γ*γ*→ηc(1S,2S) transition form factors for spacelike photons

Abstract

We derive the light-front wave function (LFWF) representation of the γ * γ * → η c (1S) , η c (2S) transition form factor F (Q 2 1 , Q 2 2 ) for two virtual photons in the initial state. For the LFWF, we use different models obtained from the solution of the Schrödinger equation for a variety of cc potentials. We compare our results to the BaBar experimental data for the η c (1S) transition form factor, for one real and one virtual photon. We observe that the onset of the asymptotic behaviour is strongly delayed and discuss applicability of the collinear and/or massless limit. We present some examples of two-dimensional distributions for F (Q 2 1 , Q 2 2 ). A factorization breaking measure is proposed and factorization breaking effects are quantified and shown to be almost model independent. Factorization is shown to be strongly broken, and a scaling of the form factor as a function ofQ 2 = (Q 2 1 + Q 2 2 )/2 is obtained.

Prompt hadroproduction of ηc(1S, 2S) in the kT-factorization approach

“…Recently in ref. [15] we discussed in detail the γ * γ * → η c (1S, 2S) form factors. These form factors were calculated there from the cc light-front (LF) wave functions obtained from different cc interaction potentials obtained in ref.…”

“…In the present paper, we will apply the formalism developed in ref. [15] using the potential approach and the Melosh spin transform to derive the proper LF wave functions of the η c (1S, 2S) states. 1 Here, we employ the same LF formalism for computation of the g * g * → η c vertex, for both gluons being off-shell.…”

“…For details of the derivation and the normalization conventions and relation to the potential model wave function of the LF radial wave function ψ(z, k), see ref. [15]. In this work, we will use the calculations of the form factor which were obtained in [15].…”

“…[15]. In this work, we will use the calculations of the form factor which were obtained in [15]. There, the representation of the γ * γ * η c transition form factor in terms of the LF wave function of the η c was derived.…”

“…In ref. [15] we also studied the NRQCD limit, where relative motion of quark and antiquark are neglected. This amounts to ψ(z, k) ∝ δ(z − 1 2 )δ (2) (k) and leads to the transition form factor…”