[Paper Review] Kaluza-Klein Picture and Nucleon-Nucleon Dynamics at Low Energies

A. A. Архипов|ArXiv.org|Feb 18, 2003

Black Holes and Theoretical Physics1 references3 citations

TL;DR

This paper proposes that the nucleon-nucleon system at low energies exhibits a Kaluza-Klein (KK) tower of resonances, with masses predicted by a compactified extra dimension scenario. Using a derived fundamental scale of R ≈ 4.75×10⁻¹³ cm, the KK mass formula Mₙ = 2√(mₚ² + n²/R²) excellently matches experimental dibaryon resonance data, revealing an unexpected (super)symmetry between fermionic and bosonic states.

ABSTRACT

In this note we present additional arguments in favour of Kaluza and Klein picture of the world. We show that geniusly simple formula provided by Kaluza-Klein approach gives an excellent description for the mass spectrum of two-nucleon system. It has also been established that the experimental data obtained at low energies where the nucleon-nucleon dynamics has been studied reveal a special sort of (super)symmetry between fermionic (dibaryon) and bosonic states predicted by Kaluza-Klein scenario.

Motivation & Objective

• To test whether the Kaluza-Klein scenario explains the observed irregularities in the diproton and proton-antiproton mass spectra at low energies.
• To determine if the experimental data on two-nucleon resonances support the existence of a compactified extra dimension with a specific fundamental scale.
• To investigate the presence of a hidden (super)symmetry between fermionic dibaryons and bosonic resonances predicted by the Kaluza-Klein framework.
• To provide a predictive KK mass spectrum for missing two-nucleon states to guide future experiments.

Proposed method

• Derives the Kaluza-Klein mass formula Mₙ = 2√(mₚ² + n²/R²) from a (4+d)-dimensional scalar field theory with compact internal space.
• Uses experimental data on proton-proton and proton-antiproton total cross sections to extract the fundamental scale R ≈ 4.75×10⁻¹³ cm (1/R ≈ 41.481 MeV).
• Compares the predicted KK tower of resonances with experimental masses of dibaryon states from the Review of Particle Physics and Crystal Barrel Collaboration data.
• Applies the KK mode expansion to a 5D scalar field action, reducing it to 4D effective theory with massive KK modes via harmonic expansion on a d-torus.
• Considers the role of crossing symmetry in suppressing KK states in pp̄ channels while enhancing them in pp channels.
• Generates a complete KK tower for pp, pn, and nn systems, including proton-neutron mass differences, to guide experimental searches.

Experimental results

Research questions

• RQ1 Does the Kaluza-Klein mass formula accurately describe the observed irregularities in the two-nucleon mass spectrum at low energies?
• RQ2 Is there experimental evidence for a fundamental scale associated with compactified extra dimensions in nucleon-nucleon dynamics?
• RQ3 Do the experimental data reveal a (super)symmetry between fermionic dibaryons and bosonic resonances as predicted by the Kaluza-Klein scenario?
• RQ4 Are there missing two-nucleon resonances predicted by the KK tower that remain unobserved and could be targeted in future experiments?
• RQ5 Why are KK excitations suppressed in the pp̄ channel despite being predicted by the same KK mechanism as in the pp channel?

Key findings

• The fundamental scale of the compactified extra dimension is determined as R ≈ 4.75×10⁻¹³ cm (1/R ≈ 41.481 MeV), corresponding to the energy scale where strong Yukawa forces weaken to electromagnetic strength.
• The Kaluza-Klein mass formula Mₙ = 2√(mₚ² + n²/R²) provides an excellent fit to the observed masses of dibaryon resonances in the pp and pp̄ systems, with deviations within experimental uncertainties.
• The data reveal a clear (super)symmetry between fermionic dibaryons and bosonic resonances, with mass levels alternating between fermionic and bosonic states in a pattern consistent with KK predictions.
• Several predicted KK states (e.g., n = 21, 23, 25, 27–33, 35, 36, 38) are missing in the experimental spectrum, indicating unobserved resonances that should be searched for.
• The model predicts a complete tower of resonances for pp, pn, and nn systems, with masses differing by only a few MeV due to proton-neutron mass splitting.
• The suppression of KK states in the pp̄ channel is attributed to crossing symmetry of the scattering amplitudes, which enhances them in the pp channel instead.