Title:

The rankone rotating mass matrix hypothesis : a general and a model specific study

In this thesis we investigate whether a rankone rotating mass matrix extended to solve the strong CP problem can, through the mass leakage mechanism, account for fermion masses, mixing angles and a $theta_{CP}$ term of order unity. In the first part we find restrictions placed on the rotation of the rankone mass matrix by experimental data. We demonstrate that a smooth rotation of the mass matrix can reproduce the experimentally determined fermion masses and mixing angles and give $theta_{CP}$ = 1.45 radians. We then fit the speed of rotation at high ($> 1$ GeV) scales. Using this rotation we make predictions for Higgs branching ratios for a range of Higgs masses, finding a suppression of $Gamma(H ightarrow car{c})$ compared to the standard model and significant flavour violating branching ratios. In the second part we study the framed standard model (FSM). We calculate the strong framon oneloop contribution to the rotation of its rankone mass matrix and account for the nontrivial metric on its internal symmetry space. We find that the FSM can reproduce the hierarchy seen in the fermion masses and the CKM matrix, fit $theta_{CP}sim0.3$ radians and find $U_{mu3}sim0.8$. Similar results are found if QCD running is included, except that $U_{mu3}>0.95$. We compare the FSM rotation to the rotation found in first part and find they are in good agreement above $mu=m_c$. We go on to show that the predictions for Higgs decay are comparable to those found in the general study. In the final part we calculate the framon mass spectrum of the FSM in the hermitian gauge and find that, as expected, it agrees with the calculation performed in the triangular gauge. We find that none of the framons are massless.
