Measuring the $\phi$ meson width in the medium from $p$ induced $\phi$ production in nuclei

We study the $A$ dependence of the $\phi$ meson production cross section in proton nucleus reactios at energies just above threshold, which are accessible in an experimental facility like COSY. This $A$ dependence has two sources: the distortion of the incident proton and the absorption of the $\phi$ in its way out of the nucleus. This second process reduces the cross section in about a factor two in heavy nuclei. Thus we show that the $A$ dependence of the cross section contains valuable information on the $\phi$ width in the nuclear medium