Gaugino-induced quark and lepton masses

It has recently been proposed that all fundamental fermion masses (whether Dirac or Majorana) come from effective dimension-five operators in the context of a truly minimal left-right model. We show how a particularly economical scheme emerges in a supersymmetric framework, where chiral symmetry breaking originates in the gaugino sector. In the standard model of particle interactions, the spontaneous breaking of the SU(2)L× U(1)Y gauge symmetry to U(1)em is achieved through the vacuum expectation value of the scalar doublet Φ = (φ, φ). At the same time, since left-handed quarks and leptons are doublets under SU(2)L×U(1)Y whereas right-handed quarks and leptons are singlets, chiral symmetry is also broken by 〈φ0〉, thus allowing quarks and leptons to acquire the usual Dirac masses. The only exception is the neutrino which gets a small Majorana mass through the unique dimension-five operator [1, 2] LΛ = fij 2Λ (νiφ 0 − eiφ+)(νjφ0 − ejφ+) +H.c. (1) Suppose we now extend the standard-model gauge symmetry to SU(3)C × SU(2)L × SU(2)R × U(1)B−L [3], then the spontaneous breaking of SU(2)R × U(1)B−L to U(1)Y is simply achieved by the scalar doublet ΦR = (φ + R, φ 0 R) ∼ (1, 1, 2, 1), (2) where the notation refers to the dimension of the non-Abelian representation or the value of the Abelian charge B − L or Y in the convention Q = I3L + I3R + 1 2 (B − L) = I3L + Y 2 , (3) while the corresponding field ΦL = (φ + L , φ 0 L) ∼ (1, 2, 1, 1), (4) becomes the same as the usual scalar doublet of the Standard Model, and breaks SU(2)L × U(1)Y in turn to U(1)em. In other words, ΦR and ΦL are sufficient by themselves for the desired breaking of the left-right gauge symmetry all the way down to U(1)em. On the other hand, chiral symmetry of the quarks and leptons remains unbroken at this stage, in contrast to the case of the