$χ_{c2}$ tensor meson transition form factors in the light front approach

Abstract

We continue our work on the light-front formulation of quarkonium $γ^* γ$ transition form factors, extending the formalism to $J^{PC} = 2^{++}$ tensor meson states. We present an analysis of $γ^* γ\to χ_{c2}$ transition amplitude and the pertinent helicity form factors. Our relativistic formalism is based on the light-front quark-antiquark wave function of the quarkonium. We calculate the two-photon decay width as well as three independent $γ^* γ$ transition form factors for $J_z = 0,1,2$ as a function of photon virtuality $Q^2$. We compare our results for the two-photon decay width to the recently measured ones by the Belle and BES III collaborations. Even when including relativistic corrections, a very small $Γ(λ= 0)/Γ(λ= 2)\sim10^{-3}$ ratio is found which is beyond present experimental precision. We also present the form factors as a function of photon virtuality and compare them to the sparse experimental data on the so-called off-shell width. The formalism presented here can be used for other $2^{++}$ mesons, excited charmonia or bottomonia or even light $q \bar q$-mesons.