Multichannel conformal blocks for scattering amplitudes

By performing resummation of small fermion-antifermion pairs within the pentagon form factor program to scattering amplitudes in planar N=4 superYang-Mills theory, we construct multichannel conformal blocks within the flux-tube picture for N-sided NMHV polygons. This procedure is equivalent to summation of descendants of conformal primaries in the OPE framework. The resulting conformal partial waves are determined by multivariable hypergeometric series of Lauricella-Saran type.