[Paper Review] A QCD Generated Mass Spectrum

B. G. Sidharth|ArXiv.org|Sep 6, 2003

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper proposes a simple formula derived from the QCD potential to predict the masses of all known elementary particles, including the Ds(2317) and a 1.5 GeV pentaquark, with errors under 3% for all but one particle. The model uses a harmonic oscillator approximation based on the pion mass and quantum numbers to generate a mass spectrum that fits experimental data remarkably well.

ABSTRACT

Using the interquark potential we obtain a formula for the mass spectrum of elementary particles. The simple formula gives the masses of all known elementary particles with an error of about three percent or less. This includes the recently discovered Ds (2317) and 1.5GeV Pentaquark particles.

Motivation & Objective

• To derive a unified formula for the mass spectrum of all known elementary particles using only the QCD potential.
• To explain the observed masses of mesons, baryons, and exotic states like the Ds(2317) and 1.5 GeV pentaquark within a single theoretical framework.
• To test whether a minimal model based on the harmonic oscillator approximation of the interquark potential can reproduce particle masses with high accuracy.
• To assess the role of the pion mass and quantum numbers in generating the mass spectrum through a simple scaling law.

Proposed method

• The QCD potential $ U(r) = -\frac{\alpha}{r} + \beta r $ is used, with $ \alpha \approx 1 $, to model quark interactions.
• A tri-quark configuration is assumed, with a central quark experiencing a restoring force approximated as $ \sim -\frac{2\alpha x}{r^3} $, leading to a harmonic oscillator potential.
• The energy levels of the harmonic oscillator are given by $ E = \left(n + \frac{1}{2}\right) m_\pi $, where $ m_\pi $ is the pion mass.
• The total mass of a particle is derived as $ m_P = m \left(n + \frac{1}{2}\right) m_\pi $, where $ m $ and $ n $ are quantum numbers from the oscillator model.
• The formula is applied to 100+ known particles, with $ (m,n) $ pairs adjusted to minimize mass prediction error.
• The model is validated by comparing predicted masses to experimental values from the Particle Data Group.

Experimental results

Research questions

• RQ1 Can a simple formula based on the QCD potential reproduce the masses of all known elementary particles with high accuracy?
• RQ2 Does the harmonic oscillator approximation of the interquark potential naturally explain the observed mass spectrum of mesons and baryons?
• RQ3 How well does the model predict the masses of recently discovered exotic states such as the Ds(2317) and 1.5 GeV pentaquark?
• RQ4 What is the role of the pion mass and quantum numbers $ (m,n) $ in generating the mass spectrum?
• RQ5 Why does the model achieve such high accuracy despite using only bare details of the QCD interaction?

Key findings

• The formula $ m_P = m \left(n + \frac{1}{2}\right) m_\pi $ predicts the masses of all known elementary particles with an error of less than 3% for 97% of particles.
• For 63% of particles, the error is less than 1%, and for 93%, it is less than 2%.
• The model successfully predicts the masses of the Ds(2317) and the 1.5 GeV pentaquark with zero error.
• The only exception is the $ \omega(782) $, with a 3.6% error, still within the 3% threshold for most particles.
• The model reproduces the masses of 100+ particles, including mesons, baryons, charmonia, bottomonia, and exotics, with consistent quantum number assignments.
• The agreement is robust even when only the leading-order QCD potential and harmonic oscillator approximation are used, suggesting deeper underlying structure.