Abstract
With some modifications, the arguments for rephasing invariance can be used to establish permutation symmetry for the standard model. The laws of evolution of physical variables, which transform as tensors under permutation, are found to obey the symmetry, explicitly. We also propose to use a set of four mixing parameters, with unique properties, which may serve to characterize flavor mixing.
Highlights
One of the long-standing puzzles in the Standard Model (SM) is the existence of three families of fundamental fermions. (Throughout this paper, SM refers to a modified version with the addition of three massive Dirac neutrinos, so that one may treat the lepton sector on a par with the quark sector)
In the SM, the physics of flavor is derived from the mixing matrices and the mass terms in the Lagrangian
Rephasing of the wave functions, which leaves the mass terms intact, can be cancelled by corresponding phases applied to Vαi
Summary
One of the long-standing puzzles in the Standard Model (SM) is the existence of three families of fundamental fermions. (Throughout this paper, SM refers to a modified version with the addition of three massive Dirac neutrinos, so that one may treat the lepton sector on a par with the quark sector). (Throughout this paper, SM refers to a modified version with the addition of three massive Dirac neutrinos, so that one may treat the lepton sector on a par with the quark sector) These fermions are endowed with properties (masses and mixing parameters) which seem to be arbitrary. Applying a permutation to any such product is seen to yield another rephasing invariant combination This means that any physical variable constructed out of Vαi must belong to a tensor under S3. The use of permutation tensors for physical variables has another property, owing to the few available representations of S3. We will identify a set of four variables, all of which transform as singlets under permutation, and can be used as physical parameters Some of their properties, including a set of RGE, are presented.
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