Fractional dynamics of fermion generations

TL;DR

This paper explores how fractional calculus applied in extra dimensions can explain fermion mass spectra and mixing, proposing new models for quark and lepton generations with potential dark matter implications.

Contribution

It introduces a fractional Lagrangian framework in extra dimensions to model fermion spectra and mixing matrices, providing a novel approach to fermion generation dynamics.

Findings

Fermion spectra depend on a single mass parameter and fractional numbers.

Neutrino spectra require an additional mass parameter and a universal fractional number.

New definitions of CKM and PMNS matrices as interference integrals in extra dimensions.

Abstract

The dynamics of fermion generations is treated in the framework of the fractional Lagrangian and Hamiltonian in the compact extra dimension. The resulting spectra for u, d, e generations are described by the only mass parameter and slightly different fractional numbers, while the neutrino spectra need another mass parameter and a single fractional number for all neutrino species. New definitions of CKM and PMNS mixing matrices with standard data are given as the interference integrals in the extra dimension. A possibility of higher fermion states as dark matter candidates is shortly discussed.