On the determination of the $D$ meson width in the nuclear medium with the transparency ratio

We have studied the feasibility of the experimental determination of the width of a $D$ meson in a nuclear medium by using the method of the nuclear transparency. The cross section for inclusive production of a $D^+$ in different nuclei is evaluated, taking care of the $D^+$ absorption in the nucleus, or equivalently, the survival probability of the $D^+$ in its way out of the nucleus from the point of production. We use present values of the in medium width of $D$ mesons and calculate ratios of the cross sections for different nuclei to the $^{12} \text{C}$ nucleus as reference. We find ratios of the order of $0.6$ for heavy nuclei, a large deviation from unity, which indicates that the method proposed is adequate to measure this relevant magnitude, so far only known theoretically.