A measurement of the ratio $R_{{\chi }_c}=({\chi }_c\to J/\psi +\gamma )/J/\psi$ in $p\mathrm{C}$, $p\mathrm{Ti}$, and $p\mathrm{W}$ interactions at $920\mathrm{GeV}/c$ ($\sqrt{s}=41.6\mathrm{GeV}$) in the Feynman-x range $-0.35<x_F^{J/\psi }<0.15$ is presented. Both ${\mu }^{+}{\mu }^{-}$ and $e^{+}{e}^{-}$ $J/\psi$ decay channels are observed with an overall statistics of about 15 000 ${\chi }_c$ events, which is by far the largest available sample in pA collisions. The result is $R_{{\chi }_c}=0.188\pm {0.013}_{\mathrm{st}}{\genfrac{}{}{0ex}{}{+0.024}{-0.022}}_{\mathrm{sys}}$ averaged over the different materials, when no $J/\psi$ and ${\chi }_c$ polarizations are considered. The ${\chi }_{c1}$ to ${\chi }_{c2}$ production ratio $R_{12}=R_{{\chi }_{c}1}/R_{{\chi }_{c}2}$ is measured to be $1.02\pm 0.40$, leading to a cross section ratio $\frac{\sigma ({\chi }_{c1})}{\sigma ({\chi }_{c2})}=0.57\pm 0.23$. The dependence of $R_{{\chi }_c}$ on the Feynman-x of the $J/\psi$, $x_F^{J/\psi }$, and its transverse momentum, $p_T^{J/\psi }$, is studied, as well as its dependence on the atomic number, A, of the target. For the first time, an extensive study of possible biases on $R_{{\chi }_c}$ and $R_{12}$ due to the dependence of acceptance on the polarization states of $J/\psi$ and ${\chi }_c$ is performed. By varying the polarization parameter, ${\lambda }_{\mathrm{obs}}$, of all produced $J/\psi$’s by two sigma around the value measured by HERA-B, and considering the maximum variation due to the possible ${\chi }_{c1}$ and ${\chi }_{c2}$ polarizations, it is shown that $R_{{\chi }_c}$ could change by a factor between 1.02 and 1.21 and $R_{12}$ by a factor between 0.89 and 1.16.

• Received 14 July 2008

DOI:https://doi.org/10.1103/PhysRevD.79.012001