Nonperturbative Transverse Momentum Effects in p$+$p and p$+$A Collisions at PHENIX

Due to the non-Abelian nature of QCD, there is a prediction that quarks can become correlated across colliding protons in hadron production processes sensitive to nonperturbative transverse momentum effects.~ Measuring the evolution of nonperturbative transverse momentum widths as a function of the hard interaction scale can help distinguish these effects from other possibilities.~ Collins-Soper-Sterman evolution comes directly from the proof of transverse-momentum-dependent (TMD) factorization for processes such as Drell-Yan, semi-inclusive deep-inelastic scattering, and e$+$e- annihilation and predicts nonperturbative momentum widths to increase with hard scale.~ Experimental results from proton-proton and proton-nucleus collisions, in which TMD factorization is predicted to be broken, will be presented.~ The results show that these widths decrease with hard scale, suggesting possible effects from TMD factorization breaking.