Pion-photon and photon-pion transition form factors in the light-cone formalism

Abstract

We derive the minimal Fock-state expansions of the pion and the photon wave functions in lightcone formalism, then we calculate the pion-photon and the photon-pion transition form factors of γ * π 0 → γ and γ * γ → π 0 processes by employing these quark-antiquark wave functions of the pion and the photon. We find that our calculation for the γ * γ → π 0 transition form factor agrees with the experimental data at low and moderately high energy scale. Moreover, the physical differences and inherent connections between the transition form factors of γ * π 0 → γ and γ * γ → π 0 have been illustrated, which indicate that these two physical processes are intrinsically related. In addition, we also discuss the π 0 → γγ form factor and the decay width Γ (π → γγ) at Q 2 = 0.

Tomography of light mesons in the light-cone quark model

“…The LCWF of the pion (or kaon) can be obtained through the transformation of the instant-form SU(6) wave functions using Melosh-Wigner rotation. The spin wave function of the pseudoscalar meson in the instant form (T) can be written as [120,125]…”

Quark Wigner distributions in a light-cone spectator model

“…The factor w = 1/ 2k + (k 0 + m), and the subscripts T and F stand for the instant form and the lightcone form spinors respectively. This transformation procedure is consistant with the results directly derived from the light-cone field theory [37]. For the spectator, the scalar one does not transform since it has spin-zero, and the axial-vector one transforms as [38] V +1…”

Heavy and light meson wavefunctions

“…[34,35]. Firstly, based on the BHL prescription, the pion leading-twist WF can be constructed as [36][37][38][39][40][41][42] where χ λ1λ2 (x, k ⊥ ) stands for the spin-space WF, λ 1 and λ 2 being the helicity states of the two constitute quarks in pion. The χ λ1λ2 (x, k ⊥ ) comes from Wigner-Melosh rotation [30], whose explicit forms are presented in Table I. Ψ R π (x, k ⊥ ) indicates the spatial WF, whose k ⊥dependent part can be constructed by using the connection between the rest frame WF Ψ c.m.…”

“…Even though these higher helicity components are usually power suppressed in large energy region, they shall lead to sizable contributions in low and intermediate energy regions. It has been observed that the introduction of higher helicity components into the light-cone formalism shall result in significant consequence in several problems concerning the applicability of perturbative QCD, such as the pion and kaon electromagnetic form factors [31][32][33][34][35], the pion-photon TFF [36][37][38][39][40][41][42][43][44][45], and etc.. It has been found that by a proper change of input parameters, especially the value of B that basically determines the longitudinal behavior of the light meson WFs, one can conveniently simulate the shape of the light meson's DA from asymptotic-like [1] to CZlike [46].…”