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Texture of Yukawa coupling matrices in general two-Higgs doublet model. Yu- Feng Zhou J. Phys. G: Nucl . Part. Phys.30 (2004) 783-792 Presented by Ardy. Introduction. Unresolved problems within the SM: the origin of the fermion masses, mixing angles and CP violation, etc.
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J. Phys. G: Nucl. Part. Phys.30 (2004) 783-792
Presented by Ardy
where and are the absolute values of the VEV of the two Higgs fields, which satisfy
We will focus on the case in which both VEVs are real, i.e. , and the effects of neutral scalar mixing are negligible.
To forbid the tree level FCNC in 2HDM, the ad hoc discrete symmetries are often imposed on the Lagrangian
which defines two types of 2HDM without tree level FCNCs, referred to as models I and II of 2HDM.
Abandoning the discrete symmetry (as type I and II), one arrives at the general type of 2HDM with small FCNCs.
the commutator will be close to zero.
The simplest way to obtain the parallel texture is to impose an permutation symmetry between and
which leads to , and .
Applying the same transformation to , one arrives at the Yukawa matrix in the mass basis
In the three-family case, a similar texture with six texture-zeros is widely discussed and which is often referred to as ‘Fritzsch Matrix’, given by
where , and .
The free parameters ,, and are assumed to be of the same order of magnitude, i.e. of order 1.
However, later studies have already shown that the base of this ansatz is in severe problem in accounting for the current data of the CKM matrix elements from the known quark masses.
where and are two phase parameter.
For a large value GeV, the six texture-zero-based mass matrix gives , which is too large compared with the current data .
In the lepton sector, the strongest constraint comes from the radiative decay which is relevant to the and elements of the Yukawa coupling matrix .
For a concrete illustration, we take the three-body lepton decays as examples, and calculate the branching ratios in the general 2HDM with two different ansatz in Eq.(26) and (19).
Using the allowed range of and from Eq.(28), the predicted branching ratios are obtained and summarized in table 1
As an example, the contribution from the general 2HDM to the lepton number violation decay modes are calculated in both ansatz.