Use of B→J/ψ f₀ decays to discern the qq̄ or tetraquark nature of scalar mesons

We consider the relative decay rates of B^̄0 and B̄s0 mesons into a J/ψ plus a light scalar meson, either the f₀(500) (σ) or the f₀(980). We show that it is possible to distinguish between the quark content of the scalars being quark-antiquark or tetraquark by measuring specific ratios of decay rates. Using current data we determine the ratio of form factors in B̄s0→J/ψf₀(980) with respect to B^̄0→J/ψf₀(500) decays to be 0.99-0.04+0.13 at a four-momentum transfer squared equal to the mass of the J/ψ meson squared. In the case where these light mesons are considered to be quark-antiquark states, we give a determination of the mixing angle between strange and light quark states of less than 29 at 90% confidence level. We also discuss the use of a similar ratio to investigate the structure of other isospin singlet states.