Off-shell photon light-cone wave functions of odd chirality in the effective low-energy theory

Distribution amplitudes of light mesons and the photon in the instanton model

“…However, it is evident, see for example [1], that these additional terms contribute to twist-4 distributions and do not touch the leading twist-2 distributions. From the other side, the full vertex including the local and nonlocal pieces is important in the soft hadronic part and has not to be neglected as it was done in [14,18] considering the photon distribution amplitudes.…”

“…Recently there have been published several papers [15][16][17][18], where in nonlocal models, similar to the one considered above, the distribution functions for pion and photon were treated inconsistently. Indeed, the typical expression (4) defining the distribution functions has two parts.…”

Off-shell photon distribution amplitudes in the low-energy effective theory of QCD

“…In the present paper, we extend our previous calculation to higher twists, and we give a complete treatment in the same way for all light-cone photon DAs up to twist four as appearing in the formalism described before in [33], which is based on the effective low-energy instanton vacuum model of QCD and a systematical Lorentz decomposition of the transition matrix element from an off-shell photon to vacuum through a nonlocal quark-antiquark bilinear current with a gauge link. We show that in our formalism there are altogether eight photon DAs up to twist four, in which only two DAs survive in the on-shell limit.…”

“…Let us review the formalism suggested in [33] with a slight modification, in which the photon DAs are defined and classified into two groups with different chiralities. According to Lorentz covariance, the nonlocal quark-antiquark current with light-like separation (z 2 = 0) sandwiched between vacuum |0 and one photon state |γ (P, λ) , characterized by its momentum P μ and the polarization vector e…”

“…Following the same line as in [23], we have calculated the off-shell photon DAs at leading twist corresponding with both Dirac structures, σ μν and γ μ [33][34][35], and the twist-two parts of the other two photon DAs (each of which contains both twist-two and twist-three parts, but we call them twistthree DAs, different from other references) of the tensor current are estimated.…”