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Linear and non-linear QCD evolutions at high energy suffer from severe issuesrelated to convergence, due to higher order corrections enhanced by largedouble and single transverse logarithms. We resum double logarithms to allorders by taking into account successive soft gluon emissions strongly orderedin lifetime. We further resum single logarithms generated by the firstnon-singular part of the splitting functions and by the one-loop running of thecoupling. The resulting collinearly improved BK equation admits stablesolutions, which are used to successfully fit the HERA data at small-x forphysically acceptable initial conditions and reasonable values of the fitparameters.

Resumming large higher-order corrections in non-linear QCD evolution