Empirical formulas for the fermion spectra and Yukawa matrices

Abstract

We present empirical relations that connect the dimensionless ratios of fermion masses for the charged lepton, up-type quark and down-type quark sectors. Explaining these relations from first principles imposes strong constraints on the search for the theory of flavor. We present a simple set of normalized Yukawa matrices, with only two real parameters and one complex phase, which accounts with precision for these mass relations and for the CKM matrix elements and also suggests a simpler parametrization of the CKM matrix. The proposed Yukawa matrices accommodate the measured CP-violation, giving a particular relation between standard model CP-violating phases, beta=Arg(2 - exp^{-i*gamma}). According to this relation, the measured value of beta is close to the maximum value that can be reached. Finally, the particular mass relations with the charged lepton sector find their simplest explanation in the context of grand unified models through the use of the Georgi-Jarlskog factor.