Polarization in Cascade Decays

AbstractThis chapter addresses the case of a vector particle produced indirectly from the decay or transformation of a particle having $$J = 0$$ ($$\chi_{c0} \to \mathrm{J}/\psi \, \gamma$$, $$\mathrm{B} \to \mathrm{J}/\psi \, \mathrm{K}$$, $$\mathrm{H} \to \mathrm{Z} \, \gamma$$, etc.), $$J = 1$$ or $$J = 2$$ ($$\chi_{c1,2} \to \mathrm{J}/\psi \, \gamma$$, $$\mathrm{Z} \to \mathrm{J}/\psi \, \gamma$$, etc.), describing the polarization frame definitions that can be adopted to represent the two-step process, and their respective advantages. We illustrate how several measurement and kinematic conditions can lead to very different observable polarizations of the vector particle, in the special but frequent case where the intermediate decay step remains unobserved and only the final dilepton angular distribution is measured. We also discuss how the peculiar observation, made at the LHC, of almost unpolarized “directly” produced J/$$\psi$$ mesons may be understood as the result of a two-step production mechanism.