χ c2 tensor meson transition form factors in the light front approach
Izabela Babiarz (Institute of Nuclear Physics, Polish Academy of Sciences, ul. Radzikowskiego 152, Kraków, PL-31-342, Poland); Roman Pasechnik (Department of Physics, Lund University, Lund, SE-223 62, Sweden); Wolfgang Schäfer (Institute of Nuclear Physics, Polish Academy of Sciences, ul. Radzikowskiego 152, Kraków, PL-31-342, Poland); Antoni Szczurek (Institute of Nuclear Physics, Polish Academy of Sciences, ul. Radzikowskiego 152, Kraków, PL-31-342, Poland, College of Mathematics and Natural Sciences, University of Rzeszów, ul. Pigonia 1, Rzeszów, PL-35-310, Poland)
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 → 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) ~ 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 $$ q\overline{q} $$ -mesons.