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We obtain the width of the meson in dense nuclear matter by taking into account (i) the free decay of the into three pions, which is dominated by mode, (ii) the processes induced by a vector-baryon interaction dominated by vector meson exchange, and (iii) the $\omega \to K \bar K\omega$ meson develops an important width in matter, coming from the dominant decay mode, with a value of MeV at normal nuclear matter density for an at rest. At finite momentum, the width of the meson increases moderately with values of 200 MeV at 600 MeV/c.

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