Overall empirical formula for mass spectra of leptons and quarks

TL;DR

This paper introduces an empirical formula that accurately models the mass spectra of leptons and quarks, predicting specific masses and suggesting applicability to neutrinos and lighter quarks.

Contribution

It provides a unified empirical formula for lepton and quark masses, with parameters that fit known data and predict unknown masses.

Findings

Predicts m_tau = 1776.80 MeV

Predicts neutrino masses with m_{nu_1} approaching 0 eV

Estimates down and strange quark masses as 5.0 MeV and 102 MeV

Abstract

We present an overall empirical formula that, after specification of its free parameters, describes precisely the mass spectrum of charged leptons and is suggested to reproduce correctly also the mass spectra of neutrinos and up and down quarks (together, twelve masses with eight free parameters are presented). Then, it predicts m_tau = 1776.80 MeV, m_{nu_1} -> 0 eV and m_d = 5.0 MeV, $m_s = 102 MeV, respectively, when the remaining lepton and quark masses, m_e, m_mu, Delta m^2_{21} = m^2_{nu_2}-m^2_{nu_1}, Delta m^2_{32} = m^2_{nu_3}-m^2_{nu_2} and m_u, m_c, m_t, m_b, are taken as an input.