Anyon Scattering from Lightcone Hamiltonian: the Singlet Channel

TL;DR

This paper computes the exact 2-to-2 scattering amplitude in the singlet channel of U(N) Chern-Simons theory with massive fermions using lightcone Hamiltonian formalism, confirming a prior conjecture.

Contribution

It introduces a regularization scheme, restores relativistic invariance, and solves the scattering problem exactly in the planar limit, providing a rigorous derivation of the S-matrix.

Findings

Exact 2-to 2 scattering amplitude in the singlet channel obtained

Regularization scheme consistent with relativistic invariance established

Result confirms previous conjecture in the literature

Abstract

We study $U(N)$ Chern-Simons theory coupled to massive fundamental fermions in the lightcone Hamiltonian formalism. Focusing on the planar limit, we introduce a consistent regularization scheme, identify the counter terms needed to restore relativistic invariance, and formulate scattering theory in terms of unambiguously defined asymptotic states. We determine the $2\to 2$ planar S-matrix element in the singlet channel by solving the Lippmann-Schwinger equation to all orders, establishing a result previously conjectured in the literature