Finite Volume Amplitudes of Two-body scattering interactions with a Light Particle Exchange. SAMANTHA GOLDBERG (University of Texas at Austin) DR. RAUL BRICENO (Thomas Jefferson National Accelerator Facility)

Quantum chromodynamics (QCD) describes the strong force and all possible interactions between quarks, with gluons serving as the principle force-carriers. Understanding interactions governed by the strong force has proven to be difficult when occurring in real time, with an infinite scattering length, and an infinite volume. Implementing a lattice model (Lattice QCD) is a non-perturbative approach to QCD in order to accommodate this problem. Within Lattice QCD, the Luescher formalism allows one to solve for the spectrum of scattering interactions within a finite, space-like cubic volume with periodic boundary conditions. One issue with the Leuscher formalism that remains to be accounted for is the Luescher formalism’s inability to calculate information about certain scattering processes due to singularities in the scattering amplitude that occur. One such interaction is a two-particle scattering process where a light particle is exchanged. First, we calculate the scattering amplitudes of two hadronic particles. Then, we introduce the Luescher formalism which describes the scattering amplitudes of two particles in a lattice box described by the finite volume function. We plot the free and interacting spectrums. After this, we find the infinite-volume scattering amplitudes over a range of energies of two-particle scattering interactions with a light particle exchange. As the project continues, we will implement these scattering interactions into the Leuscher formalism, in the hopes of developing a method to produce a resulting spectrum. This project is significant to the field of Lattice QCD due to its potential for novel insight about previously forbidden scattering processes in a finite volume. These findings ultimately help us to understand how a variety of particles interact via the strong force in the Universe.