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In this work, we adress the phenomenological consequences of explicit CPviolation on direct Higgs-boson searches at high energy colliders. Having arestricted parameter space, we concentrate on the recently proposedgluino-axion model, and investigate the CP violation capability of the modelsubject to the recent experimental data. It is shown that the Higgs masses aswell as their CP compositions are quite sensitive to the supersymmetric CPphases. The lightest Higgs is found to be nearly CP even to a goodapproximation whilst the remaining two heavy scalars do not have definite CPparities.Comment: 20 pp, 14 eps figs, title is changed, the manuscript is improved  using the latest experimental data, some figures and references adde

THE HIGGS MASSES AND EXPLICIT CP VIOLATION IN THE GLUINO–AXION MODEL