Application of Effective Field Theory in Nuclear Physics

The production of heavy quarkonium in heavy ion collisions has been used as an important probe of the quark-gluon plasma (QGP). Due to the plasma screening effect, the color attraction between the heavy quark antiquark pair inside a quarkonium is significantly suppressed at high temperature and thus no bound states can exist, i.e., they ``melt". In addition, a bound heavy quark antiquark pair can dissociate if enough energy is transferred to it in a dynamical process inside the plasma. So one would expect the production of quarkonium to be considerably suppressed in heavy ion collisions. However, experimental measurements have shown that a large amount of quarkonia survive the evolution inside the high temperature plasma. It is realized that the in-medium recombination of unbound heavy quark pairs into quarkonium is as crucial as the melting and dissociation. Thus, phenomenological studies have to account for static screening, dissociation and recombination in a consistent way. But recombination is less understood theoretically than the melting and dissociation. Many studies using semi-classical transport equations model the recombination effect from the consideration of detailed balance at thermal equilibrium. However, these studies cannot explain how the system of quarkonium reaches equilibrium and estimate the time scale of the thermalization. Recently, another approach based on the open quantum system formalism started being used. In this framework, one solves a quantum evolution for in-medium quarkonium. Dissociation and recombination are accounted for consistently. However, the connection between the semi-classical transport equation and the quantum evolution is not clear.

In this dissertation, I will try to address the issues raised above. As a warm-up project, I will first study a similar problem: $\alpha$-$\alpha$ scattering at the $^8$Be resonance inside an $e^-e^+\gamma$ plasma. By applying pionless effective field theory and thermal field theory, I will show how the plasma screening effect modifies the $^8$Be resonance energy and width. I will discuss the need to use the open quantum system formalism when studying the time evolution of a system embedded inside a plasma. Then I will use effective field theory of QCD and the open quantum system formalism to derive a Lindblad equation for bound and unbound heavy quark antiquark pairs inside a weakly-coupled QGP. Under the Markovian approximation and the assumption of weak coupling between the system and the environment, the Lindblad equation will be shown to turn to a Boltzmann transport equation if a Wigner transform is applied to the open system density matrix. These assumptions will be justified by using the separation of scales, which is assumed in the construction of effective field theory. I will show the scattering amplitudes that contribute to the collision terms in the Boltzmann equation are gauge invariant and infrared safe. By coupling the transport equation of quarkonium with those of open heavy flavors and solving them using Monte Carlo simulations, I will demonstrate how the system of bound and unbound heavy quark antiquark pairs reaches detailed balance and equilibrium inside the QGP. Phenomenologically, my calculations can describe the experimental data on bottomonium production. Finally I will extend the framework to study the in-medium evolution of heavy diquarks and estimate the production rate of the doubly charmed baryon $\Xi_{cc}^{++}$ in heavy ion collisions.