Quantum Groups and Cabibbo Mixing

When keeping the first two quark families, only the parameter λ ≈ 0.22 (the sine of Cabibbo angle θC) persists. Cabibbo mixing [1] is known to play basic role in describing weak decays of mesons and baryons by means of flavor changing (e.g., strangeness changing) quark currents. Our goal is to discuss some other, unusual implications of the Cabibbo mixing which are deduced on the base of adopting instead of the flavor groups SU(n) their quantum counterparts Uq(su(n)). Note that the idea of using [2] in place of SU(n) the quantum groups (or q-deformed algebras) Uq(sun) and their representations [3] in order to treat hadronic flavor symmetries is natural, easily justifiable and very fruitful, leading to many interesting implications [2, 4]. The most important one is the possibility to link the q-parameter with the angle θC, and this enables to find novel connections for the concept of Cabibbo mixing. Say, the earliest modified (improved) version of the Gell-Mann–Okubo (GMO) mass relation for the SU(3) octet baryons 12 + derived in a particular version [5] of ‘diquark-quark’ model (the LTK model), involves certain parameters characterizing diquark and separate quark. The alternative improved version of GMO for octet baryons is the extremely precise mass sum rule (MSR) obtained with Uq(sun). It exploits fixed value of the q-parameter linked in a simple way to θC, and this fact allows to find direct connection, through the fixed q, of the parameters of LTK diquark-quark model to the angle θC. Besides this, we discuss the connections of the θC with such concepts as anyonic statistics parameter from the anyonic picture, as intercepts of the twoand three-pion (-kaon) correlation functions drawn in recent experiments on relativistic heavy ion collisions.