]) and the band at the left frame shows
the distance at which string breaking is expected in 2-flavor QCD at T = 0 and quark mass mnr/rnp ~ 0.7
A simple Ansatz to study the possible existence of bound states above the critical temperature
is to use effective temperature dependent potentials that model the medium modifications of strong
interactions in a quark gluon plasma. To what extend a suitable effective potential at finite tem-
perature can be defined by quark antiquark free or internal energies and furthermore how realistic
such (simple) descriptions of bound states in a deconfined medium are is still an open question.
By comparing the screening radii obtained from lattice results on singlet free energies in 2-flavour
QCD to the mean squared charge radii we obtain first estimates on the temperatures where char-
monium bound states may be influenced by medium effects. In more realistic potential model
calculations effective temperature dependent potentials that model medium effects are used in the
Schrodinger equation. We present the heavy quark free energies and their contributions, i.e. en-
tropy and internal energy, and discuss the different results obtained using those contributions in
2. Screening radii and medium modifications
In Fig. 1 (left) we show results for the heavy quark anti-quark free energies in 2-flavour QCD
. While in the limit of short distances F (r, T) shows no or only little medium effects, i.e. Fl (r -+
0) ~ V(r), at large distances the free energies approach temperature dependent constant values,
F (T) F1 (r -+ , T). To characterise distances at which medium effects become important we
introduce a screening radius, rnzed, defined by the distance at which the value of the zero temperature
r [fml rmed
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ZANTOW, F. & KACZMAREK, O. STATIC QUARK ANTI-QUARK FREE AND INTERNAL ENERGY IN 2-FLAVOR QCD AND BOUND STATES IN THE QGP., article, July 25, 2005; [Upton, New York]. (https://digital.library.unt.edu/ark:/67531/metadc780757/m1/4/: accessed April 18, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.