χc0,c2→ρρdecays and theρpolarization: Massless versus constituent quarks

We compute the helicity density matrix of vector mesons produced in the decays ${\chi }_{c0,c2\mathrm{}}\to M_1{M}_2$, in the framework of perturbative QCD, allowing for mass corrections. Both the case in which the light quarks inside the final mesons are treated as massless current quarks and the case in which they are seen as constituent massive ones are considered. Explicit results are given for the helicity density matrix of $\rho$ mesons, $\rho \left(\rho \right)$, showing significant differences between the two cases; the measurement of $\rho \left(\rho \right)$ should then allow a precise evaluation of these mass effects.