Unitarity based phenomenology of fermion mixing matrix

Abstract

The present thesis has rigorously derived 9 independent Cartesian representations of the CKM matrix and their relationship with the already known representations has been discussed. Expectedly, these 9 representation yield same value for the Jarlskog s rephrasing invariant parameter J. Interestingly, in case of the CP violating defining parameter and#1013;k, in the K and#8722;K system, however, one finds that 3 representations are not able to reproduce the data which perhaps finds its explanation due to the hierarchical nature of the CKM matrix. Present analysis also reveals PDG representation appears to be a preferred representation for carrying out phenomenological investigations as in this case the 3 mixing angles capture the hierarchy of the well measured 3 CKM matrix elements. A rigorous unitarity based analysis of the PDG representation reveals the following hierarchy for the elements of the CKM matrix |Vtb| gt |Vud| gt |Vcs| gt |Vus| gt |Vcd| gt |Vcb| gt |Vts| gt |Vtd| gt |Vub|. After a rigorous analysis of the implications of unitarity for the 3 generation mixing matrix we attempt to carry out similar analysis for the 4 generation mixing matrix. In the present work, we have explicitly constructed a particular representation of 4×4 quark mixing matrix, referred to as PDG4, which can be easily reduced to the PDG representation of 3 × 3 quark mixing matrix. As a first step of our analysis, using inputs from the constraints of 3 generation mixing matrix, we have derived the constraints on the hierarchy of 4th generation elements which comes out as Vtand#8242;band#8242; gt Vtand#8242;d gt Vuband#8242; gt Vcband#8242; gt Vtand#8242;s gt Vtand#8242;b gt Vtband#8242; . As a next step, corresponding to the Jarlskog s repahsing invariant parameter J in the 3 generation case, we have explicitly constructed the 9 rephasing invariant parameters in 4th generation denoted as J4×4. These 9 invariants have been numerically evaluated using the presently available constraints on the 4th generation elements. These values may provide valuable clues regarding the 4th generation as the inputs become more refined.