The Rotating Mass Matrix, the Strong CP Problem and Higgs Decay

We investigate a recent solution to the strong CP problem, obtaining a theta-angle of order unity, and show that a smooth trajectory of the massive eigenvector of a rank-one rotating mass matrix is consistent with the experimental data for both fermion masses and mixing angles (except for the masses of the lightest quarks). Using this trajectory we study Higgs decay and find suppression of $\mathrm{\Gamma }(H\to c\bar{c})$ compared to the standard model predictions for a range of Higgs masses. We also give limits for flavour violating decays, including a relatively large branching ratio for the ${\tau }^{-}{\mu }^{+}$ mode.