Radiative transitions in charmonium from lattice QCD

Abstract

Radiative transitions between charmonium states offer an insight into the internal structure of heavy-quark bound states within QCD. We compute, for the first time within lattice QCD, the transition form-factors of various multipolarities between the lightest few charmonium states. In addition, we compute the experimentally unobservable, but physically interesting vector form-factors of the ηc, J/ψ and χc0.To this end we apply an ambitious combination of lattice techniques, computing three-point functions with heavy domain wall fermions on an anisotropic lattice within the quenched approximation.With an anisotropy ξ = 3 at as ∼ 0.1 fm we find a reasonable gross spectrum and a hyperfine splitting ∼ 90MeV, which compares favourably with other improved actions.In general, after extrapolation of lattice data at non-zero Q 2 to the photopoint, our results agree within errors with all well measured experimental values. Furthermore, results are compared with the expectations of simple quark models where we find that many features are in agreement; beyond this we propose the possibility of constraining such models using our extracted values of physically unobservable quantities such as the J/ψ quadrupole moment.We conclude that our methods are successful and propose to apply them to the problem of radiative transitions involving hybrid mesons, with the eventual goal of predicting hybrid meson photoproduction rates at the GlueX experiment.

Lattice QCD study of the radiative decays J/ψ → η c γ and h c → η c γ

“…[24], V (0) = 1.85(4), is only slightly lower than ours, while the one obtained at single lattice spacing with N f = 2 light flavors in ref. [25], V (0) = 2.01(2), is larger than our values at β = 4.05 listed in table 2.…”

“…That methodology has been adopted in refs. [24,25]. In this work, instead, we will use the so called twisted boundary conditions [26][27][28] which allow us to work directly at q 2 = 0.…”

“…[24] where the authors computed relevant matrix elements for a number of decay channels in the quenched approximation of QCD and with one lattice spacing. That computation has been extended to the case of N f = 2 dynamical light quark flavors at single lattice spacing [25].…”

“…For the physical process, i.e. with the photon on-shell q 2 = 0, the decay rate is given by [24] Γ(J/ψ → η c γ) = 64 27…”

Hadronic loop contributions to J/ψ and ψ′ radiative decays into γLi1, Zhao2 2008Physics Letters B430161View full textAdd to dashboardCite

“…Theoretical studies of the heavy quarkonium M1 transitions with relativistic corrections are various in the literature [24,25,26,27,28,29,30,31]. Relativistic quark model calculations show that a proper choice of the Lorentz structure of the quark-antiquark interaction in a meson is crucial for explaining the J/ψ → γη c data [27].…”