In quantum field theory, tree-level diagrams and loop diagrams represent different orders of perturbation theory calculations for particle interactions. Here's an explanation of the differences between these two types of diagrams:
Tree-level diagrams: Tree-level diagrams are the simplest Feynman diagrams and represent the leading-order contributions to a scattering or interaction process. They involve the direct interactions between particles without any loops. Each line in a tree-level diagram represents a particle propagating from an initial state to a final state, and the vertices represent the interaction points between the particles. Tree-level diagrams are often associated with classical descriptions of particle interactions and provide a good approximation for many processes.
Loop diagrams: Loop diagrams, also known as quantum corrections or higher-order diagrams, involve virtual particles and loops. Virtual particles are particles that can temporarily pop into existence and interact with other particles before disappearing again. In loop diagrams, these virtual particles can circulate in closed loops, contributing to the overall calculation of the process. Loop diagrams arise due to quantum fluctuations and represent higher-order corrections beyond the tree-level approximation.
Loop diagrams introduce additional complexity because they involve integrations over all possible momenta of the virtual particles in the loop. The contributions from loop diagrams are generally smaller than those from tree-level diagrams but can lead to significant modifications of the tree-level results. They account for quantum effects, such as corrections to particle masses, electromagnetic interactions, and the Lamb shift, among others.
Loop calculations require careful treatment to handle infinities that arise in some calculations, a phenomenon known as ultraviolet divergences. Techniques like renormalization are employed to remove these divergences and obtain meaningful, finite results.
In summary, tree-level diagrams represent the leading-order contributions to a process without virtual particles or loops, while loop diagrams involve virtual particles circulating in loops and provide higher-order corrections to the tree-level approximation, taking into account quantum effects.