Transverse-momentum distribution of inclusive pions

We study the transverse-momentum distribution of pions that come from the decay of ρ's. We find that the inclusive transverse-momentum distribution of such pions will exhibit a turning over as $k_{⟂}^{{}^2}\to 0$. This effect is strictly kinematic and will appear in any model where π's come from the decay of unpolarized low-mass clusters which have a $p_{⟂}^{{}^2}$ distribution that is peaked at $p_{⟂}^{{}^2}=0$.