QCD's Partner needed for Mass Spectra and Parton Structure Functions

TL;DR

This paper discusses the development of Lorentz-invariant wave functions for hadronic spectra and parton distributions, emphasizing the need for QCD corrections to connect theoretical models with experimental data.

Contribution

It introduces a Lorentz-invariant harmonic oscillator framework for hadronic spectra and highlights the necessity of QCD corrections for accurate parton distribution calculations.

Findings

Lorentz-invariant wave functions generate hadronic mass spectra.

Boosted wave functions require QCD corrections for accurate parton distributions.

The framework links wave functions to parton structure functions.

Abstract

As in the case of the hydrogen atom, bound-state wave functions are needed to generate hadronic spectra. For this purpose, in 1971, Feynman and his students wrote down a Lorentz-invariant harmonic oscillator equation. This differential equation has one set of solutions satisfying the Lorentz-covariant boundary condition. This covariant set generates Lorentz-invariant mass spectra with their degeneracies. Furthermore, the Lorentz-covariant wave functions allow us to calculate the valence parton distribution by Lorentz-boosting the quark-model wave function from the hadronic rest frame. However, this boosted wave function does not give an accurate parton distribution. The wave function needs QCD corrections to make a contact with the real world. Likewise QCD needs the wave function as a starting point for calculating the parton structure function.