Scaled momentum distributions for the strange hadrons K0s and Lambda/bar Lambda were measured in deep inelastic ep scattering with the ZEUS detector at HERA using an integrated luminosity of 330 pb-1. The evolution of these distributions with the photon virtuality, Q2, was studied in the kinematic region 10<Q2<40000 GeV2 and 0.001<x<0.75, where x is the Bjorken scaling variable. Clear scaling violations are observed. Predictions based on different approaches to fragmentation were compared to the measurements. Leading-logarithm parton-shower Monte Carlo calculations interfaced to the Lund string fragmentation model describe the data reasonably well in the whole range measured. Next-to-leading-order QCD calculations based on fragmentation functions, FFs, extracted from e+e- data alone, fail to describe the measurements. The calculations based on FFs extracted from a global analysis including e+e-, ep and pp data give an improved description. The measurements presented in this paper have the potential to further constrain the FFs of quarks, anti-quarks and gluons yielding K0s and Lambda/bar Lambda strange hadrons.
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