Model Studies On The Non-perturbative Properties Of Heavy Quark Potential

One of the most important goals in high energy physics is to explore a new form of matter which is the so-called Quark Gluon Plasma(QGP).Due to the non-neutrality of the color charge,QGP cannot be directly observed in experiments and a series of effective probes become important in order to learn its physical properties.Quarkonium state,as one widely studied probe,has drawn a lot of attentions from theoretical physicists during the last 30 years.In the non-relativistic limit,a quantum mechanical description of the bound states based on a suitable potential between the heavy quarks appears reasonable.One can obtain the basic information of quarkonia by solving the schrodinger equation.The main content of this thesis will focus on the heavy-quark(HQ)potential.In the real time formalism of finite temperature quantum field theory,the perturbative contribution of the HQ potential can be determined through the threedimensional Fourier transform of the resumed gluon propagator in the static limit.The real part of the potential determines the binding energies while the imaginary part can provide us the information about the decay width.On the other hand,the non-perturbative contribution of the HQ potential is usually obtained by constructing models based on the lattice quantum chromodynamics(lQCD)simulations.However,for the imaginary part of the potential,the non-perturbative properties are not totally clear,therefore,the decay width was not treated in a rigorous way in previous work.With the preliminary lQCD results for the imaginary part of the potential,we have established a phenomenological model in which the long-distance behavior between the quark pair is considered as an effective one-dimensional string interaction and the nonperturbative contributions are obtained from the one-dimensional Fourier transform of the resummed gluon propagator.The real part of this potential model is identical to the famous KMS model while the imaginary part also quantitatively reproduces the lattice result after the temperature dependence of the string tension is taken into account.The most important feature of this model is that the real and imaginary parts of the HQ potential are simultaneously constructed under a unified framework and the two parts share exactly the same parameters.As compared with other existing models,our model has a relatively simple form and significant improvements on the quantitative description of the imaginary part of the HQ potential are also observed.