[Paper Review] Lepton and meson masses

Gustavo R. González-Martín|ArXiv.org|May 19, 2004

Particle physics theoretical and experimental studies4 references3 citations

TL;DR

This paper proposes a geometric unified theory where leptons arise as topological excitations of the electron or neutrino, predicting lepton masses via geometric mass ratios. It calculates the muon mass at 107.59 MeV and the tau mass at 1770.3 MeV, while attributing 140.88 MeV and 494.76 MeV to the pion and kaon masses respectively through geometric interaction energy, with corrections accounting for experimental discrepancies.

ABSTRACT

The lepton mass ratios are calculated using a geometric unified theory, taking the leptons as the only three possible families of topological excitations of the electron or the neutrino. The theoretical results give 107.5916 Mev for the muon mass and 1770.3 Mev for the tau mass using the mass ratios. Using the additional geometric interaction energy in a muon-neutrino system, the main leptonic mass contribution to the pion and kaon mass is calculated to be, respectively, 140.88 Mev and 494.76 Mev. The necessary first order corrections, due to the interaction of the excitations, should be of the order of the discrepancies with experimental values. The three geometric families of leptonic excitations may be related to a quark structure.

Motivation & Objective

• To explain lepton mass ratios using a geometric unified theory based on topological excitations of the electron or neutrino.
• To derive the masses of the muon and tau lepton from geometric mass ratios without relying on the Higgs mechanism.
• To calculate the main geometric contribution to the pion and kaon masses using interaction energy in muon-neutrino systems.
• To identify first-order corrections due to excitation interactions as responsible for discrepancies between theoretical and experimental masses.
• To explore potential connections between the three geometric families of leptonic excitations and quark structure.

Proposed method

• Theoretical framework uses topological excitations of the electron or neutrino as the origin of three lepton families.
• Mass ratios are derived from geometric principles, assuming a unified topological structure for leptons.
• The muon and tau masses are calculated numerically from these geometric ratios, yielding 107.59 MeV and 1770.3 MeV respectively.
• Geometric interaction energy in a muon-neutrino system is used to estimate the dominant mass contribution to the pion and kaon.
• First-order corrections are introduced to account for deviations from experimental values, based on excitation interactions.
• The model suggests a possible link between the three geometric lepton families and quark structure through symmetry or unification.

Experimental results

Research questions

• RQ1 Can lepton mass ratios be derived from a geometric unified theory of topological excitations of the electron or neutrino?
• RQ2 What is the predicted value of the muon mass based on geometric mass ratios alone?
• RQ3 How does the geometric interaction energy in a muon-neutrino system contribute to the pion and kaon masses?
• RQ4 What role do first-order corrections from excitation interactions play in reconciling theoretical predictions with experimental masses?
• RQ5 Is there a structural connection between the three geometric families of leptonic excitations and quark-based hadron constituents?

Key findings

• The theoretical muon mass is calculated as 107.59 MeV, derived from geometric mass ratios of topological excitations.
• The theoretical tau lepton mass is predicted to be 1770.3 MeV, consistent with the geometric framework.
• The main geometric contribution to the pion mass is calculated as 140.88 MeV, arising from muon-neutrino interaction energy.
• The main geometric contribution to the kaon mass is calculated as 494.76 MeV, based on the same interaction energy model.
• Discrepancies between theoretical and experimental values are attributed to first-order corrections from excitation interactions.
• The model suggests a possible geometric unification of leptonic families with potential implications for quark structure.