Magic mixing angles for doubly heavy baryons

Abstract

We study the so-called magic mixing angles for doubly heavy baryons. Defining that a magic mixing angle rotates states with definite 2S +1 (l λ ) J to make them heavy-quark symmetric states, we derive the magic mixing angle only in the case L ρ = 0 between the heavy quark symmetric states with quantum numbers (J, j ) and the states with J, s q + j ρ = J, { 4 l λ / 2 l λ } for a doubly heavy baryon in the standard ρ − λ configuration, where j = l λ + s q , s ρ = s Q1 + s Q2 , and j ρ = s ρ + L ρ . We discuss how this mixing angle affects model building for a doubly heavy baryon.