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

TL;DR

This paper extends an empirical mass formula from charged leptons to predict the masses of up and down quarks across three generations, achieving close agreement with experimental values using minimal parameters.

Contribution

It introduces a novel three-parameter empirical mass formula for quarks, building on a successful charged-lepton formula, and simplifies parameter determination for accurate mass predictions.

Findings

Predicted strange quark mass m_s = 101 MeV matches experimental value.

Accurately predicts tau lepton mass using two parameters.

Provides a unified empirical framework for lepton and quark masses.

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.