On the Universal Texture in the PA-2HDM for the V-SPIN case

In a Partially Aligned Two Higgs Doublet Model, where only is allowed flavor violation between third and second generation of fermions, we propose a mechanism to generate the second Yukawa matrix through a Unitary V-Spin flavor transformation on the mass matrix for quarks and leptons. Also we assume that this flavor transformation is universal, this is, we use the same parameters to generate Yukawa matrix elements in both sectors, reducing drastically the number of free parameters. As consequence we obtained a serie of relations between Yukawa matrix elements, that we called the Universality Constraint. Also, we obtained an interval of values for the second Yukawa matrix elements, expressed in terms of the Cheng and Sher ansatz, for $\tau\to\ mu\mu^+\mu^-$ and $\tau\to\gamma\mu$ coming from the Universality Constraint and experimental bounds for light scalar masses. Finally, we show the allowed region of parameters for the flavor transformation from $B_s\to\mu\mu$ decays, $B_s^0-\bar{B}_s^0$ mixing, $\tau\to\mu\mu^+\mu^-$ and $\tau\to\gamma\mu$ experimental bounds.