Computation of Structure Functions From a Lattice Hamiltonian

TL;DR

This paper presents a method to compute structure functions in a Hamiltonian lattice framework, successfully describing continuum physics and reproducing key features of QCD-like behavior.

Contribution

It introduces a physically motivated regularisation linking parton number to lattice size, enabling continuum physics description in Hamiltonian lattice calculations.

Findings

Successful computation of the critical line and mass spectrum near criticality.

Observation of scaling behavior consistent with previous lattice results.

Distribution functions exhibit QCD-like $Q^2$ dependence and a peak at $x_B ightarrow 0$.

Abstract

We compute structure functions in the Hamiltonian formalism on a momentum lattice using a physically motivated regularisation that links the maximal parton number to the lattice size. We show for the $\phi ^4 _{3+1}$ theory that our method allows to describe continuum physics. The critical line and the renormalised mass spectrum close to the critical line are computed and scaling behaviour is observed in good agreement with L{\"u}scher and Weisz' lattice results. We then compute distribution functions and find a $Q^2$ behaviour and the typical peak at $x_B\rightarrow 0$ like in $QCD$.