Family gauge symmetry as an origin of Koide's mass formula and charged lepton spectrum

Abstract

Family gauge symmetry as an origin of Koide's mass formula and charged lepton spectrum Abstract: Koide's mass formula is an empirical relation among the charged lepton masses which holds with a striking precision. We present a model of charged lepton sector within an effective field theory with U(3) × SU(2) family gauge symmetry, which predicts Koide's formula within the present experimental accuracy. Radiative corrections as well as other corrections to Koide's mass formula have been taken into account. We adopt a known mechanism, through which the charged lepton spectrum is determined by the vacuum expectation value of a 9-component scalar field Φ. On the basis of this mechanism, we implement the following mechanisms into our model: (1) The radiative correction induced by family gauge interaction cancels the QED radiative correction to Koide's mass formula, assuming a scenario in which the U(3) family gauge symmetry and SU(2) L weak gauge symmetry are unified at 10 2 -10 3 TeV scale; (2) A simple potential of Φ invariant under U(3) × SU(2) leads to a realistic charged lepton spectrum, consistent with the experimental values, assuming that Koide's formula is protected; (3) Koide's formula is stabilized by embedding U(3) × SU(2) symmetry in a larger symmetry group. Formally fine tuning of parameters in the model is circumvented (apart from two exceptions) by appropriately connecting the charged lepton spectrum to the boundary (initial) conditions of the model at the cut-off scale. We also disucss some phenomenological implications.

Non-abelian family symmetries in Pati-Salam unification

“…In [4] a toy model exemplified quite clearly how two SU (3) factors would forbid undesirable Yukawa terms that with a single non-Abelian symmetry could not be disallowed (regardless of any extra Abelian auxiliary symmetries employed). Examples of works using two non-Abelian family symmetries for other purposes include [5][6][7].…”

Mass-spectrum of Charged Leptons from the Planck Mass

“…Nevertheless, there are papers (see e.g. [14] and references cited therein) studying gauge symmetry, which could lead to (3) for leptons and quarks.…”

Charged lepton mass spectrum and supersymmetric yukawaon model

“…(1.12) as values which should be explained in this paper. In reference to this topic, recently, Sumino [5] has proposed an interesting idea that a flavor gauge symmetry induces an effect which exactly cancels the deviation of ε K (µ) at any energy scale µ. However, differently from Sumino's idea, in this paper, we adopt the standpoint that K pole = 2/3 is accidental.…”