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The properties of jets produced in p+p collisions at sqrt(s)=200 GeV are measured using the method of two particle correlations. The trigger particle is a leading particle from a large transverse momentum jet while the associated particle comes from either the same jet or the away-side jet. Analysis of the angular width of the near-side peak in the correlation function determines the jet fragmentation transverse momentum j_T . The extracted value, sqrt(<j_T^2>)= 585 +/- 6(stat) +/- 15(sys) MeV/c, is constant with respect to the trigger particle transverse momentum, and comparable to the previous lower sqrt(s) measurements. The width of the away-side peak is shown to be a convolution of j_T with the fragmentation variable, z, and the partonic transverse momentum, k_T . The is determined through a combined analysis of the measured pi^0 inclusive and associated spectra using jet fragmentation functions measured in e^+e^-. collisions. The final extracted values of k_T are then determined to also be independent of the trigger particle transverse momentum, over the range measured, with value of sqrt(<k_T^2>) = 2.68 +/- 0.07(stat) +/- 0.34(sys) GeV/c.

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... The ATLAS collaboration has measured the charged particle pull angle in tt events, showing that it is sensitive to the color flow in the process [96]. The p T of a two-particle pair is shown as a function of √ s for a variety of two-particle correlations processes [119]. . . . . . . . . . . . . . . 36 1.16 A cartoon illustrating the basic features of a dijet or dihadron twoparticle correlation measurement. . . . . . . . . . . . . . . . . . . . ...

... The solid (dashed) lines are fits to the π 0 -h ± (γ − h ± ) per-trigger yields. 118 4.7 p out per-trigger yields are constructed in pythia for 2π in azimuth and |η| < 0. 35 119 4.8 The relative error on p 2 out =3 GeV/c is shown as a red line when the quantity is extracted from the fit function in Eq. 4.1 [119]. The additional lines correspond to alternative assumptions in extracting p 2 out ; for example, with the assumption that p 2 out =p assoc T sin σ A where σ A is extracted from a Gaussian fit to the ∆φ correlation function. ...

... Twoparticle correlation measurements were first proposed as a way to measure initial-state transverse momentum during the early development of QCD [117]. Correlation measurements have since been used to measure the partonic transverse momentum k T over a large range of center-of-mass energies [118,119,120,121]. The correlations are sensitive to the initial-state k T of the colliding partons since at LO, they should emerge exactly back-to-back simply due to transverse momentum conservation; however, NLO k T effects can cause the jets to be acoplanar in the transverse plane. ...

New predictions regarding the role of color flow in high energy Quantum Chromodynamics (QCD) processes have emerged in the last decade. Novel effects due to the non-Abelian nature of QCD have been predicted and are just now accessible experimentally due to significantly improved facilities that are able to measure multidifferential observables. High energy proton-proton collisions provide a testing ground to study nonperturbative QCD in a regime where perturbative calculations should be applicable; thus theoretical tools within a perturbative framework can be used to probe and constrain nonperturbative functions and effects in QCD. In particular, the role of color flow is now being explored through many different observables throughout various subfields of QCD; one such observable is nearly back-to-back hadron correlations in proton-proton collisions which are predicted to be sensitive to states that are entangled via their QCD color charge. The PHENIX detector at the Relativistic Heavy Ion Collider (RHIC) is well suited to study potential effects from color flow. In 2013 and 2015 the PHENIX experiment recorded data from proton-proton and proton-nucleus collisions. Angular correlations between two nearly back-to-back hadrons or a direct photon and hadron are measured to study the prediction of color entanglement; this refers to a novel entangled state of the two hard-scattering partons across the colliding hadronic system. These correlations can be treated in a transverse-momentum-dependent framework where sensitivity to these non-Abelian effects from color are predicted. The measurements presented here are the first ever to search for experimental evidence of these entangled states and furthermore will help establish color flow in hadronic interactions as a new area of focus within QCD research. Results are presented for proton-proton collisions at center-of-mass energies of 200 and 510 GeV and proton-nucleus collisions at nucleon-nucleon center-of-mass energies of 200 GeV. World measurements of processes where factorization is predicted to hold are also compiled and analyzed to compare to the new experimental results presented here. The measured results, which include the first measurements of nonperturbative momentum widths in processes predicted to break factorization, do not indicate any obvious qualitative differences from observables where factorization is predicted to hold. This indicates that quantitative comparisons with phenomenological calculations will be necessary to identify the magnitude of effects from color entanglement. Future calculations will therefore have the opportunity to establish the magnitudes of non-Abelian color effects in hadronic collisions with comparisons to these results. In addition, future measurements of similar observables have the potential to further identify nontrivial effects from color interactions and color entangled states in hadronic collisions. As QCD is the only non-Abelian quantum field theory known to exist in nature that admits bound states, it will be essential to continue exploring unique QCD phenomena due to color interactions in controlled ways in the coming years.

... Following the methods of Feynman,Field and Fox [7], CCOR [8] and PHENIX [9], the k 2 T for di-hadrons is computed from Fig. 2 as: ...

... a)x h for a given p T t can be calculated from the p Ta distribution: The ratio of the away jet to the trigger jet transverse momenta,x h =p T t /p Ta , can be calculated (Fig. 5) from the away particle x h = p Ta /p T t distributions, which were also given in the STAR paper. The formula is [9], where n is the power of the p T spectra: [4] to the STAR away-side z T distributions [10] in Au+Au 0-12% centrality, and p+p, for 12 < p T t < 20 GeV/c. The Au+Au curve is a fit witĥ x AA h = 0.36 ± 0.05 with error corrected by χ 2 /dof. ...

... This is why π 0 can be used in place of the parent jet. However because the trigger π 0 spectrum for a given p T t in Au+Au for 0-10% centrality is shifted down by δ p T /p pp T = 20% in p T compared to p+p [13], the z t for A+A and compensated p+p should be calculated [9] from the measured p+p π 0 p T spectrum at p pp T t /(1 −δ p T /p pp T ). (For the present discussion, STAR measured z t = 0.80 ± 0.05 from their p+p data [10].) ...

... The ATLAS collaboration has measured the charged particle pull angle in tt events, showing that it is sensitive to the color flow in the process [96]. The p T of a two-particle pair is shown as a function of √ s for a variety of two-particle correlations processes [119]. . . . . . . . . . . . . . . 36 1.16 A cartoon illustrating the basic features of a dijet or dihadron twoparticle correlation measurement. . . . . . . . . . . . . . . . . . . . ...

... The solid (dashed) lines are fits to the π 0 -h ± (γ − h ± ) per-trigger yields. 120 4.7 p out per-trigger yields are constructed in pythia for 2π in azimuth and |η| < 0. 35 The relative error on p 2 out =3 GeV/c is shown as a red line when the quantity is extracted from the fit function in Eq. 4.1 [119]. The additional lines correspond to alternative assumptions in extracting p 2 out ; for example, with the assumption that p 2 out =p assoc T sin σ A where σ A is extracted from a Gaussian fit to the ∆φ correlation function. ...

... Twoparticle correlation measurements were first proposed as a way to measure initial-state transverse momentum during the early development of QCD [117]. Correlation measurements have since been used to measure the partonic transverse momentum k T over a large range of center-of-mass energies [118,119,120,121]. The correlations are sensitive to the initial-state k T of the colliding partons since at LO, they should emerge exactly back-to-back simply due to transverse momentum conservation; however, NLO k T effects can cause the jets to be acoplanar in the transverse plane. ...

New predictions regarding the role of color flow in high energy Quantum Chromodynamics (QCD) processes have emerged in the last decade. In particular, the role of color flow is now being explored through many different observables; one such observable is nearly back-to-back hadron correlations in proton-proton collisions which are predicted to be sensitive to states that are entangled via their QCD color charge. The PHENIX detector at the Relativistic Heavy Ion Collider is well suited to study potential effects from color flow. Angular correlations between nearly back-to-back hadrons or a direct photon-hadron are measured to study the prediction of color entanglement or factorization breaking. The correlations can be treated in a transverse-momentum-dependent framework where sensitivity to non-Abelian effects from color are predicted. These measurements are the first ever to search for experimental evidence of these entangled states and will help establish color flow in hadronic interactions as a new area of focus within QCD research. Results are presented for proton-proton collisions at center-of-mass energies of 200 and 510 GeV and proton-nucleus collisions at nucleon-nucleon center-of-mass energies of 200 GeV. World measurements of processes where factorization is predicted to hold are also compiled and analyzed to compare to the new experimental results presented here. The measured results do not indicate any obvious qualitative differences from observables where factorization is predicted to hold. This indicates that quantitative comparisons with phenomenological calculations will be necessary to identify the magnitude of effects from color entanglement. As QCD is the only non-Abelian quantum field theory known to exist in nature that admits bound states, it will be essential to continue exploring unique QCD phenomena due to color interactions in controlled ways in the coming years.

... Following the methods of Feynman,Field and Fox [7], CCOR [8] and PHENIX [9], the k 2 T for di-hadrons is computed from Fig. 2 as: ...

... a)x h for a given p T t can be calculated from the p Ta distribution: The ratio of the away jet to the trigger jet transverse momenta,x h =p T t /p Ta , can be calculated (Fig. 5) from the away particle x h = p Ta /p T t distributions, which were also given in the STAR paper. The formula is [9], where n is the power of the p T spectra: [4] to the STAR away-side z T distributions [10] in Au+Au 0-12% centrality, and p+p, for 12 < p T t < 20 GeV/c. The Au+Au curve is a fit witĥ x AA h = 0.36 ± 0.05 with error corrected by χ 2 /dof. ...

... This is why π 0 can be used in place of the parent jet. However because the trigger π 0 spectrum for a given p T t in Au+Au for 0-10% centrality is shifted down by δ p T /p pp T = 20% in p T compared to p+p [13], the z t for A+A and compensated p+p should be calculated [9] from the measured p+p π 0 p T spectrum at p pp T t /(1 −δ p T /p pp T ). (For the present discussion, STAR measured z t = 0.80 ± 0.05 from their p+p data [10].) ...

In the BDMPSZ model, the energy loss of an outgoing parton in a medium $-dE/dx$ is the transport coefficient $\hat{q}$ times $L$ the length traveled. This results in jet quenching, which is well established. However BDMPSZ also predicts an azimuthal broadening of di-jets also proportional to $\hat{q}L$ which has so far not been observed. The broadening should produce a larger $k_T$ in A$+$A than in p$+$p collisions. This presentation introduces the observation that the $k_T$ measured in p$+$p collisions for di-hadrons with $p_{Tt}$ and $p_{Ta}$ must be reduced to compensate for the energy loss of both the trigger and away parent partons when comparing to the $k_T$ measured with the same di-hadron $p_{Tt}$ and $p_{Ta}$ in A$+$A collisions. This idea is applied to a recent STAR di-hadron measurement in Au$+$Au at $\sqrt{s_{NN}}$=200 GeV, [Phys. Lett. B760 (2016) 689], with result $<{\hat{q}L}>=2.1\pm 0.6$ GeV$^2$. This is more precise but in agreement with a theoretical calculation of $<{\hat{q}L}>=14^{+42}_{-14}$ GeV$^2$ using the same data. Assuming a length $<{L}>\approx 7$ fm for central Au$+$Au collisions the present result gives $\hat{q}\approx 0.30\pm 0.09$ GeV$^2$/fm, in fair agreement with the JET collaboration result from single hadron suppression of $\hat{q}\approx 1.2\pm 0.3$ GeV$^2$/fm at an initial time $\tau_0=0.6$ fm/c in Au$+$Au collisions at $\sqrt{s_{NN}}=200$ GeV. There are several interesting details to be discussed: for a given $p_{Tt}$ the $<{\hat{q}L}>$ seems to decrease then vanish with increasing $p_{Ta}$; the di-jet spends a much longer time in the medium ($\approx 7$ fm/c) then $\tau_0=0.6$ fm/c which likely affects the value of $\hat{q}$ that would be observed.

... To have sensitivity to possible factorization breaking and modified TMD evolution effects, a particular observable must be sensitive to a small scale on the order of Λ QCD and measured over a range of hard scales. Nearly back-to-back dihadron production has long been used as a proxy for measuring initial-state partonic transverse momentum k T [45][46][47][48], which is defined in Fig. 1. First used in predictions by Ref. [49] as a method for understanding large differences in hard scattering cross sections between theory and data, nearly back-to-back twoparticle and dijet angular correlations have since been used to measure k T over a large range of center of mass energies [45,47,50,51]. ...

... Nearly back-to-back dihadron production has long been used as a proxy for measuring initial-state partonic transverse momentum k T [45][46][47][48], which is defined in Fig. 1. First used in predictions by Ref. [49] as a method for understanding large differences in hard scattering cross sections between theory and data, nearly back-to-back twoparticle and dijet angular correlations have since been used to measure k T over a large range of center of mass energies [45,47,50,51]. Direct photon-hadron correlations are of particular interest because the photon comes directly from the partonic hard scattering, and thus carries initial-state information without any final-state fragmentation effects. ...

... where p assoc T is the p T of the associated hadron and ∆φ is the azimuthal angular separation between the trigger and associated particle as shown in Fig. 1. Reference [45] has shown that the root mean square of p out and k T are related by z T k 2 T ˆ x h = 1 x h p 2 out − j 2 Ty (1 + x 2 h ) (2) ...

Dihadron and isolated direct photon-hadron angular correlations are measured in p+p collisions at s=510 GeV. Correlations of charged hadrons of 0.7<pT<10 GeV/c with π0 mesons of 4<pT<15 GeV/c or isolated direct photons of 7<pT<15 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 pout perpendicular to the axis of the trigger particle, which is the high-pT direct photon or π0. Nonperturbative evolution effects are extracted from Gaussian fits to the away-side inclusive-charged-hadron yields for different trigger-particle transverse momenta (pTtrig). The Gaussian widths and root mean square of pout are reported as a function of the interaction hard scale pTtrig to investigate possible transverse-momentum-dependent evolution differences between the π0−h± and direct photon-h± correlations and factorization breaking effects. The widths are found to decrease with pTtrig, 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.

... The determination of the required quantities is well known to older PHENIXians who have read Ref. [19] or my book [22] as outlined below: ...

... (C)x h , the ratio of the away-jet to the trigger jet transverse momenta can be measured by the away particle p Ta distribution for a given trigger particle p Tt taking x E = x h cos ∆φ ≈ x h = p Ta /p Tt [19]: The fits in Figure 36 work very well, with excellent χ 2 /dof. However, it is important to notice that the dashed curve in Au+Au does not fit the data as well as the solid red curve which is the sum of Equation (6) with free parameters + a second term with the form of Equation (6) but with thex h fixed at the p+p value. ...

Results from Relativistic Heavy Ion Collider Physics in 2018 and plans for the future at Brookhaven National Laboratory are presented.

... The correlations are constructed similarly to previous PHENIX two-particle correlation analyses; see, e.g., Refs. [31][32][33]. 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/dφ 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. ...

... However, the away-side correlations are sensitive to both initial and final-state transverse momentum. Because the initialstate k T is much larger than final-state j T (see, e.g., [31,32]), 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. ...

The PHENIX collaboration has measured high-pT dihadron correlations in p+p, p+Al, and p+Au collisions at sNN=200 GeV. The correlations arise from inter- and intrajet correlations and thus have sensitivity to nonperturbative effects in both the initial and final states. The distributions of pout, the transverse-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 widths, sensitive to fragmentation transverse momentum, show no significant broadening between p+Au, p+Al, and p+p. The away-side nonperturbative pout 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 pout broadening is a function of Ncoll, the number of binary nucleon-nucleon collisions, in the interaction. The potential implications of these results with regard to initial- and final-state transverse-momentum broadening and energy loss of partons in a nucleus, among other nuclear effects, are discussed.

... Previously j T has been measured for example by correlating the particles inside a jet cone with the reconstructed jet axis [1, 2, 3] or by calculating it from the azimuthal correlation function [4]. Only one component for j T is extracted in these studies, describing the whole time evolution of the jet. ...

... Based on earlier results [1, 4] the hadronization component is expected to be universal, meaning that it is √ s independent and that similar jets in different p Tt (same x bin) give the same j 2 T results. It can be seen from Figure 5that the narrow component results show a flat trend as a function of p Tt and that there is no difference between results from pp and p–Pb data. ...

QCD color coherence phenomena, like angular ordering, can be studied by looking at jet fragmentation. As the jet is fragmenting, it is expected to go through two different phases. First, there is QCD branching that is calculable in perturbative QCD. Next, the produced partons hadronize in a non-perturbative way later in a hadronization process. The jet fragmentation can be studied using the method of two particle correlations. A useful observable is the jet transverse fragmentation momentum $j_{\mathrm{T}}$, which describes the angular width of the jet. In this contribution, a differential study will be presented in which separate $j_{\mathrm{T}}$ components for branching and hadronization will be distinguished from the data measured by the ALICE experiment. The $p_{\mathrm{Tt}}$ dependence of the hadronization component $\sqrt{\left<j_{\mathrm{T}}^{2}\right>}$ is found to be rather flat, which is consistent with universal hadronization assumption. However, the branching component shows slightly rising trend in $p_{\mathrm{Tt}}$. The $\sqrt{s} = 7\,\mathrm{TeV}$ pp and $\sqrt{s_{\mathrm{NN}}} = 5.02\,\mathrm{TeV}$ p-Pb data give the same results within error bars, suggesting that this observable is not affected by cold nuclear matter effects in p-Pb collisions. The measured data will also be compared to the results obtained from PYTHIA8 simulations.

... As known, two-particle correlations were intensively used in the past at study of particles and jets in high energy physics (see, for example, [296][297][298][299][300]). At the present time, there are well developed methods of jet recognition [301,302] and analysis of thier properties. ...

This paper contains suggestions for experiments with usage of the Spin Physics Detector (SPD) at the first stage of the SPD NICA Programme developing at JINR. Double polarized pp-, dd- and pd- collisions at c.m.s. NN energies of 3.4-10 GeV, which will be accessible at the initial stage of experiments, allow one to study spin dependence of the NN interaction, search for multiquark states at double strangeness, charm and beauty thresholds, study the short-range structure of the deuteron. Double polarized pd scattering offer a possibility to test the Standard Model through the search for T-invariance violation.

... In PHENIX, a lot of jet properties from di-hadron correlation in p + p collisions have been studied [61]. The sum of transverse momentum of two leading hadrons from two jets statistically (may not be in event-by-event basis) carries the information of k ⊥ , which is defined as q t as shown in Figure 2.6. ...

The spin structure of the proton has been revealed to be extremely complex. The proton spin is composed of the spins and the orbital angular momenta of quarks and gluons in the proton. The first results from polarized deep inelastic scattering (pDIS) experiments in the late 1980s and early 1990s revealed that quarks do not carry a significant fraction of the proton's spin. The recent global analysis on gluon spin including RHIC results showed that gluons have a very small contribution on the spin of proton. Therefore, it is extremely important for physicists understanding the contribution from the orbital angular momenta of quarks and gluons. However, it is very difficult for the current experiments measuring the orbital angular momentum directly and accurately. The Sivers-type single transverse spin asymmetry provides us a window to study the orbital angular momentum. In this thesis, results for the single transverse spin asymmetry of forward charged hadrons in polarized proton collisions measured with the PHENIX detector are presented. A predicted sizable asymmetry has been observed which is consistent with the results from other experiments. A correlation between neutral pions and charged hadrons measured in the central region of the PHENIX detector has been used to extract the single transverse spin asymmetry due to the Sivers effect. The Sivers effect describes the relation of the proton's spin and its intrinsic transverse momentum. The latter one has been thought to originate from the orbital angular momentum of proton.

Dihadron and isolated direct photon-hadron angular correlations are measured in
p
+
p
collisions at
√
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
Δ
ϕ
∼
π
. To have sensitivity to small transverse momentum scales, nonperturbative momentum widths of
p
out
, the out-of-plane transverse-momentum component perpendicular to the trigger particle, are measured. In this region, the evolution of
p
out
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
√
s
=
510
GeV
. The nonperturbative jet widths also appear to increase with
√
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

Di-hadron correlations in proton-proton collisions at are interpreted in terms of a fragmentation width and a momentum imbalance. A fragmentation width of 580±50 GeV/c is obtained, and the momentum imbalance gives an ‘intrinsic’ transverse momentum width of partons in the proton of 2.6±0.2 GeV/c.

The access to LHC energies in heavy-ion collisions will shed light on a completely unexplored regime of QCD. The study of jets provides the natural ground to investigate the medium formed in such collisions. We review some of the new ideas stimulated by the RHIC experimental data and their relevance to the future LHC program.

We present measurements from events with two isolated prompt photons in [ital [bar p]p] collisions at [radical][ital s] =1.8 TeV. The differential cross section, measured as a function of transverse momentum ([ital P][sub [ital T]]) of each photon, is about 3 times what next-to-leading-order QCD calculations predict. The cross section for photons with [ital P][sub [ital T]] in the range 10--19 GeV is 86[plus minus]27(stat)[sub [minus]23][sup +32](syst) pb. We also study the correlation between the two photons in both azimuthal angle and [ital P][sub [ital T]]. The magnitude of the vector sum of the transverse momenta of both photons, [ital K][sub [ital T]]=[vert bar][bold P][sub [ital T]1]+[bold P][sub [ital T]2][vert bar], has a mean value of [l angle][ital K][sub [ital T]][r angle]=5.1[plus minus]1.1 GeV.

The theoretical framework for describing the production of direct
photons in hadronic collisions is reviewed. A detailed comparison
between the theoretical predictions and existing data is presented along
with a critical evaluation of the various sources of theoretical
uncertainty. The information available from direct-photon experiments is
contrasted with that learned from jet or single-hadron production.
Prospects for new types of measurements in future experiments are also
presented.

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