Nonperturbative-transverse-momentum effects and evolution in dihadron and direct photon-hadron angular correlations in $p+p$ collisions at $\sqrt{s}=510\mathrm{GeV}$

Dihadron and isolated direct photon-hadron angular correlations are measured in $p+p$ collisions at $\sqrt{s}=510\mathrm{GeV}$. Correlations of charged hadrons of $0.7<p_T<10\mathrm{GeV}/c$ with ${\pi }^0$ mesons of $4<p_T<15\mathrm{GeV}/c$ or isolated direct photons of $7<p_T<15\mathrm{GeV}/c$ are used to study nonperturbative effects generated by initial-state partonic transverse momentum and final-state transverse momentum from fragmentation. The nonperturbative behavior is characterized by measuring the out-of-plane transverse momentum component $p_{\mathrm{out}}$ perpendicular to the axis of the trigger particle, which is the high-$p_T$ direct photon or ${\pi }^0$. Nonperturbative evolution effects are extracted from Gaussian fits to the away-side inclusive-charged-hadron yields for different trigger-particle transverse momenta ($p_T^{\mathrm{trig}}$). The Gaussian widths and root mean square of $p_{\mathrm{out}}$ are reported as a function of the interaction hard scale $p_T^{\mathrm{trig}}$ to investigate possible transverse-momentum-dependent evolution differences between the ${\pi }^0\text{−}{\mathrm{h}}^{\pm }$ and direct photon-${\mathrm{h}}^{\pm }$ correlations and factorization breaking effects. The widths are found to decrease with $p_T^{\mathrm{trig}}$, which indicates that the Collins-Soper-Sterman soft factor is not driving the evolution with the hard scale in nearly back-to-back dihadron and direct photon-hadron production in $p+p$ collisions. This behavior is in contrast to Drell-Yan and semi-inclusive deep-inelastic scattering measurements.

Figure 1

A diagram showing the hard-scattering kinematics of (a) a dihadron and (b) a direct photon-hadron event in the transverse plane. Two hard-scattered partons with transverse momenta ${\widehat{p}}_T^{\mathrm{trig}}$ and ${\widehat{p}}_T^{\text{assoc}}$ [red lines] are acoplanar due to the initial-state ${\overrightarrow{k}}_T^1$ and ${\overrightarrow{k}}_T^2$ from each parton. These result in a trigger and associated jet fragment $p_T^{\mathrm{trig}}$ and $p_T^{\text{assoc}}$ with a transverse momentum component perpendicular to the jet axis $j_{T_y^{\mathrm{trig}}}$ and $j_{T_y^{\text{assoc}}}$ in the transverse plane, which are assumed to be Gaussian such that $\sqrt{⟨j_T^2⟩}=\sqrt{2⟨j_{T_y^{\mathrm{trig}}}^2⟩}=\sqrt{2⟨j_{T_y^{\text{assoc}}}^2⟩}$. For direct photons (b) only one jet fragment $p_T^{\text{assoc}}$ is produced because the direct photon is produced from the hard scattering. The quantity $p_{\mathrm{out}}$ [blue] is the transverse momentum component of the away-side hadron perpendicular to the trigger particle axis.

Figure 2

Cross section view along the beam line of the PHENIX detector, showing the detectors composing the central arms in 2012 and 2013. The relevant subsystems for this analysis are described in the text.

Figure 3

Measured $R_{\gamma }^{\mathrm{iso}}$ for use in the statistical subtraction, Eq. (5). The boxes quantify the systematic uncertainty.

Figure 4

Per-trigger yield of charged hadrons shown as a function of the azimuthal angle between the ${\pi }^0$ or direct photon trigger particle and associated charged hadron. The dashed [black] lines show an estimate of the underlying event yield and are drawn to guide the eye in distinguishing the underlying event from the away-side jet. The solid lines through the open squares [red] and open circles [blue] are fits to extract the widths of the near and away sides. A 9% overall normalization uncertainty on the charged hadron yields is not shown in the figure.

Figure 5

The $\sqrt{⟨j_T^2⟩}$ shown as a function of $p_T^{\mathrm{trig}}$ is determined with Eq. (9) and has been shown to be approximately constant with $\sqrt{s}$ and $p_T$ in the limited $p_T$ range examined here. The line shows a constant fit to average over $p_T^{\mathrm{trig}}$.

Figure 6

$\sqrt{⟨p_{\mathrm{out}}^2⟩}$ for ${\pi }^0$ and direct photon triggers as a function of $p_T^{\text{assoc}}$ in several $p_T^{\mathrm{trig}}$ bins.

Figure 7

$\sqrt{⟨p_{\mathrm{out}}^2⟩}$ for ${\pi }^0$ and direct photon triggers as a function of $p_T^{\mathrm{trig}}$ in two different $p_T^{\text{assoc}}$ bins.

Figure 8

$\sqrt{⟨p_{\mathrm{out}}^2⟩}$ for ${\pi }^0$ and direct photon triggers as a function of $p_T^{\text{jet}}$ in two different $p_T^{\text{assoc}}$ bins. For ${\pi }^0$ triggers, $p_T^{\text{jet}}=p_T^{\mathrm{trig}}/⟨z_T^{{\pi }^0}⟩$ where $⟨z_T^{{\pi }^0}⟩$ was determined from pythia.

Figure 9

Per-trigger yields of charged hadrons as a function of $p_{\mathrm{out}}$. The ${\pi }^0$ and direct photon distributions are fit with Gaussian functions at small $p_{\mathrm{out}}$ and Kaplan functions over the whole range, showing the transition from nonperturbative behavior generated by initial-state $k_T$ to perturbative behavior generated by hard gluon radiation. A 9% overall normalization uncertainty on the charged hadron yields is not shown in the figure.

Figure 10

Gaussian widths of $p_{\mathrm{out}}$ for ${\pi }^0$ and direct photon triggers as a function of $p_T^{\mathrm{trig}}$.

Figure 11

Gaussian widths of $p_{\mathrm{out}}$ for ${\pi }^0$ and direct photon triggers as a function of $p_T^{\text{jet}}$, where $p_T^{\text{jet}}$ is $p_T^{\mathrm{trig}}$ for the direct photons and $p_T^{\mathrm{trig}}/⟨z_T^{{\pi }^0}⟩$ for the ${\pi }^0$ triggers. $⟨z_T^{{\pi }^0}⟩$ was determined from a pythia simulation.

Figure 12

The fractional contribution of partonic scattering processes to (a) inclusive ${\pi }^0$ and (b) direct-photon production at LO in $p+p$ collisions at $\sqrt{s}=510\mathrm{GeV}$ in the PHENIX pseudorapidity region. Note that the process $q\overline{q}\to gg$ is not drawn in panel (a) because its contribution is less than one percent in this $p_T$ range.

Figure 13

Gaussian widths extracted from pythia Drell-Yan $p_{\mathrm{out}}$ distributions. In Drell-Yan factorization breaking is not predicted. Here the widths show a positive slope with the invariant mass of the dilepton, as predicted by CSS evolution. The solid red line shows a log fit over the full invariant mass range and the blue dotted line shows a linear fit in the region $5–10\mathrm{GeV}/c^2$.

Figure 14

${\pi }^0\text{−}{\mathrm{h}}^{\pm }$ and direct photon-${\mathrm{h}}^{\pm }$ $p_{\mathrm{out}}$ distributions from pythia correlations. The nonperturbative region was fit with Gaussian functions similarly to what was done with the data. pythia shows similar behavior to the data: a clear nonperturbative region transitioning to a perturbative power-law tail.

Figure 15

Gaussian widths extracted from pythia $p_{\mathrm{out}}$ distributions are shown compared to the results measured at PHENIX. pythia produces consistent evolution rates as what was determined in PHENIX, although there is a 10%–15% difference in the quantitative values in each $p_T^{\mathrm{trig}}$ bin.