Nonperturbative transverse momentum broadening in dihadron angular correlations in $\sqrt{s_{NN}}=200$ GeV proton-nucleus collisions

The PHENIX collaboration has measured high $p_T$ dihadron correlations in $p$$+$$p$, $p$+Al, and $p$+Au collisions at $\sqrt{s_{NN}}=200$ GeV. The correlations arise from inter- and intra-jet correlations and thus have sensitivity to nonperturbative effects in both the initial and final states. The distributions of $p_{out}$, the momentum component of the associated hadron perpendicular to the trigger hadron, are sensitive to initial and final state transverse momenta. These distributions are measured multi-differentially as a function of $x_E$, the longitudinal momentum fraction of the associated hadron with respect to the trigger hadron. The near-side $p_{out}$ momentum widths, sensitive to fragmentation transverse momentum, show no significant broadening between $p$+Au, $p$+Al, and $p$$+$$p$. The away-side nonperturbative momentum widths are found to be broadened in $p$+Au when compared to $p$$+$$p$, however, there is no significant broadening in $p$+Al compared to $p$$+$$p$ collisions. The data also suggest that the away-side transverse momentum broadening is a function of $N_{coll}$, the number of binary nucleon-nucleon collisions, in the interaction. The potential implications of these results with regard to transverse momentum broadening and energy loss of partons in a nucleus, among other nuclear effects, are discussed.

The PHENIX collaboration has measured high-pT dihadron correlations in p+p, p+Al, and p+Au collisions at √ s N N = 200 GeV. The correlations arise from inter-and intra-jet correlations and thus have sensitivity to nonperturbative effects in both the initial and final states. The distributions of pout, the momentum component of the associated hadron perpendicular to the trigger hadron, are sensitive to initial and final state transverse momenta. These distributions are measured multidifferentially as a function of xE, the longitudinal momentum fraction of the associated hadron with respect to the trigger hadron. The near-side pout momentum widths, sensitive to fragmentation transverse momentum, show no significant broadening between p+Au, p+Al, and p+p. The awayside nonperturbative momentum widths are found to be broadened in p+Au when compared to p+p; however, there is no significant broadening in p+Al compared to p+p collisions. The data also suggest that the away-side transverse momentum broadening is a function of N coll , the number of binary nucleon-nucleon collisions, in the interaction. The potential implications of these results with regard to transverse momentum broadening and energy loss of partons in a nucleus, among other nuclear effects, are discussed.

I. INTRODUCTION
High energy collisions of protons with nuclei provide a testing ground for quantum chromodynamics (QCD). In particular, when large transverse momentum scales are involved, the collisions can probe the quark and gluon, collectively referred to as partons, structure of the nucleus. Proton-nucleus (p+A) collisions have traditionally been used as a control to identify final-state nuclear effects in high energy nucleus-nucleus collisions where a strongly interacting quark-gluon plasma (QGP) is formed [1]. However, measurements in p+A collisions have revealed many surprising results that have yet to be completely reconciled with each other; these have shown that understanding and explaining many different "cold" nuclear matter effects is already a challenging endeavor [2][3][4][5].
For example, in the initial-state, nuclei are known to be more complex than just a simple linear superposition of nucleons (see e.g. Ref. [2] for a review). Nuclear parton distribution functions (PDFs) are known to have several regions where they deviate from simple superpositions of nucleon PDFs as a function of the longitudinal momentum fraction x that the parton carries of the nucleon. Understanding how the partonic degrees of freedom lead to nuclear structure will be a major achievement of QCD; however, there is still significant effort required in understanding the physical origin of these measured nuclear modifications. Final-state hadronization from a nucleus can also be modified similarly to nuclear PDFs in the initial state. In particular, semi-inclusive deep-inelastic scattering (SIDIS) experiments have shown that high z hadrons are suppressed in electron-nucleus relative to electron-deuterium collisions [6], where z is the longitudinal momentum fraction of the outgoing hadron with respect to the fragmenting parton. This suppression was found to be dependent on the nuclear target size [7]. In addition, a particle species dependence was observed, which may reflect differences in the nuclear modification of quark and/or antiquark fragmentation functions and possible differences in meson versus baryon production from nuclei [6,7].
Several proposed signatures of the QGP have also been measured in p+A collisions where the overall system size created in the collision was once expected to * PHENIX Spokesperson: akiba@rcf.rhic.bnl.gov † Deceased be too small. Collective behavior has been observed across large pseudorapidity ranges in high multiplicity p+A collisions [3,[8][9][10]. Additionally, the enhancement of strangeness in hadron production in high multiplicity p+A collisions has recently been measured [11]. Surprisingly, both of these phenomena have also been observed in high multiplicity p+p collisions [12,13]. However, the suppression of high p T inclusive hadrons or jets in p+A collisions with respect to p+p collisions has not been measured [14,15]. These results were first used to establish final-state QGP interactions as the cause of high p T hadron suppression in nucleus-nucleus collisions [5,16]. However, the recent addition of collective and strange hadron measurements but lack of hadron suppression in p+A collisions has complicated the idea that a QGP may be formed in smaller collision systems.
Another unexpected physical effect in p+A collisions is the so-called "Cronin" effect, which refers to an enhancement in the inclusive hadron p T spectrum with respect to p+p collisions at moderate p T of approximately 2 < p T < 6 GeV/c which persists over a wide range of center-of-mass energies [4,14,17]. This effect has also been observed at moderate p T in electron-nucleus collisions [6], where a significant dependence of the enhancement on the longitudinal momentum fraction z of the hadron was found [7]. While this was first proposed to be due to multiple scattering effects in the nuclear medium, more recent measurements have shown that hadronization also plays a role [18]. Additional measurements that go beyond single inclusive hadrons may be able to shed further light on this phenomenon in p+A collisions. For example, dijet measurements in the kinematic regime of the Cronin effect have shown that the initial-state partonic transverse momentum is a function of the nucleus size [19], which has not been observed at large jet transverse momentum [20].
The lack of understanding of the underlying physical sources of these phenomena motivates measurements in new kinematic regimes with different observables. Here we present a measurement of dihadron angular correlations in p+p, p+Al, and p+Au collisions at midrapidity collected by the PHENIX experiment at the Relativistic Heavy Ion Collider (RHIC). The unique capabilities of RHIC allow for a nuclear size dependence to be studied in √ s N N = 200 GeV p+A collisions. High p T two-particle angular correlations have been theoretically considered as a probe for energy loss in p+A and A+A collisions via their transverse momentum broadening [21][22][23]; however, the various aforementioned effects should also be considered as they will play a role in both collision systems.
The present measurements will contribute to our understanding of the rich phenomena in hadronic interactions involving nuclei.

II. METHODS
In 2015, the PHENIX experiment [24] at RHIC collected data from p+p, p+Al, and p+Au collisions at √ s N N = 200 GeV. A total minimum bias integrated luminosity of 60, 0.69, and 0.21 pb −1 for p+p, p+Al, and p+Au, respectively, was used for the analysis of dihadron correlations. From these total integrated luminosities, data quality assurance and collision vertex position |z vtx | < 30 cm cuts were applied. The PHENIX detector measures two-particle angular correlations of neutral pions and charged hadrons, π 0 -h ± , with its electromagnetic calorimeter (EMCal) and drift chamber (DC) and pad chamber (PC) tracking system. These central arms cover an azimuthal range of ∆φ ≈ π radians and a pseudorapidity range of |η| < 0.35. Detailed descriptions of the PHENIX central arms can be found in Refs. [25,26]. In p+A collisions, the centrality class is determined with the forward beam-beam counters (BBCs) [27], where the centrality percentiles are defined by the multiplicity measured in the nucleus-going BBC following the procedure in Ref. [28].
The EMCal is used to identify high p T neutral pions to construct the correlation functions. A high-energyphoton trigger is used to identify events with a high p T photon from a π 0 → γγ decay. Photons are identified using a shower shape cut that removes charged hadrons as well as most high energy clusters that overlap with another photon. The neutral pions are reconstructed via their two photon decay, where the granularity of the EM-Cal allows π 0 reconstruction up to approximately 20 GeV in this channel. In this analysis neutral pions are collected in the p T range 5 < p T < 9 GeV/c.
The DC and PC tracking system measures nonidentified charged hadrons in the event with the triggered high p T photon. Two PCs, located radially behind the DC, are used to identify and match tracks in the DC with hits in the PCs. This track matching condition reduces background from secondary tracks due to conversions or decays. A ring-imagingČerenkov system is also used to reject electrons from the charged hadron sample. With these conditions, the DC and PC tracking system is also used to reject tracks in the EMCal that happen to shower and are thus background for the π 0 → γγ identification. Nonidentified charged hadrons are collected between 0.5 < p T < 10 GeV/c in correlation with the high p T π 0 .
The correlations are constructed similarly to previous PHENIX two-particle correlation analyses, see e.g. Refs. [29][30][31]. Per-trigger yields are constructed for a given observable, such as ∆φ, which show the yield of charged hadrons per-trigger π 0 and are defined by To account for the PHENIX acceptance, the raw correlations are divided by a mixed-event background correlation function, dN/d∆φ mixed . The background correlation is constructed with neutral pions and charged hadrons from the same data taking period but different event number; the events are required to have a similar centrality and z-vertex. To account for the efficiency of the PHENIX detector, the correlation functions are also corrected by a charged hadron efficiency defined as (p T ) in Eq. 1, which is determined with a single particle Monte Carlo generator as well as a full GEANT description of the PHENIX apparatus [32]. After these corrections, the correlations are normalized by the total number of trigger particles measured to construct the per-trigger yield and correspond to full azimuthal acceptance within |η| < 0.35. Correlation functions are typically constructed in terms of the azimuthal angle ∆φ between the trigger and associated particle. Here we choose to construct the correlations as a function of the momentum space vector component p out and x E , defined as and The quantities p out and x E give the transverse momentum component and longitudinal momentum fraction, respectively, of the associated hadron with respect to the trigger π 0 . These quantities are schematically diagrammed in Fig. 1, where the Figure shows a twoparticle correlation in the transverse plane and quantities in bold represent vectors. In this diagram, two hadrons (black vectors) fragment from two high p T partons (red vectors) from a two-to-two partonic scattering. The partons are originally acoplanar due to their initialstate transverse momenta (k T ); the two hadrons may acquire additional acoplanarity due to final-state transverse momentum (j T ) during the fragmentation process.
In the diagram the final-state transverse momentum is perpendicular to the parton axis and denoted as j T trig y and j T assoc y , which are assumed to be Gaussian such that The quantity p out can be nonzero because of these transverse momentum contributions, while x E is a proxy for the momentum fraction z that the final-state hadron carries with respect to the parton. In the figure, x E is shown multiplied by p trig T to explicitly show the comparison between x E and z. When p out is small, the two-particle correlation is nearly back-to-back and the acoplanarity is generated by nonperturbative k T and j T [31,33]. Additional nonperturbative interactions within the nucleus may contribute to this quantity in p+A collisions.
Systematic uncertainties are assigned for the charged hadron efficiency and for the underlying event background subtraction procedure. The systematic uncertainty on the charged hadron yields is determined to be an overall normalization uncertainty of 9% on the per-trigger yields. The dominant contribution is due to the uncertainty that arises from matching tracks in the PHENIX drift chamber to the outermost pad chamber; however, there are also contributions from the overall tracking resolution of the detector and the Monte Carlo determination of the nonidentified charged hadron efficiency. The underlying event background is statistically subtracted with fits to the away-side ∆φ correlation functions as described in Ref. [33]; these fits determine the percentage of underlying event background level with respect to the jet yield. The systematic uncertainty is determined by altering the underlying event region by ±1σ based on the fit results. This uncertainty varies from less than 1% at small p out to several percent at large p out where the underlying event contribution, and thus background-to-signal, is larger.

III. RESULTS
Examples of the away-side per-trigger yields as a function of p out are shown in several bins of x E in Fig. 2. The per-trigger yields for p+Au and p+p collisions are shown as open and filled points, respectively. A transition from nonperturbative behavior in the nearly back-to-back p out ≈0 (∆φ ≈ π) region to perturbative next-to-leading order behavior at larger p out can be seen at varying values of p out , depending on the x E bin. This change in shape is highlighted by Gaussian fits to the small p out region, drawn in Fig. 2 as dotted and solid lines for p+Au and p+p, respectively. The fit ranges vary depending on the x E bin as the nonperturbative region is a function of p assoc T and thus x E [31]. The fit ranges are chosen to give the best χ 2 /NDF, and a systematic uncertainty is assigned based on this choice as described later. These fits clearly do not describe the data at larger values of p out where the data exhibit a more power-law like behavior. This transition indicates a change from sensitivity to nonperturbative to perturbative physics effects. Examples of the near-side per-trigger yields as a function of p out are shown in several bins of x E in Fig. 3. The near-side per-trigger yields show a much narrower distribution than the away-side per-trigger yields due to the differences between intra-jet correlations and interjet correlations, respectively. In particular, the near-side correlations are only sensitive to fragmentation transverse momentum, because the π 0 and hadron are frag-mented from the same hard parton. However, the awayside correlations are sensitive to both initial and final state transverse momentum. Because the initial-state k T is much larger than final-state j T (see e.g. [29,30]), this leads to a broader p out distribution on the away-side than the near-side. Nonetheless, a nonperturbative Gaussian region can still be identified on the near side as shown in Fig. 3, similarly to the away side, with a power law spectrum at larger p out that is not well described by the Gaussian fit.
To measure the nonperturbative momentum widths, the Gaussian widths are extracted from the fits to both the near and away side p out distributions. Systematic uncertainties on the Gaussian widths are estimated by increasing the fit range by 0.2 GeV/c in p out and taking the absolute value of the difference of the resulting Gaussian width. To study any modification in p+A compared to p+p collisions the squared width difference is determined between the p+A and p+p Gaussian widths, mathematically defined as p 2 out p+A − p 2 out p+p . These differences are shown in Fig. 4 as a function of x E for the near and away side correlation functions, for both p+Al and p+Au collisions. The near-side width differences in the left column of Fig. 4 show no significant modification within uncertainties between both p+Al or p+Au and p+p collisions at all values of x E . Similar results have been seen in dihadron correlations [34] and fragmentation function studies with full jet reconstruction [35] in p+Pb collisions. However, the away-side width differences in p+Au and p+p collisions show modification as seen in the bottom-right panel of Fig. 4. There is no significant away-side broadening between p+Al and p+p collisions as seen in the top right panel of Fig. 4 within the assigned systematic uncertainties.
There is an indication that the away-side squared Gaussian width differences depend on the nucleus size as indicated in the right column of Fig. 4. To study this further, the p out per-trigger yields were split into two centrality bins in the p+Au data and the same analysis was performed. The centrality in p+A collisions is converted to values of N coll with the method in Ref. [28], where N coll is defined as the average number of nucleon-nucleon collisions in a given event class. Figure 5 shows the squared width differences in p+A and p+p collisions as a function of N coll in the two x E bins where a nonzero Gaussian width difference is observed. The values of these squared width differences are shown in Tab respectively, where the statistical and systematic uncertainties on the slopes were added in quadrature. This suggests that the interpretation of no transverse momentum broadening in p+A compared to p+p is inconsistent with the data.

IV. DISCUSSION
There are a number of different physical processes that could be contributing to the apparent broadening of the away-side nonperturbative momentum widths in p+A compared to p+p collisions, as discussed in the Introduction. The apparent lack of broadening on the nearside indicates that additional nonperturbative radiation during fragmentation in p+A is small. This may suggest that the fragmentation of the hard scattered parton into hadrons occurs outside any nuclear medium that is present; therefore, this fragmentation is similar between p+A and p+p collisions and is independent of the presence of a nucleus in the kinematic region probed by this data.
In the last decade, significant emphasis has been placed on the observation of collective effects in p+A collisions. The effects of contributions from v 2 and v 3 Fourier harmonics were studied and found to be negligible in the present analysis; this is because the Gaussian widths are almost entirely constrained by correlations in the range of ∆φ±0.2 radians around ∆φ = π. In this small ∆φ range, any modulation from collective dynamics was found to contribute on average less than 1% to the normalization of the p out correlation functions. Additionally, the correlations are collected in the midrapidity |η| < 0.35 region where the ∆η between the high p T trigger and associated particle is small and thus the jet dynamics will be dominant. For this reason, any contribution from collective dynamics can be neglected in these results.
The modification observed in this analysis is found in a similar kinematic region to where the so-called "Cronin" peak has been observed. In the x E bins where the broadened widths are observed, associated hadrons corresponding to trigger neutral pions in the range 5 < p trig T < 9 GeV/c are approximately in the range 1 < p assoc T < 2.5 GeV/c. The Cronin effect was once attributed to multiple scattering of partons within a nuclear medium; however, recent measurements revealed a particle ID dependence and have shown that additional final-state effects must also be present [18]. Additional nonperturbative initial-state partonic k T can also contribute to the Cronin peak, to which this measurement is sensitive. Nonetheless, multiple scattering interactions within the nucleus could manifest themselves as collisional energy loss or elastic scatterings leading to an angular broadening, both of which could lead to the observed away-side momentum width broadening in p+A collisions. Two-particle correlations may provide additional constraints on the underlying physical mechanism which leads to this phenomenon. Future measurements with particle identification will play an important role in identifying the cause of the Cronin peak, as a particle species dependence has been measured in d+Au [18] collisions. In Ref. [7] a strong dependence on z to the inclusive charged hadron enhancement in e+A collisions was found. In particular, the largest enhancement was found for 0.2 < z < 0.4 hadrons. Figure 6 shows the correlation between x E and z for π 0 -hadron correlations in √ s = 200 GeV p+p collisions as determined in a PYTHIA6 [36] simulation with the default tune. The correlations are determined in the Monte Carlo simulation in the same kinematic regime as the data to draw a better comparison between z and x E to this analysis. Figure 6 shows that 0.25 < x E < 0.5, where the transverse momentum broadening is observed to be the largest, corresponds approximately to a range of z covering 0.07 < z < 0.2. This is in a similar region to where Ref. [7] sees the largest inclusive hadron enhancement in e+A collisions. However, it should also be considered that the two measurements cover a much different Q 2 range, which may also be relevant in this comparison.
Nuclear PDFs can also play a role; in particular the nuclear PDFs are known to vary with the longitudinal momentum fraction of the parton probed [2,37]. These measurements are in a kinematic region that may be sensitive to the anti-shadowing region around x ≈0.1. The p out correlation functions are also sensitive to a small transverse momentum scale, and thus can also probe the transverse-momentum-dependent parton distribution functions of the nucleus. Dijet measurements, where the jets have an average p T > 4 GeV/c, have shown that there is a larger ∆φ acoplanarity in p+A compared to p+p collisions [19], indicating that there is a nuclear size dependence to initial-state partonic transverse momentum in the kinematic regime where Cronin effects may be expected to be relevant. However, the observation from the present measurement that the broadening depends on N coll could indicate that the broadening is not simply due to additional transverse momentum from the nucleus size.
The transverse momentum broadening may also be due to soft radiative energy loss within the nucleus. Energy loss in cold nuclear matter has been previously studied with the Drell-Yan process [38]. Transverse momentum broadening has also been measured to be nonzero in SIDIS interactions [39]. While the Drell-Yan measurement is only sensitive to initial-state partonic energy loss, the SIDIS measurement and the measurement presented here are sensitive to both initial and final state energy loss. Global analyses which utilize all of these data may provide further insight into the origins of the measured transverse momentum broadening in nuclear Drell-Yan, SIDIS, and p+A → dihadrons processes. The difference in p out between A+A and p+p collisions has been used to estimate the energy loss per unit length within the QGP in Au+Au collisions [23]. Given that there is an observed difference in the p out widths between p+A and p+p collisions this indicates that small energy losses have been measured in these dihadron correlations. Calculations for energy loss in a nucleus have been performed for both RHIC and Large-Hadron-Collider energies in the dijet and direct photon-hadron channel as well as in e+A collisions [40].

V. CONCLUSION
In summary, high p T dihadron correlations have been measured in √ s N N = 200 GeV p+p, p+Al, and p+Au collisions. The p out distributions are measured on the near and away side of the trigger hadron and the distributions are fit with Gaussian functions to extract the non-perturbative transverse momentum width in each system. The widths are compared across the various collision systems to search for modifications present in the nuclear collisions. No near-side modification is observed within uncertainties in the p+A collisions, indicating that intrajet radiation effects from nuclei are small in these systems. In contrast, the away-side widths are broadened in p+Au compared to p+p at moderate values of x E , while no significant modification was observed in p+Al compared to p+p. This was observed to be a function of the centrality or N coll of the p+A collision, which suggests a path length dependence to the transverse momentum broadening.
A number of different physical effects may contribute to the measured transverse momentum broadening in p+A collisions. In particular, contributions from long range correlations were systematically studied and found to be small. The correlations are constructed in a kinematic regime where "Cronin" effects are known to be large; therefore, multiple initial-state scatterings or parton recombination effects in the final state may be contributing to the broadening. The correlations are also sensitive to the partonic initial-state transverse momentum, and thus may indicate additional primordial partonic k T in nuclei when compared to a free nucleon. However, the dependence of the broadening on N coll suggests a path length dependence to hard scattered partonic energy loss, which may be due to radiative or elastic interactions with the nuclear remnants. Considering these different qualitative physics mechanisms, and the many different processes and/or observables with which they have been measured, will be an important endeavor in understanding hadronic interactions involving nuclei. Future measurements, especially at an electron-ion collider, will continue to shed light on the many physical phenomena that occur in proton-nucleus collisions.