Constituent quarks and systematic errors in mid-rapidity charged multiplicity $dN_{\rm ch}/d\eta$ distributions

Centrality definition in A$+$A collisions at colliders such as RHIC and LHC suffers from a correlated systematic uncertainty caused by the efficiency of detecting a p$+$p collision ($50\pm 5\%$ for PHENIX at RHIC). In A$+$A collisions where centrality is measured by the number of nucleon collisions, $N_{\rm coll}$, or the number of nucleon participants, $N_{\rm part}$, or the number of constituent quark participants, $N_{\rm qp}$, the error in the efficiency of the primary interaction trigger (Beam-Beam Counters) for a p$+$p collision leads to a correlated systematic uncertainty in $N_{\rm part}$, $N_{\rm coll}$ or $N_{\rm qp}$ which reduces binomially as the A$+$A collisions become more central. If this is not correctly accounted for in projections of A$+$A to p$+$p collisions, then mistaken conclusions can result. A recent example is presented in whether the mid-rapidity charged multiplicity per constituent quark participant $({dN_{\rm ch}/d\eta})/{N_{\rm qp}}$ in Au$+$Au at RHIC was the same as the value in p$+$p collisions.