Unitarity triangle angles explained: a predictive new quark mass matrix texture - P. F. Harrison; W. G. Scott (Journal of High Energy Physics)
Abstract We propose a novel quark mass matrix texture-pair with five free parameters, which fits the four quark mass ratios m s /m b , m d /m b , m c /m t , m u /m t , and the four CKM quark mixing observables. The matrices each have one texture zero, but the main innovation here is a “geometric” ansatz exploiting a pair of small complex expansion parameters, based on the geometry of the Unitarity Triangle. The fit to the observables is in good agreement with current experimental values renormalised to ~ 104 TeV, and offers decisive tests against future high-precision measurements of the unitarity triangle angles at the weak scale. We identify two novel symmetries of these mass matrices which explain the phenomenologically-successful relations α ≡ ϕ 2 ≃ π 2 $$ \frac{π }{2} $$ and β ≡ ϕ 1 ≃ π 8 $$ \frac{π }{8} $$ .