  The azimuthal collimation of di-hadrons with large rapidity separations in
high multiplicity p+p collisions at the LHC is described in the Color Glass
Condensate (CGC) effective theory [1] by N_c^2 suppressed multi-ladder QCD
diagrams that are enhanced \alpha_S^(-8) due to gluon saturation in hadron
wavefunctions. We show that quantitative computations in the CGC framework are
in good agreement with data from the CMS experiment on per trigger di-hadron
yields and predict further systematics of these yields with varying trigger pT
and charged hadron multiplicity. Radial flow generated by re-scattering is
strongly limited by the structure of the p+p di-hadron correlations. In
contrast, radial flow explains the systematics of identical measurements in
heavy ion collisions.
