Towards a Born term for hadrons

TL;DR

This paper investigates bound states of an abelian gauge theory in 1+1 dimensions, deriving a Born-term-like approximation for hadrons, and analyzing their wave functions, form factors, and parton distributions within a covariant framework.

Contribution

It introduces a gauge-invariant, covariant approach to bound states in 1+1D gauge theory, proposing a Born-term approximation for hadrons based on a boundary condition for the confining potential.

Findings

Discrete bound state masses for fermion-antifermion pairs

Wave functions consistent with parton model at high kinetic energy

Gauge-invariant form factors and large sea contributions at low Bjorken x

Abstract

We study bound states of abelian gauge theory in D=1+1 dimensions using an equal-time, Poincare-covariant framework. The normalization of the linear confining potential is determined by a boundary condition in the solution of Gauss' law for the instantaneous A^0 field. As in the case of the Dirac equation, the norm of the relativistic fermion-antifermion (f\bar{f}) wave functions gives inclusive particle densities. However, while the Dirac spectrum is known to be continuous, we find that regular f\bar{f} solutions exist only for discrete bound state masses. The f\bar{f} wave functions are consistent with the parton picture when the kinetic energy of the fermions is large compared to the binding potential. We verify that the electromagnetic form factors of the bound states are gauge invariant and calculate the parton distributions from the transition form factors in the Bjorken limit. For relativistic states we find a large sea contribution at low Bjorken x. Since the potential is independent of the gauge coupling the bound states may serve as "Born terms" in a perturbative expansion, in analogy to the usual plane wave in and out states.