Treelevel

Tree level refers to the lowest order term in perturbative quantum field theory for a given process, represented by Feynman diagrams with no closed loops. These loopless diagrams form a tree-like topology, hence the term. The tree-level amplitude is obtained by applying the Feynman rules to all such diagrams and summing them; this is the leading contribution in the expansion in the coupling constants and usually provides the simplest analytic result for cross sections or decay rates.

Examples: electron-positron annihilation into fermions via photon or Z exchange at tree level; QCD processes such as qqbar → qqbar or gg → qqbar often have tree-level contributions from gluon exchange.

While tree-level diagrams are free from loop integrals, they can still be subject to infrared or collinear divergences in certain massless theories when integrating over phase space; but ultraviolet divergences and renormalization appear at loop level.

Tree-level results serve as a starting point for precision predictions; higher-order corrections include one-loop (and multi-loop) diagrams and real emission, collectively referred to as radiative corrections. These loop contributions can be numerically significant when couplings are sizable or when high precision is required, and they test the consistency and renormalizability of the theory.

Tree-level concepts also appear in gravity, where the simplest, non-loop (tree) diagrams describe basic graviton interactions in perturbative quantum gravity frameworks, though a complete quantum gravity theory remains unsettled.