Production of the charmonium states chi_c1 and chi_c2 in proton nucleus interactions at sqrt(s)=41.6 GeV

A measurement of the ratio R_chi_c=(chi_c-->J/psi+gamma)/J/psi in pC , pTi , and pW interactions at 920 GeV/c ( sqrt(s)=41.6 Gev ) in the Feynman-x range -0.35<x^J/psi_F<0.15 is presented . Both mu^+ mu^- and e^+ e^- J/psi decay channels are observed with an overall statistics of about 15000 chi_c events , which is by far the largest available sample in pA collisions . The result is R_chi_c=0.188+/-0.013^+0.024_st-0.022sys 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_c1/R_chi_c2 is measured to be 1.02+/- 0.40 , leading to a cross section ratio sigma(chi_c1)/sigma(chi_c2)=0.57+/-0.23 . The dependence of R_chi_c on the Feynman-x of the J/psi , x^J/psi_F , and its transverse momentum , p^J/psi_T , 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_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 R_12 by a factor between 0.89 and 1.16 .