In the approach to hadronic flavour symmetries based on the q-algebras U_q(su_N) and proved to be realistic, the known construction of U_q(su_N) in terms of anyonic oscillators residing on 2d lattice is utilized. Anyonic Fock-like realization of basis state vectors is given for baryons (3/2)^+ from the 10-plet of U_q(su_3) embedded, via 20-plet of U_q(su_4), into the "dynamical" representation [4000] of U_q(su_5). Within the anyonic picture, we reobtain the universal q-deformed decuplet mass relation M_\Omega-M_{ \Xi^*}+M_{ \Sigma^*}-M_{ \Delta}=[2]_q (M_{ \Xi^*}-M_{ \Sigma^*}), where [2]_q=q+q^{ -1}=2 cos{ \theta}. Consistency with data for baryon masses requires \theta\simeq\frac{ \pi}{ 14}. As a result, anyons with anyonic statistics parameter \nu = 1/14 can be put into correspondence, at least formally, with the constituent quarks of decuplet baryons.
Categories: hep-ph hep-lat hep-th nucl-th quant-ph