A satisfactory empirical mass sum rule for charged leptons

Abstract

In the framework of a mass formula proposed previously (transforming in a specific way three free parameters into three masses), a simple empirical sum rule for three charged-lepton masses is found, predicting m_\tau = 1776.9926 MeV, when the experimental values of m_e and m_\mu are used as an input. The experimental value to be compared with is m_\tau = 1776.99^{+0.29}_{-0.26} MeV. This satisfactory sum rule (equivalent to a simple parameter constraint in the mass formula) is linear in masses and involves integers as its coefficients. The author believes that such a simple and precise mass sum rule for charged leptons may help in the process of developing realistic models for mass spectra of fundamental fermions. In the second part of the paper, another equivalent parametrization of the charged-lepton mass formula is described, corresponding to an oscillatory picture of their mass matrix, where two matrices appear playing the role of annihilation and creation operators in the generation space.