Mass decomposition of the pion in the 't Hooft model

TL;DR

This paper analyzes the mass decomposition of the pion in the 't Hooft model, deriving the energy-momentum tensor and quantifying quark and gluon contributions to the pion's mass using a variational approach.

Contribution

It provides a detailed decomposition of the pion mass into quark and gluon parts within the 't Hooft model, including numerical results for the energy split.

Findings

All light front momentum is carried by quarks.

Gluons carry the self-energy of dressed quarks.

Numerical results for pion mass breakdown.

Abstract

We obtain the energy-momentum tensor (EMT) in the 't Hooft model of two-dimensional quantum chromodynamics. The EMT is decomposed into contributions from quark and gluon fields, with all of the (plus component of) the light front momentum being carried by the quark field. The energy is split between quark and gluon fields, with the gluon field carrying the self-energy of the dressed quarks. We consider the pion in the limit of small but non-zero quark masses -- which has previously withstood numerical treatment -- as as a concrete example. We solve for the pion wave function using a variational method and obtain numerical results for its energy breakdown into quark and gluon contributions.