Theoretical Study on Compositeness in Hadron Physics

In this thesis, we study the consistency and evaluation of compositeness under a theoretical approach.Compositeness is a quantity first proposed by Steven Weinberg in order to account for the problem of whether a particle is elementary or not.Compositeness is defined as a proportion of the origin of a bound state that can be attributed to a scattering state, and elementariness is the proportion attributed to an elementary state in a similar manner.However, the calculation of the deuteron compositeness generates unrealistic quantity, and we attempt to solve this problem.We first attempt to perform numerical calculation of the deuteron using a modern interpretation of compositeness with different models, in the hope of finding a type of interaction that can recover the deuteron properties and yield physical compositeness at the same time.We attempt low energy constants (LEC) models, one pion exchange potential (OPEP), Yamaguchi potential, and square well potential.However, none of the interactions can succeed in both deuteron property and physical compositeness.This raises the suspicion that the unphysical compositeness is caused by a deeper physical reason rather than the absence of a good interaction model.We postulate that the unphysical compositeness is a consequence of attributing any energy dependency into other states, which we call the surjective interpretation.To test this postulation, we formalize a modified definition of compositeness with explicit energy dependency in interaction.Utilizing this method, we are able to perform a perturbative calculation of compositeness and confirm our postulation.We conclude that an attractive energy-dependent perturbation from an energy-independent theory is highly likely to enhance the compositeness from unity, which is the case of the deuteron.Our outcome indicates that, rather than the lack of a realistic interaction potential, it is the formalism of compositeness that requires modification.The first proposed solution is to explicitly separate different contributions from the interaction potential.In the deuteron, the pions play an important role, and it may be counterintuitive to attribute such interaction to elementariness due to the lack of a one-body state.We propose a new quantity interactioness to account for this contribution and combine interactionesss into compositeness considering its dynamical origin.However, this proposed solution makes compositeness no longer model-independent, diminishing its meaning in a phenomenology setting.We then propose a second solution, which tries to be model-independent as well as always generates physical quantity.We are motivated by S. Weinberg's notion when compositeness was originally defined and the extreme case that the hydrogen atom is always considered a composite particle.We observe that the energy scale is of great importance in this process.As a result, we define energy decomposition as compositeness.For the delta function in the 1-dimensional scenario, it yields the same outcome as the original definition.