Order Lambda**3 Parameterization of Neutrino (e,muon, tau, tau(prime)) Flavor Oscillations in a Simplified SM4 Model and Associated VCKM, VMNS, and VBIMAX Matrixes

TL;DR

This paper develops a mathematical framework for neutrino flavor oscillations within a four-generation Standard Model, introducing a Lambda^3 parameterization of the CKM matrix and analyzing implications for CP violation and baryogenesis.

Contribution

It presents a novel Lambda^3 order parameterization of the four-generation CKM matrix and estimates the neutrino MNS matrix using a unitary bimaximal scheme, extending the Standard Model to four generations.

Findings

Derived a Wolfenstein parameterization valid to order Lambda^3 for VCKM.

Estimated the four-generation neutrino MNS matrix incorporating CP-violating phases.

Discussed experimental implications and baryogenesis scenarios in the four-generation model.

Abstract

Arguments are presented based on particle phenomenology and the requirement for Unitarity for a complex valued postulated four generation CKM Matrix (VCKM ) based on a Sequential Fourth Generation Model (sometimes named SM4). A modified four generation QCD Standard Model Lagrangian is utilized per SM4. A four generation neutrino mass mixing MNS Matrix, (VMNS) is estimated utilizing a Unitary (to Order (Lambda**k), k = 1, 2, 3, 4, etc) 4 x 4 Bimaximal Matrix, VBIMAX. The Unitary VBIMAX is based on a weighted 3 x 3 VBIMAX scheme and is studied in conjunction with the postulated four generation VCKM complex Unitary Matrix. A single parameter has been utilized in our analysis along with three complex DELTA(i,j) phases. A four generation Wolfenstein Parameterization of VCKM is deduced which is valid for order Lambda**3. Experimental implications of the model are discussed. The issues of Baryogenesis in the context of Leptogenesis associated with MNS Matrix neutrino mixing and Baryogenesis associated with CKM Matrix quark mixing are discussed. These issues are studied in the context of the postulated complex four generation CKM Matrix and resulting complex MNS Matrix, predicted CP violating parameters, and a Fourth Generation Neutrino mass bound of equal to or greater than 50 GeV. Our analysis is valid to and includes order Lambda**3 terms. Our work is a mathematical analysis of the consequences of such model. Classification Codes (PACS-1996): 14.60.Pq, 23.40.Bw, 98.80.Cq 14.60.Pq Neutrino mass and mixing 23.40.Bw Weak-interaction and lepton (including neutrino) aspects 98.80.Cq Particle-theory and field- theory models of the early Universe Keywords: Neutrino Oscillations, Neutrino Flavor Oscillations, Fourth Generation,Unitarity, Baryogenesis, Leptogenesis, CP Violations