These anti-collinear emissions can violate the correct time-ordering for time-like cascades and result in large radiative corrections enhanced by double collinear logs, making the BMS evolution unstable beyond leading order. Such a regime occurs when the jets are highly collimated (boosted) and the relative angles between successive soft gluon emissions are strongly increasing. We identify a new physical regime where, besides the energy logarithms, one has to also resum (anti)collinear logarithms. We consider the Banfi-Marchesini-Smye (BMS) equation which resums `non-global' energy logarithms in the QCD evolution of the energy lost by a pair of jets via soft radiation at large angles. Resumming double non-global logarithms in the evolution of a jet The first numerical studies of the collinearly-improved BK equation demonstrate the essential role of the resummation in both stabilizing and slowing down the evolution.Â«Â less We extend this resummation to the next-to-leading order BFKL and BK equations.

This equation can be equivalently rewritten inmoreÂ Â» local form, but with modified kernel and initial conditions, which resum double collinear logs to all orders. These corrections can be resummed to all orders by solving an evolution equation which is non-local in rapidity. Via an explicit calculation of Feynman graphs in light cone (time-ordered) perturbation theory, we show that the corrections enhanced by double logarithms (either energy-collinear, or double collinear) are associated with soft gluon emissions which are strictly ordered in lifetime. The higher-order perturbative corrections, beyond leading logarithmic accuracy, to the BFKL evolution in QCD at high energy are well known to suffer from a severe lack-of-convergence problem, due to radiative corrections enhanced by double collinear logarithms. Resumming double logarithms in the QCD evolution of color dipoles

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