Mass Eigenstate Mixing in the 4-Generation Dirac-Kaehler Extension of   the SM
  We derive the canonical form of mixing of the mass eigenstates in the lepto-quark sector of the 4-generation Dirac-Kaehler extension of the SM (DK-SM) [1,2]. The 4 x 4 CKM matrix of DK-SM is expressed in terms two U(2) matrices. It depends on 2 real parameters and 3 phases. The resulting observed 3 x 3 CKM matrix exhibits previously unknown tree-level algebraic relations among its elements. The simplest two, V_ts = V_cb and V_cs = V_tb, are supported by the experimental data [3]. The 4 x 4 CKM matrix can be fully reconstructed from the experimental values of the 3 x 3 CKM matrix. Thus, except for masses of the fourth generation, the quark sector of the DK-SM theory can be reconstructed in its entirety using the 3 x 3 CKM matrix precision measurements. 
Alexander N. Jourjine
hep-ph