document: Brodsky and Lepage [8] have proposed a formula for meson pair production which looks similar to (25), except for a different charge factor and the appearance of the timelike electromagnetic meson form factor instead of the annihilation form factor R(s). This formula was obtained from the leading-twist result by neglecting part of the amplitudes with opposite photon helicities. As has been pointed out in [9], this part is however not approximately independent of the pion distribution amplitude and not generically small. We also remark that the appearance of Fπ(s) in the γγ→π+π− amplitude is no longer observed if corrections from partonic transverse momentum in the hard scattering process are taken into account, and that these corrections are not numerically small for the values of s we are dealing with [13]. Notice further that two-photon annihilation produces two pions in a C-even state, whereas the electromagnetic form factor projects on the C-odd state of a pion pair. In contrast, our annihilation form factor R2π(s) is C-even as discussed after (24). Finally, due to a particular charge factor, the Brodsky–Lepage formula leads to a vanishing cross section for γγ annihilation into pairs of neutral pseudoscalars.
doc_bio_tags: O O O O O O O B O B I O O O O O O O O O O O O O O O O O O B I O O O O O B I I O O B O O O O O O O B I I I I I I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O B I I O O O O O O O B I O O O B I I O O O O O O O O O O O O O O O B I O O O B I I I I I O O O B I
extractive_keyphrases: annihilation form factor brodsky–lepage formula electromagnetic form factor electromagnetic meson formula hard scattering process meson pair neglecting part of the amplitudes with opposite photon helicities neutral pseudoscalars partonic transverse momentum pion pair pions vanishing cross section for γγ annihilation
abstractive_keyphrases: formula for meson pair production meson pair production photon photon helicities r2π(s) two-photon annihilation