Constituent quarks and systematic errors in mid-rapidity charged multiplicity dN(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 +/- 5% for PHENIX at RHIC). In A + A collisions where centrality is measured by the number of nucleon collisions, N-coll, or the number of nucleon participants, N-part, or the number of constituent quark participants, N-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-part, N-coll or N-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(ch)/d eta)/N-qp in Au + Au at RHIC was the same as the value in p + p collisions.