Predictive empirical mass formula for up and down quarks of three generations

Abstract

The starting point in this note is the charged-lepton mass formula successfully predicting the figure m_\tau = 1776.80 MeV for \tau-lepton mass versus its recent experimental value m_\tau = 1776.82 \pm 0.16 MeV. There, two experimental masses m_e and m_\mu are the only input. This two-parameter empirical mass formula is extended to a pair of three-parameter empirical mass formulae for up and down quarks of three generations where, subsequently, a third pair of its free parameters is conjectured to be specified in a suggestive way, being replaced by one free parameter. Then, the new quark mass formulae predict one quark mass m_s = 101 MeV versus its experimental value m_s = 101^{+29}_{-21} MeV. Here, five experimental masses m_u, m_c, m_t and m_d, m_b (their central values, for simplicity) are the only input.