${\chi }_{c2}$ tensor meson transition form factors in the light front approach

Abstract

We continue our work on the light-front formulation of quarkonium ${\gamma }^{\ast }\gamma$ transition form factors, extending the formalism to $J^{PC}=2^{++}$ tensor meson states. We present an analysis of ${\gamma }^{\ast }\gamma \to {\chi }_{c2}$ 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 ${\gamma }^{\ast }\gamma$ 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 $\Gamma (\lambda =0)/\Gamma (\lambda =2)\sim 10^{-3}$ 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.

19 pages, 4 figures, 3 tables