The Cabibbo angle : an algebraic calculation

Abstract

We show that the Cabibbo angle theta\_c satisfies the relation tan(2 theta\_c)=-+/- 1/2 when universality for diagonal neutral currents of mass eigenstates is satisfied at the same level of accuracy as the absence of their off-diagonal counterparts. The predicted value is cos theta\_c \approx 0.9732, only 7/10000 away from experimental results. No mass ratio appears in the calculation. theta\_c occurs a priori for both quark species, and, showing that one recovers the standard dependence of leptonic and semi-leptonic decays of pseudoscalar mesons, we advocate, like for neutrinos and charged leptons, for a symmetrical treatment of u and d-type quarks.