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Dihadron and isolated direct photon-hadron angular correlations are measuredin $p$$+$$p$ collisions at $\sqrt{s}=200$ GeV. The correlations are sensitiveto nonperturbative initial-state and final-state transverse momentum $k_T$ and$j_T$ in the azimuthal nearly back-to-back region $\Delta\phi\sim\pi$. In thisregion, transverse-momentum-dependent evolution can be studied when severaldifferent hard scales are measured. To have sensitivity to small transversemomentum scales, nonperturbative momentum widths of $p_{\rm out}$, theout-of-plane transverse momentum component perpendicular to the triggerparticle, are measured. These widths are used to investigate possible effectsfrom transverse-momentum-dependent factorization breaking. When accounting forthe longitudinal momentum fraction of the away-side hadron with respect to thenear-side trigger particle, the widths are found to increase with the hardscale; this is qualitatively similar to the observed behavior in Drell-Yan andsemi-inclusive deep-inelastic scattering interactions. The momentum widths arealso studied as a function of center-of-mass energy by comparing to previousmeasurements at $\sqrt{s}=510$ GeV. The nonperturbative jet widths also appearto increase with $\sqrt{s}$ at a similar $x_T$, which is qualitativelyconsistent to similar measurements in Drell-Yan interactions. To quantify themagnitude of any transverse-momentum-dependent factorization breaking effects,calculations will need to be performed to compare to these measurements.

physical review. d/physical review. d.

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