On Quark–Lepton Mixing and the Leptonic CP Violation

In the absence of a Grand Unified Theory framework, connecting the values of the mixing parameters in the quark-and-lepton sector is a difficult task, unless one introduces ad hoc relations among the matrices that diagonalize such different kinds of fermions. In this paper, we discuss in detail the possibility that the PMNS matrix is given by the product <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>U</mi><mrow><mi>P</mi><mi>M</mi><mi>N</mi><mi>S</mi></mrow></msub><mo>=</mo><msubsup><mi>V</mi><mrow><mi>C</mi><mi>K</mi><mi>M</mi></mrow><mo>★</mo></msubsup><mspace width="0.166667em"></mspace><msup><mi>T</mi><mo>★</mo></msup></mrow></semantics></math></inline-formula>, where <i>T</i> comes from the diagonalization of a see-saw like mass matrix that can be of a Bimaximal (BM), Tri-Bimaximal (TBM) and Golden Ratio (GR) form, and identify the leading corrections to such patterns that allow for a good fit to the leptonic mixing matrix as well as to the CP phase. We also show that the modified versions of BM, TBM and GR can easily accommodate the solar and atmospheric mass differences.