Under the approximations U13^e = 0 and U23^e = 0, the Fritzsch-Xing CP phase equals the sum of the neutrino-intrinsic phase and the relative phase between the first two generations.
Four-Zero Texture of Hermitian Quark Mass Matrices and Current Experimental Tests
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abstract
We show that the four-zero texture of Hermitian quark mass matrices can survive current experimental tests: it is able to yield sufficiently large predictions for the flavor mixing parameter $|V_{ub}/V_{cb}|$ and the CP-violating parameter $\sin 2\beta$, without fine-tuning of the input values of quark masses, provided the (2,2), (2,3) and (3,3) elements of up and down mass matrices roughly satisfy a geometrical hierarchy. The successful relations $|V_{us}| \approx \sqrt{m_u/m_c + m_d/m_s}$ and $|V_{td}/V_{ts}| \approx \sqrt{m_d/m_s}$ obtained previously from the six-zero texture of Hermitian quark mass matrices remain unchanged in the new ansatz.
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Rephasing invariant structure of CP phase for simplified mixing matrices in Fritzsch--Xing parametrization
Under the approximations U13^e = 0 and U23^e = 0, the Fritzsch-Xing CP phase equals the sum of the neutrino-intrinsic phase and the relative phase between the first two generations.