Nonperturbative transverse-momentum-dependent effects in dihadron and direct photon-hadron angular correlations in $p+p$ collisions at $\sqrt{s}=200$ GeV

Dihadron and isolated direct photon-hadron angular correlations are measured in p + p collisions at root s = 200 GeV. The correlations are sensitive to nonperturbative initial-state and final-state transverse momenta k(T) and j(T) in the azimuthal nearly back-to-back region. Delta phi similar to pi. To have sensitivity to small transverse momentum scales, nonperturbative momentum widths of pout, the out-of-plane transversemomentum component perpendicular to the trigger particle, are measured. In this region, the evolution of pout can be studied when several different hard scales are measured. These widths are used to investigate possible effects from transverse-momentum-dependent factorization breaking. When accounting for the longitudinal-momentum fraction of the away-side hadron with respect to the near-side trigger particle, the widths are found to increase with the hard scale; this is qualitatively similar to the observed behavior in Drell-Yan and semi-inclusive deep-inelastic scattering interactions, where factorization is predicted to hold. The momentum widths are also studied as a function of center-of-mass energy by comparing to previous measurements at root s = 510 GeV. The nonperturbative jet widths also appear to increase with root s at a similar x(T), which is qualitatively consistent to similar measurements in Drell-Yan interactions. Future detailed global comparisons between measurements of processes where transverse-momentum-dependent factorization is predicted to hold and be broken will provide further insight into the role of color in hadronic interactions.