We consider the recent proposal that the distribution of the difference between azimuthal angles of the two accompanying jets in gluon-fusion induced Higgs-plus-two-jet events at LHC reflects the CP of the Higgs boson produced. We point out that the hierarchy between the Higgs boson mass and the jet transverse energy makes this observable vulnerable to logarithmically enhanced higher-order perturbative corrections. We present an evolution equation that describes the scale variation of the

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... hal angular correlation for the two jets. The emission of extra partons leads to a significant suppression of the correlation. Using the HERWIG Monte Carlo event generator, we carry out a parton-shower analysis to confirm the findings.