[Paper Review] Use of nuclei fractal properties for help to determine some unknown particle spins and unknown nuclei excited level spins

B. Tatischeff|arXiv (Cornell University)|Dec 6, 2011

Advanced Mathematical Theories and Applications1 references3 citations

TL;DR

This paper proposes using fractal scaling laws—specifically, log-linear alignment of particle and nucleus masses versus rank—to infer unknown spins of mesons, baryons, and excited nuclear states. By testing whether unknown states fit existing log-linear trends for known spins, the method identifies likely spin assignments, with success varying by system and mass spacing.

ABSTRACT

The fractal property stipulates that the same physical laws apply for different scales of a given physics. This property is applied to particles and nuclei, in order to study the possibility to use it to help for determination of unknown spins of some particles or excited nuclei levels.

Motivation & Objective

• To investigate whether fractal scaling in mass-rank distributions can assist in determining unknown spins of elementary particles and excited nuclear states.
• To test the hypothesis that discrete scale invariance in mass spectra implies log-linear trends for particles of the same spin.
• To provide a predictive tool for spin assignment when experimental data are incomplete or ambiguous.
• To evaluate the method's reliability across different particle families (mesons, baryons, light nuclei) and mass ranges.
• To determine the conditions under which the fractal method yields unambiguous spin predictions versus ambiguous or inconclusive results.

Proposed method

• Plot the natural logarithm of particle or nucleus masses against their rank in a sequence to identify log-linear trends for known spins.
• Apply the principle of discrete scale invariance, where mass distributions for a given spin should follow a power law: M ∝ R^α.
• Test whether an unknown state fits the log-linear trend of a specific spin class by checking alignment when the state is inserted at its rank.
• Use visual and quantitative assessment of linearity to exclude spins that disrupt the trend; prefer spins that maintain or improve alignment.
• Compare multiple possible spin assignments for a given state by testing each in the context of the full sequence of known states.
• Account for experimental uncertainties by assigning a 50 MeV mass error when not specified, and consider the impact of missing states in the mass range.

Experimental results

Research questions

• RQ1 Can fractal scaling in mass-rank plots reliably predict the spin of unknown mesons and baryons?
• RQ2 To what extent does the method succeed in assigning spins to excited nuclear states with uncertain spin quantum numbers?
• RQ3 How does the presence of missing or uncertain states affect the reliability of spin predictions using this method?
• RQ4 Which spin assignments are most consistent with the observed log-linear trends in the mass spectra?
• RQ5 Under what conditions does the method fail or produce ambiguous results?

Key findings

• The X(1835) meson is unlikely to have spin J = 0 or J = 4, but J = 1, 2, or 3 remain possible due to consistent alignment across multiple spin sequences.
• For the unflavoured meson at 2231.1 MeV, the method cannot distinguish between J = 2 and J = 4, as both maintain linearity in their respective sequences.
• The strange meson at 1630 MeV is most likely J = 0, with J = 2 or 4 also possible, but J = 1 and J = 3 excluded due to loss of linearity upon removal.
• The strange meson at 3100 MeV is most probably J = 3, though the result is uncertain due to potential missing states in the 2500–3100 MeV range.
• For the 20F nucleus, the most probable spin assignments are J = 1 for the 3.587 MeV and 3.680 MeV levels, and J = 3 for the 3.761 MeV level, based on sequential alignment.
• The 24Mg excited state at 9.30 MeV is most likely J = 3, as linearity is preserved in the J = 3 sequence and not disrupted by inclusion of this state.