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Hard scattering yields in centrality-selected proton-- and deuteron--nucleus($p$+A) collisions are generally compared to nucleon--nucleon ($NN$)cross-sections scaled to the appropriate partonic luminosity using geometricmodels derived from an analysis of minimum bias $p$+A interactions. In general,these models assume that hard process rates and the magnitude of the soft eventactivity in the underlying $NN$ collisions is uncorrelated. When included,these correlations influence the measured yield in a nominal centralityinterval, an effect typically referred to as a "centrality bias". In this work,the impact of a positive correlation between the hard scattering yield and theunderlying event activity in individual $NN$ collisions is investigated. Thiscorrelation is incorporated into the centrality calculations used by ATLAS andPHENIX, both based on a similar Monte Carlo Glauber approach but with differentmodels of the per-collision or per-participant event activity. It is found thatthe presence of this correlation tends to increase the yield measured in morecentral events and decrease it in peripheral events. Numerical factors tocorrect measured yields for the centrality bias effect are calculated for $p$+Acollisions at RHIC and the LHC. Reasonable agreement with a previouscalculation of these factors by PHENIX is found, despite differences in theimplementation of the underlying bias.

Calculation of centrality bias factors in $p$+A collisions based on a positive correlation of hard process yields with underlying event activity