# Nonperturbative-transverse-momentum broadening in dihadron angular correlations in √sNN=200 GeV proton-nucleus collisions

August 27, 2019
###### Abstract

The PHENIX collaboration has measured high- dihadron correlations in , Al, and Au collisions at 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 , 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 , the longitudinal momentum fraction of the associated hadron with respect to the trigger hadron. The near-side momentum widths, sensitive to fragmentation transverse momentum, show no significant broadening between Au, Al, and . The away-side nonperturbative momentum widths are found to be broadened in Au when compared to ; however, there is no significant broadening in Al compared to collisions. The data also suggest that the away-side transverse momentum broadening is a function of , 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.

PHENIX Collaboration

## 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 (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 Adcox et al. (2005). However, measurements in 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 Hen et al. (2017); Chatrchyan et al. (2013); Cronin et al. (1975); Adcox et al. (2002).

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. Hen et al. (2017) 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 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 hadrons are suppressed in electron-nucleus relative to electron-deuterium collisions Airapetian et al. (2003), where 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 Airapetian et al. (2007). 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 Airapetian et al. (2003, 2007).

Another unexpected physical effect in A collisions is the so-called “Cronin” effect, which refers to an enhancement in the inclusive hadron spectrum with respect to collisions at moderate of approximately GeV/ which persists over a wide range of center-of-mass energies Cronin et al. (1975); Adler et al. (2003a); Aad et al. (2016b). This effect has also been observed at moderate in electron-nucleus collisions Airapetian et al. (2003), where a significant dependence of the enhancement on the longitudinal momentum fraction of the hadron was found Airapetian et al. (2007). 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 Adare et al. (2013). Additional measurements that go beyond single inclusive hadrons may be able to shed further light on this phenomenon in 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 Corcoran et al. (1991), which has not been observed at large jet transverse momentum Adam et al. (2015).

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 , Al, and 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 = 200 GeV A collisions. High two-particle angular correlations have been theoretically considered as a probe for energy loss in A and A+A collisions via their transverse momentum broadening Baier et al. (1997, 2000); Tannenbaum (2017); 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 Adcox et al. (2003a) at RHIC collected data from , Al, and Au collisions at  GeV. A total minimum bias integrated luminosity of 60, 0.69, and 0.21 pb for , Al, and Au, respectively, was used for the analysis of dihadron correlations. From these total integrated luminosities, data quality assurance and collision vertex position cm cuts were applied. The PHENIX detector measures two-particle angular correlations of neutral pions and charged hadrons, -h, with its electromagnetic calorimeter (EMCal) and drift chamber (DC) and pad chamber (PC) tracking system. These central arms cover an azimuthal range of   radians and a pseudorapidity range of . Detailed descriptions of the PHENIX central arms can be found in Refs. Adcox et al. (2003b); Aphecetche et al. (2003). In A collisions, the centrality class is determined with the forward beam-beam counters (BBCs) Ikematsu et al. (1998), where the centrality percentiles are defined by the multiplicity measured in the nucleus-going BBC following the procedure in Ref. Adare et al. (2014).

The EMCal is used to identify high neutral pions to construct the correlation functions. A high-energy-photon trigger is used to identify events with a high photon from a 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 EMCal allows reconstruction up to approximately 20 GeV in this channel. In this analysis neutral pions are collected in the range GeV/.

The DC and PC tracking system measures nonidentified charged hadrons in the event with the triggered high 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-imaging erenkov 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 identification. Nonidentified charged hadrons are collected between GeV/ in correlation with the high .

The correlations are constructed similarly to previous PHENIX two-particle correlation analyses, see e.g. Refs. Adler et al. (2006); Adare et al. (2010); Aidala et al. . Per-trigger yields are constructed for a given observable, such as , which show the yield of charged hadrons per-trigger and are defined by

 1NtrigdNdΔϕ=1NtrigdN/dΔϕrawdN/dΔϕmixedϵ(pT) (1)

To account for the PHENIX acceptance, the raw correlations are divided by a mixed-event background correlation function, . 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 in Eq. 1, which is determined with a single particle Monte Carlo generator as well as a full GEANT description of the PHENIX apparatus Adler et al. (2003b). 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 .

Correlation functions are typically constructed in terms of the azimuthal angle between the trigger and associated particle. Here we choose to construct the correlations as a function of the momentum space vector component and , defined as

 pout=|passocT|sinΔϕ (2)

and

 xE=−ptrigT⋅passocT|ptrigT|2=−|passocT||ptrigT|cosΔϕ. (3)

The quantities and give the transverse momentum component and longitudinal momentum fraction, respectively, of the associated hadron with respect to the trigger . These quantities are schematically diagrammed in Fig. 1, where the Figure shows a two-particle correlation in the transverse plane and quantities in bold represent vectors. In this diagram, two hadrons (black vectors) fragment from two high partons (red vectors) from a two-to-two partonic scattering. The partons are originally acoplanar due to their initial-state transverse momenta (); the two hadrons may acquire additional acoplanarity due to final-state transverse momentum () during the fragmentation process. In the diagram the final-state transverse momentum is perpendicular to the parton axis and denoted as and , which are assumed to be Gaussian such that . The quantity can be nonzero because of these transverse momentum contributions, while is a proxy for the momentum fraction that the final-state hadron carries with respect to the parton. In the figure, is shown multiplied by to explicitly show the comparison between and . When is small, the two-particle correlation is nearly back-to-back and the acoplanarity is generated by nonperturbative and  Aidala et al. ; Adare et al. (2017). Additional nonperturbative interactions within the nucleus may contribute to this quantity in 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 correlation functions as described in Ref. Adare et al. (2017); 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 based on the fit results. This uncertainty varies from less than 1% at small to several percent at large 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 are shown in several bins of in Fig. 2. The per-trigger yields for Au and collisions are shown as open and filled points, respectively. A transition from nonperturbative behavior in the nearly back-to-back 0 ( ) region to perturbative next-to-leading order behavior at larger can be seen at varying values of , depending on the bin. This change in shape is highlighted by Gaussian fits to the small region, drawn in Fig. 2 as dotted and solid lines for Au and , respectively. The fit ranges vary depending on the bin as the nonperturbative region is a function of and thus  Aidala et al. . The fit ranges are chosen to give the best /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 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 are shown in several bins of 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 inter-jet correlations, respectively. In particular, the near-side correlations are only sensitive to fragmentation transverse momentum, because the and hadron are fragmented from the same hard parton. However, the away-side correlations are sensitive to both initial and final state transverse momentum. Because the initial-state is much larger than final-state (see e.g. Adler et al. (2006); Adare et al. (2010)), this leads to a broader 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 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 distributions. Systematic uncertainties on the Gaussian widths are estimated by increasing the fit range by 0.2 GeV/ in and taking the absolute value of the difference of the resulting Gaussian width. To study any modification in A compared to collisions the squared width difference is determined between the A and Gaussian widths, mathematically defined as . These differences are shown in Fig. 4 as a function of for the near and away side correlation functions, for both Al and Au collisions. The near-side width differences in the left column of Fig. 4 show no significant modification within uncertainties between both Al or Au and collisions at all values of . Similar results have been seen in dihadron correlations Viinikainen (2017) and fragmentation function studies with full jet reconstruction Aaboud et al. (2018) in Pb collisions. However, the away-side width differences in Au and collisions show modification as seen in the bottom-right panel of Fig. 4. There is no significant away-side broadening between Al and 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 per-trigger yields were split into two centrality bins in the Au data and the same analysis was performed. The centrality in A collisions is converted to values of with the method in Ref. Adare et al. (2014), where is defined as the average number of nucleon-nucleon collisions in a given event class. Figure 5 shows the squared width differences in A and collisions as a function of in the two bins where a nonzero Gaussian width difference is observed. The values of these squared width differences are shown in Tab. 1. The data are fit with linear functions which are shown on the figure and indicate that the squared width differences exhibit a positive correlation with . The slopes of the fits were found to be  (stat)  (sys) and 0.015  (stat)  (sys) for the smaller and larger bins, respectively. When the data is fit to a constant of 0, the per number of degree of freedom becomes approximately 5 for and approximately 8 for . The measured slopes differ from a slope of 0 with p values of approximately 0.055 and 0.01, for the smaller and larger bin 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 A compared to 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 A compared to collisions, as discussed in the Introduction. The apparent lack of broadening on the near-side indicates that additional nonperturbative radiation during fragmentation in 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 A and 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 A collisions. The effects of contributions from and 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 radians around . In this small range, any modulation from collective dynamics was found to contribute on average less than 1% to the normalization of the correlation functions. Additionally, the correlations are collected in the midrapidity region where the between the high 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.

In Ref. Airapetian et al. (2007) a strong dependence on to the inclusive charged hadron enhancement in collisions was found. In particular, the largest enhancement was found for hadrons. Figure 6 shows the correlation between and for -hadron correlations in = 200 GeV collisions as determined in a PYTHIA6 Sjostrand et al. 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 and to this analysis. Figure 6 shows that , where the transverse momentum broadening is observed to be the largest, corresponds approximately to a range of covering . This is in a similar region to where Ref. Airapetian et al. (2007) sees the largest inclusive hadron enhancement in collisions. However, it should also be considered that the two measurements cover a much different 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 Geesaman et al. (1995); Hen et al. (2017). These measurements are in a kinematic region that may be sensitive to the anti-shadowing region around 0.1. The 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 GeV/, have shown that there is a larger acoplanarity in A compared to collisions Corcoran et al. (1991), 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 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 Vasilev et al. (1999). Transverse momentum broadening has also been measured to be nonzero in SIDIS interactions Airapetian et al. (2010). 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 A  dihadrons processes. The difference in between A+A and collisions has been used to estimate the energy loss per unit length within the QGP in AuAu collisions Tannenbaum (2017). Given that there is an observed difference in the widths between A and 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 collisions Xing et al. (2012).

## V Conclusion

In summary, high dihadron correlations have been measured in  GeV , Al, and Au collisions. The distributions are measured on the near and away side of the trigger hadron and the distributions are fit with Gaussian functions to extract the nonperturbative 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 A collisions, indicating that intra-jet radiation effects from nuclei are small in these systems. In contrast, the away-side widths are broadened in Au compared to at moderate values of , while no significant modification was observed in Al compared to . This was observed to be a function of the centrality or of the 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 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 in nuclei when compared to a free nucleon. However, the dependence of the broadening on 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.

###### Acknowledgements.
We thank the staff of the Collider-Accelerator and Physics Departments at Brookhaven National Laboratory and the staff of the other PHENIX participating institutions for their vital contributions. We acknowledge support from the Office of Nuclear Physics in the Office of Science of the Department of Energy, the National Science Foundation, Abilene Christian University Research Council, Research Foundation of SUNY, and Dean of the College of Arts and Sciences, Vanderbilt University (U.S.A), Ministry of Education, Culture, Sports, Science, and Technology and the Japan Society for the Promotion of Science (Japan), Conselho Nacional de Desenvolvimento Científico e Tecnológico and Fundação de Amparo à Pesquisa do Estado de São Paulo (Brazil), Natural Science Foundation of China (People’s Republic of China), Croatian Science Foundation and Ministry of Science and Education (Croatia), Ministry of Education, Youth and Sports (Czech Republic), Centre National de la Recherche Scientifique, Commissariat à l’Énergie Atomique, and Institut National de Physique Nucléaire et de Physique des Particules (France), Bundesministerium für Bildung und Forschung, Deutscher Akademischer Austausch Dienst, and Alexander von Humboldt Stiftung (Germany), J. Bolyai Research Scholarship, EFOP, the New National Excellence Program (ÚNKP), NKFIH, and OTKA (Hungary), Department of Atomic Energy and Department of Science and Technology (India), Israel Science Foundation (Israel), Basic Science Research Program through NRF of the Ministry of Education (Korea), Physics Department, Lahore University of Management Sciences (Pakistan), Ministry of Education and Science, Russian Academy of Sciences, Federal Agency of Atomic Energy (Russia), VR and Wallenberg Foundation (Sweden), the U.S. Civilian Research and Development Foundation for the Independent States of the Former Soviet Union, the Hungarian American Enterprise Scholarship Fund, the US-Hungarian Fulbright Foundation, and the US-Israel Binational Science Foundation.

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