[Paper Review] Relations between elementary particle masses

B. Tatischeff, I. Brissaud|arXiv (Cornell University)|May 3, 2010

Advanced Mathematical Theories and Applications1 references3 citations

TL;DR

This paper proposes a unified power-law framework using the fine structure constant α ≈ 1/137.036 and fundamental masses (proton, pion, neutron) to derive relations between elementary particle masses—quarks, gauge bosons, and leptons—without arbitrary parameters. It predicts the Higgs boson mass at 122 GeV and 128.6 GeV, with high accuracy for known masses like top quark (171.3 GeV vs. 171.2±2.1 GeV) and W/Z bosons.

ABSTRACT

Relations between elementary particles masses are given using only known physical constants, without any arbitrary number.

Motivation & Objective

• To establish parameter-free relations between elementary particle masses using only known physical constants.
• To explore fractal-like patterns in mass hierarchies of quarks, leptons, and gauge bosons.
• To predict unobserved particle masses, especially the Higgs boson and fourth-generation fermions.
• To unify quark, gauge boson, and lepton masses through common physical constants like α and nucleon masses.
• To provide a predictive framework for new physics beyond the Standard Model, including possible fourth-generation particles.

Proposed method

• Uses a power-law recurrence relation: $ m^{(1)}_{n+1} = 2^{2(2-n)} m^{(1)}_n / \alpha $ for quark families, with α as the fine structure constant.
• Applies a modified power-law: $ m^{(2)}_{n+1} = (m_\pi/m_p)^n m^{(2)}_n / \alpha $ for second-family quarks, incorporating pion-to-proton mass ratio.
• Employs a generalized formula $ m^{(k)} = m_\pi \alpha^{(2-n)} r^{n(n+1)+1/2} (2+(-1)^n)/h(n) $ for leptons, with h(n) avoiding division by zero.
• Uses $ M = m_p \alpha^{-1} (n/10)^{1/2} $ to predict gauge boson masses, with n=4 for W and n=5 for Z bosons.
• Derives proton and pion masses from quark and gauge boson relations, establishing a closed mass network.
• Validates predictions against PDG experimental values, calculating relative differences for all particles.

Experimental results

Research questions

• RQ1 Can elementary particle masses be related via a single, parameter-free power-law framework based on fundamental constants?
• RQ2 Do the observed mass ratios of quarks and leptons follow a fractal-like scaling pattern governed by α and nucleon masses?
• RQ3 Can the Higgs boson mass be predicted with high precision using this model, and what are the predicted values?
• RQ4 Do the model's predictions for fourth-generation fermions (t', b') align with current experimental lower bounds?
• RQ5 How do the predicted masses of unobserved gauge bosons (n=1 to 3, 6–8) compare to possible new physics signals?

Key findings

• The top quark mass is predicted at 171.3 GeV, matching the PDG value of 171.2±2.1 GeV with a relative difference of only 5.6×10⁻⁴.
• The W boson mass is predicted at 81.319 GeV, deviating from the experimental value of 80.398±0.025 GeV by only 1.15×10⁻².
• The Z boson mass is predicted at 90.917 GeV, with a relative deviation of 3×10⁻³ from the experimental value of 91.1876±0.0021 GeV.
• The Higgs boson mass is predicted at 122 GeV and 128.6 GeV using n=9 and n=10 in the gauge boson formula, consistent with experimental limits of 110–200 GeV.
• The tau lepton mass is predicted at 1768.97 MeV, deviating by 4.4×10⁻³ from the experimental value of 1776.84 MeV.
• The model predicts a fourth-generation lepton at approximately 505.5 GeV, close to Nottale’s earlier estimate of 502 GeV, and consistent with current lower bounds of m ≥ 100 GeV.