[Paper Review] Unified Lepto-Quark Mixing

Alexander N. Jourjine|arXiv (Cornell University)|May 20, 2012

Particle physics theoretical and experimental studies18 references3 citations

TL;DR

This paper proposes a unified framework for lepton and quark mixing by introducing a discrete Z2 symmetry acting on bi-spinor fermions, which naturally generates tri-bimaximal mixing for leptons and Wolfenstein-parameterized textures for quarks. The key result is a common origin for the differing textures of the PMNS and CKM matrices through symmetry assignment, resolving a long-standing puzzle in flavor physics.

ABSTRACT

We describe a solution to a long standing puzzle about the difference in textures of quark CKM and lepton PMNS mixing matrices by deriving their common representation. We show how the difference in texture of the two matrices arises from assignment of lepton and quark pairs to different representation of a discrete two element symmetry group. The symmetry is absent in the Standard Model. It appears if, instead of Dirac spinors, one describes fermions in terms of bi-spinors and induces essentially unique textures: tri-bimaximal for lepton and O(λ) of Wolfenstein parameterization for quark mixing.

Motivation & Objective

• To resolve the long-standing puzzle of why the PMNS and CKM mixing matrices have different textures despite similar underlying symmetries.
• To unify lepton and quark mixing within a single theoretical framework based on fermion representation under a discrete symmetry group.
• To show that the difference in mixing textures arises from assigning lepton and quark pairs to different representations of a Z2 symmetry group.
• To derive the observed tri-bimaximal mixing for neutrinos and Wolfenstein-parameterized quark mixing from a single, consistent bi-spinor formalism.

Proposed method

• Fermions are described using bi-spinors instead of Dirac spinors, introducing a new structure that allows for a unified treatment of leptons and quarks.
• A discrete Z2 symmetry is imposed on the bi-spinor fields, with lepton and quark pairs assigned to different representations of this group.
• The symmetry breaking pattern leads to distinct mixing textures: tri-bimaximal for leptons and O(λ) for quarks, matching experimental observations.
• The model derives the PMNS matrix as tri-bimaximal and the CKM matrix as consistent with Wolfenstein parameterization through symmetry assignment.
• The framework is extended to include a transition from 4 to 3 generations, clarifying the origin of mixing in the Standard Model.
• The approach is consistent with the Standard Model at low energy but introduces new structure at high scales via bi-spinor representation.

Experimental results

Research questions

• RQ1 How can the differing textures of the PMNS and CKM mixing matrices be unified under a single theoretical framework?
• RQ2 What symmetry mechanism can naturally generate tri-bimaximal mixing for leptons and Wolfenstein-type quark mixing?
• RQ3 Why does the Standard Model fail to explain the observed difference in mixing patterns between quarks and leptons?
• RQ4 Can a unified description of lepton and quark mixing be achieved using bi-spinor fermions and a discrete symmetry?
• RQ5 What is the role of representation assignment under a Z2 symmetry in generating the observed mixing patterns?

Key findings

• The model successfully derives the tri-bimaximal mixing pattern for neutrinos as a consequence of Z2 symmetry assignment to lepton bi-spinors.
• The quark mixing matrix is found to naturally exhibit the O(λ) structure of the Wolfenstein parameterization, consistent with experimental data.
• The difference in mixing textures arises solely from the assignment of lepton and quark pairs to different representations of the Z2 group.
• The framework provides a unified origin for flavor mixing in both quarks and leptons, resolving a long-standing puzzle in flavor physics.
• The model explains the origin of mixing in the Standard Model through the bi-spinor formalism and Z2 symmetry, with a clear transition from 4 to 3 generations.
• The approach is consistent with the observed mixing angles and offers a new perspective on the flavor structure of the Standard Model.