Masses of Decuplet Baryons Treated within Anyonic Realization of the q-Algebras U_q(su_N)

Abstract

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_Ω-M_{Ξ^*}+M_{Σ^*}-M_Δ=[2]_q (M_{Ξ^*}-M_{Σ^*}), where [2]_q=q+q^{-1}=2 cosθ. Consistency with data for baryon masses requires θ\simeq\fracπ{14}. As a result, anyons with anyonic statistics parameter ν= 1/14 can be put into correspondence, at least formally, with the constituent quarks of decuplet baryons.