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

Abstract

The Lorentz decomposition of the light-cone distribution amplitudes is carried out up to twist four. The Wandzura-Wilczek-like relations associated with the transverse photon wave function are derived in the same way as for the rho meson. The on-shell and off-shell photon wave functions with odd chirality at the leading twist in the effective low-energy theory derived from the instanton vacuum of QCD are calculated. The explicit expression of the transverse photon wave function, ${\ensuremath{\phi}}_{\ensuremath{\gamma}\ensuremath{\perp}}(u,{P}^{2})$, is worked out, and the twist-two parts of the other two photon wave functions, ${h}_{\ensuremath{\gamma}\ensuremath{\parallel}}^{(s),\mathrm{twist}\text{ }\mathrm{two}}(u,{P}^{2})$ and ${h}_{\ensuremath{\gamma}\ensuremath{\parallel}}^{(t),\mathrm{twist}\text{ }\mathrm{two}}(u,{P}^{2})$, are calculated based on the Wandzura-Wilczek-like relations. The dependence of the coupling ${f}_{\ensuremath{\gamma}}^{\ensuremath{\perp}}({P}^{2})$ and the light-cone photon wave functions with respect to the virtuality, ${P}^{2}$, are analyzed, and the end-point behavior as well as the middle-point behavior of the photon wave functions is discussed.