document: the hadronic final state of  collisions at 200 gev may provide a reference for other high - energy nuclear collisions at the relativistic heavy ion collider ( rhic ) and large hadron collider ( lhc ) . 
   claims for novel physics at higher energies or in ,  or   collision systems should be based on an accurate and self - consistent phenomenology for conventional  processes at 200 gev . however , current theoretical and experimental descriptions of high - energy  collisions appear to be incomplete . 
   several unresolved aspects of  collisions are notable : ( a ) the role of  collision centrality in relation to the low-@xmath3 gluon transverse structure of the proton  @xcite , ( b ) the nature and systematics of the  _ underlying event _ ( ue ) defined as complementary to contributions from an event - wise - triggered high - energy dijet  @xcite , ( c ) the systematics of _ minimum - bias _ 
   ( mb ) dijet ( minijet ) production manifested in  spectra and angular correlations  @xcite and ( d ) possible existence and phenomenology of a _ nonjet azimuth quadrupole _ component in  2d angular correlations previously studied in   collisions ( as quantity @xmath4 )  @xcite , especially in connection with a claimed same - side ridge observed in lhc  angular correlations  @xcite . 
   a more detailed discussion of those issues is presented in sec . 
   [ issues ] .    in the present study 
   we establish a more complete mathematical model for  phenomenology based on the @xmath5 dependence of single - particle ( sp ) @xmath6 spectra and -integral @xmath2 densities and -integral 2d angular correlations . 
   we confront several issues : is there any connection between @xmath5 and  centrality ? is  centrality a relevant concept ? 
   a nonjet ( nj ) quadrupole component in   collisions is the complement to jet - related and projectile - fragment correlations . 
   is there an equivalent phenomenon in  collisions , and what might a  nj quadrupole component reveal about  centrality or ue structure ? 
   the  phenomenological model should offer a conceptual context with two manifestations : ( a ) as a mathematical framework to represent  data systematics efficiently , and ( b ) as a theoretical framework to provide physical interpretation of model elements via comparisons between data structures and qcd theory . 
   preliminary responses to such questions were presented in ref . 
   they are supplemented here by new  sp density and 2d angular - correlation measurements . 
   we emphasize the @xmath5 dependence of angular correlations from  collisions , extending the  two - component model ( tcm ) to include a nj quadrupole component previously extrapolated from measurements in  collisions  @xcite and now obtained directly from  2d angular correlations . 
   we establish @xmath5-dependent phenomenology for soft ( projectile proton dissociation ) , hard ( parton fragmentation to mb dijets ) and nj quadrupole components in a _ 
   three_-component model and explore possible correspondence with  centrality , ue structure , dijet production and the partonic structure of projectile protons . 
   we also present a tcm for the  systematics of hadron densities on pseudorapidity @xmath2 . 
   this article is arranged as follows : section  [ issues ] summarizes open issues for  collisions . 
   section  [ methods ] reviews analysis methods for two - particle correlations . 
   section  [ pptcm ] describes a two - component model for hadron production in  collisions . 
   section  [ ppangcorr ] presents measured 2d angular correlations for 200 gev  collisions . 
   section  [ modelfits ] summarizes the parametric results of 2d model fits to those  correlation data . 
   section  [ jetcorr1 ] describes jet - related data systematics . 
   section  [ njcorr ] describes nonjet data systematics . 
   section  [ etadensity ] presents a two - component model for @xmath2 densities and the @xmath2-acceptance dependence of transverse - rapidity  spectra . 
   section  [ syserr ] discusses systematic uncertainties . 
   section  [ ridgecms ] reviews  same - side `` ridge '' properties and a proposed mechanism . 
   sections  [ disc ] and  [ summ ] present discussion and summary . 
   we present a summary of issues introduced in sec . 
   i including  centrality in relation to a conjectured underlying event , manifestations of mb dijets in spectra and correlations and existence and interpretation of a nj quadrupole component of  2d angular correlations . 
   item ( a ) of sec . 
   [ intro ] relates to interpretations of deep - inelastic scattering ( dis ) data to indicate that low-@xmath3 gluons are concentrated within a transverse region of the proton substantially smaller than its overall size . 
   it is argued that a high-@xmath6 dijet trigger may select more - central  collisions with greater soft - hadron production  @xcite . 
   the soft ( nonjet ) multiplicity increase should be observed most clearly within a narrow azimuth _ transverse region _ ( tr ) centered at @xmath8 and thought to _ exclude contributions from the triggered jets _ centered at 0 and @xmath9 . 
   item ( b ) relates to measurements of charge multiplicity @xmath10 within the tr vs trigger condition @xmath11 and @xmath12 spectra employed to characterize the ue  @xcite . 
   substantial increase of @xmath10 with higher @xmath11 relative to a minimum - bias or non - single - diffractive ( nsd ) value is interpreted to reveal novel contributions to the ue , including _ multiple parton interactions _ ( mpi ) corresponding to a high rate of dijet production  @xcite . 
   monte carlo  collision models such as pythia  @xcite are tuned to accommodate such results  @xcite .    in ref . 
   @xcite items ( a ) and ( b ) were considered in the context of a two - component ( soft+hard ) model ( tcm ) of hadron production as manifested in yields and spectra . 
   it was observed that imposing a  trigger condition on events does lead to selection for _ hard events _ ( containing at least one dijet ) but that the soft component of the selected events is not significantly different from a mb event sample , in contrast to expectations from ref . 
   @xcite that increased dijet frequency should correspond to more - central  collisions and therefore to a larger soft component from low-@xmath3 gluons . 
   since  apparently determines dijet rates directly  @xcite it might also control  centrality , but ref . 
   @xcite concluded that further  correlation measurements are required to explore that possibility . 
   the present study responds with the  dependence of mb dijet correlations and nj quadrupole systematics that speak to the issue of  centrality and ue systematics . 
   item ( c ) relates to the role of mb dijets in yields , spectra and various types of two - particle correlations . 
   the contribution of mb dijets ( minijets  @xcite ) to sp  spectra was established in refs . 
   @xcite , and the contribution of minijets to 2d angular correlations was identified in refs . 
   however , further effort is required to establish a complete and self - consistent description of mb dijets in  and   yields , spectra and correlations .    in ref . 
   @xcite item ( c ) was addressed with 2d model fits applied to angular correlations from  collisions at 62 and 200 gev to isolate several correlation components , including structures attributed to mb dijets and a nj quadrupole , with emphasis on the former in that study . 
   the systematics of two components ( soft + hard ) are consistent with the tcm . 
   the dijet ( hard - component ) trend on centrality exhibits a _ sharp transition _ near 50% fractional cross section below which  collisions appear to be simple linear superpositions of  binary collisions ( transparency ) and above which _ quantitative _ changes in the dijet component appear , but not in the nj quadrupole component  @xcite . the mb dijet interpretation has been questioned variously , for more - central   collisions  @xcite or for all nuclear collisions  @xcite . 
   we wish to confirm the role of mb dijets as such via a self - consistent description of  _ and _  collisions based on qcd theory . 
   although a tcm for  yields and spectra vs  has been established  @xcite the systematics of mb dijet production in  collisions is incomplete . 
   mb 2d angular correlations for  collisions have been decomposed into soft and hard components via a single  cut ( at 0.5 gev / c )  @xcite , but a tcm for  angular correlations vs  has not been available . in ref . 
   @xcite  mb jet - related correlation structure vs centrality was related quantitatively to spectrum hard components ( dijets ) to establish a direct link of both data formats with pqcd predictions . in the present study 
   we carry out a similar analysis of  vs   trends . 
   we also extend the  tcm established on marginal   to the 2d @xmath13 system to determine the distribution of minijets on the full sp momentum space . 
   the extension to @xmath2 may provide further evidence that a mb dijet interpretation of the inferred tcm hard component is _ necessary _ as a distinct element of hadron production . 
   item ( d ) relates to the possibility of a significant amplitude for a unique azimuth quadrupole in  collisions . 
   ( the nj quadrupole should be distinguished from the quadrupole component of a _ jet - related _ 
   2d peak projected onto 1d azimuth . ) 
   measurements of a nj quadrupole component of angular correlations in  collisions ( conventionally represented by parameter @xmath4 ) are found to be consistent with a simple universal trend on centrality and collision energy extrapolating to a nonzero value for  collisions  @xcite . 
   the extrapolation is consistent with a qcd - theory prediction for @xmath4 in  collisions  @xcite . 
   the  nj quadrupole may be related to a same - side `` ridge '' reported in  collisions at 7 tev ( with special cuts on  and  imposed )  @xcite . 
   it has been suggested that the  same - side ridge arises from the same mechanism proposed for   collisions based on collective motion ( flows ) coupled to initial - state collision geometry . 
   systematics of a possible nj quadrupole in  collisions have thus emerged as an important new topic . 
   reference  @xcite considered extrapolation of nj quadrupole centrality systematics in 200 gev  collisions to  collisions , and further extrapolation to lhc energies based on measured rhic energy dependence . 
   in that scenario the same - side ridge observed in lhc  collisions corresponds to one lobe of the nj quadrupole . 
   the other lobe is obscured by the presence of a dominant away - side ( as ) 1d jet peak . 
   quantitative correspondence was observed in ref . 
   @xcite suggesting that the nj quadrupole may play a significant role in  collisions , but no direct  quadrupole measurements existed . 
   this study offers a response to that issue . 
   measurement of nj quadrupole trends may shed light on the question of  centrality [ item ( a ) ] by analogy with   quadrupole systematics wherein the nj quadrupole measured by a _ per - particle _ 
   variable first increases rapidly with centrality and then falls sharply toward zero with decreasing   eccentricity , as described by a glauber model based on the eikonal approximation . since dijet production vs  in  collisions suggests that the eikonal approximation is not valid for that system  @xcite the nj quadrupole trend could provide a critical test of the eikonal assumption for  collisions . 
   we review technical aspects of two - particle angular - correlation analysis methods applied to  collisions at the rhic . 
   further method details appear in refs . 
   @xcite . 
   high - energy nuclear collisions produce final - state hadrons as a distribution within cylindrical 3d momentum space @xmath14 , where @xmath6 is transverse momentum , @xmath2 is pseudorapidity and @xmath15 is azimuth angle . 
   transverse mass is @xmath16 with hadron mass @xmath17 . 
   pseudorapidity is @xmath18 $ ] ( @xmath19 is polar angle relative to collision axis @xmath20 ) , and @xmath21 near @xmath22 . to improve visual access to low-@xmath6 structure and 
   simplify description of the -spectrum hard component ( defined below ) we present spectra on transverse rapidity @xmath23 $ ] . for unidentified hadrons @xmath1 , with pion 
   mass assumed ( about 80% of hadrons ) , serves as a regularized logarithmic @xmath6 measure . a typical detector acceptance @xmath24 gev / c corresponds to @xmath25 . 
   correlations are observed in two - particle momentum space @xmath26 . 
   autocorrelation _ on angular subspace @xmath27 ( where @xmath28 or @xmath15 ) is derived by averaging pair density @xmath29 along diagonals on @xmath27 parallel to the sum axis @xmath30  @xcite . 
   the averaged pair density @xmath31 on defined _ difference variable _ 
   @xmath32 is then an autocorrelation . 
   the notation @xmath33 rather than @xmath34 for difference variables is adopted to conform with mathematical notation conventions and to retain @xmath34 as a measure of a detector acceptance on parameter @xmath3 . 
   for correlation structure approximately independent of @xmath35 over some limited acceptance @xmath34 ( stationarity , typical over @xmath36 azimuth and within some limited pseudorapidity acceptance @xmath37 ) angular correlations remain undistorted ( no information is lost in the projection by averaging ) . 
   -integral 2d angular autocorrelations are thus lossless projections of 6d two - particle momentum space onto angle difference axes @xmath38 . 
   the @xmath39 axis is divided into _ same - side _ ( ss , @xmath40 ) and _ away - side _ ( as , @xmath41 ) intervals .      for collisions between two composite projectiles the collision final state ( fs ) may depend on the transverse separation of the collision partners ( impact parameter @xmath42 ) and the phase - space distribution of constituents within each projectile , 
   collectively the initial - state ( is ) geometry . 
   we wish to determine how the is geometry relates to an observable derived from fs hadrons and how the is influences fs hadron yields , spectra and correlations .    for a - a collisions 
   the projectile constituents are nucleons @xmath43 all sharing a common lab velocity ( modulo fermi motion ) and distributed over a nuclear volume . 
   based on a glauber model of   collisions ( assuming the eikonal approximation ) nucleons are classified as participants ( total number @xmath44 ) or spectators , and the mean number of  binary encounters @xmath45 is estimated . 
   the relation @xmath46 is a consequence of the eikonal approximation . 
   parameters @xmath44 and @xmath45 , depending on   impact parameter @xmath42 , are in turn related to macroscopic fs observable  within some angular acceptance via the mb cross - section distribution @xmath47 .    for  collisions 
   the constituents are partons distributed on the transverse configuration space of projectile protons _ and _ on longitudinal - momentum fraction @xmath3 ( fraction of proton momentum carried by a parton ) . 
   one could apply a similar glauber approach to  is geometry , including assumed eikonal approximation as in the   description ( e.g.  default pythia  @xcite ) . as noted in the introduction , 
   it is conjectured that imposing a dijet trigger should favor more - central  collisions and therefore a substantial increase in soft - hadron production from low-@xmath3 gluons  @xcite 
   . however , some aspects of  collision data appear to be inconsistent with such a description , specifically parton transverse position and a  impact parameter . 
   nevertheless , fs measures for number of participant low-@xmath3 partons and their binary encounters may be relevant and experimentally accessible  @xcite . 
   @xmath49 represents a basic pair density on 6d pair momentum space . 
   the event - ensemble - averaged pair density @xmath50 derived from sibling pairs ( pairs drawn from single events ) includes the correlation structures to be measured . 
   @xmath51 is a density of mixed pairs drawn from different but similar events . 
   @xmath52 denotes a minimally - correlated reference - pair density derived from ( a ) a mixed - pair density or ( b ) a cartesian product of sp angular densities @xmath53 via a factorization assumption . 
   differential correlation structure is determined by comparing a sibling - pair density to a reference - pair density in the form of difference @xmath54 representing a correlated - pair density or _ covariance _ density . _ per - particle 
   _ measure @xmath55 has the form of pearson s normalized covariance  @xcite wherein the numerator is a covariance and the denominator is approximately the geometric mean of marginal variances . in the poisson limit a marginal variance may correspond to @xmath56 . since @xmath57 it follows that the geometric mean of variances is given by @xmath58 and the normalized covariance density is a per - particle measure  @xcite . 
   the number of final - state charged hadrons @xmath59 in the denominator can be seen as a place holder . 
   other particle degrees of freedom may be more appropriate for various physical mechanisms ( e.g.  number of participant nucleons in   collisions , number of participant low-@xmath3 partons in  collisions ) as described below . 
   we define @xmath60 where pair ratio @xmath61 cancels instrumental effects . that per - particle measure is not based on a physical model . in some analyses 
   a correlation amplitude is defined as @xmath62 with @xmath63  @xcite , but such an amplitude then relies on a specific detector acceptance , is not `` portable . '' 
   to assess the relation of data to is geometry we convert per - charged - hadron model - fit results to @xmath64 $ ] , the quantity in square brackets representing the _ number of correlated pairs _ within the detector acceptance . for this  analysis 
   we assume the soft - component density @xmath65 is an estimator for  is @xmath66 ( low-@xmath3 parton participants ) . 
   given the simplified notation @xmath67 we plot @xmath68 to convert `` per - particle '' from fs hadrons to is low-@xmath3 partons and obtain a more interpretable  per - particle measure . 
   correlations on two - particle momentum space @xmath69 can be factorized into distributions on 2d transverse - momentum space @xmath70 or transverse - rapidity space @xmath71  @xcite and on 4d angle space @xmath72 reducible with negligible information loss to autocorrelations on difference variables @xmath38  @xcite . in this study 
   we focus on minimum - bias ( @xmath1-integral ) 2d angular correlations . 
   each of the several features appearing in  2d angular correlations ( a correlation _ component _ ) can be modeled within acceptance @xmath37 by a simple functional form ( a model _ element _ ) , including 1d and 2d gaussians and azimuth sinusoids uniform on @xmath73 . 
   the cosine elements @xmath74 represent _ cylindrical multipoles _ with pole number @xmath75 , e.g. , dipole , quadrupole and sextupole for @xmath76 . 
   angular correlations can be formed separately for like - sign ( ls ) and unlike - sign ( us ) charge combinations , as well as for charge - independent ( ci = ls + us ) and charge - dependent ( cd = ls @xmath77 us ) combinations  @xcite . 
   the azimuth quadrupole ( @xmath78 fourier ) component is a prominent feature of   angular correlations , represented there by symbol @xmath79 . 
   the mean value is nominally relative to an estimated   reaction plane  @xcite . 
   @xmath4 data are conventionally interpreted to represent elliptic flow , a hydrodynamic ( hydro ) response to is asymmetry in non - central   collisions  @xcite .    if 2d angular correlations are projected onto 1d azimuth _ 
   any _ resulting distribution can be expressed exactly in terms of a fourier series . 
   the density of correlated pairs is then [ nf ] ( _ ) & = & |_sib - _ ref = v_0 ^ 2 + 2_m=1^ v_m^2 ( m _ ) , defining the _ power - spectrum _ 
   elements @xmath80 of autocorrelation density @xmath81 . 
   the corresponding _ per - pair _ correlation measure is the ratio & = & v_0 ^ 2 + 2_m=1^v_m^2 ( m _ ) .    some fourier amplitudes from analysis of 1d azimuth projections may include contributions from more than one mechanism . 
   for example , @xmath4 data from conventional 1d analysis may include contributions from jet - related ( `` nonflow '' ) as well as nj ( `` flow '' ) mechanisms  @xcite . 
   in contrast , a complete model of 2d angular correlations _ with @xmath73-dependent elements _ permits isolation of several production mechanisms including a nj quadrupole component  @xcite . 
   fourier components from 2d correlation analysis are denoted by @xmath82 or @xmath83 , and only the @xmath84 and 2 ( dipole and quadrupole ) fourier terms are _ required _ by 2d data histograms ( see sec .  [ ppangcorr ] )  @xcite . for measure @xmath55 data derived from model fits to 2d angular correlations the quadrupole component is denoted by @xmath85 since the factorized reference density is @xmath86 .    in the present study of  2d angular correlations 
   we admit the possibility that a significant nj quadrupole component may persist in high - energy  collisions ( not necessarily of hydro origin ) and retain the corresponding model element in the 2d data model function eq . 
   ( [ modelfunc ] ) .    the measured -integral nj 
   quadrupole data for  collisions are represented above 13 gev by  @xcite [ loglog ] a_q\{}(b , ) & & |_0(b ) v_2 ^ 2\{}(b , ) + & = & c r ( ) n_bin(b ) _ 
   2,opt^2(b ) , where @xmath87 , the energy - dependence factor is @xmath88 , @xmath45 is the estimated number of  binary encounters in the glauber model , and @xmath89 is the  @xmath78 overlap eccentricity assuming a continuous ( optical - model ) nuclear - matter distribution . 
   equation  ( [ loglog ] ) describes measured @xmath1-integral azimuth quadrupole data in heavy ion collisions for all centralities down to  collisions and energies above @xmath90 gev and represents factorization of energy and centrality dependence for the nj quadrupole . 
   the 2d quadrupole data are also consistent with @xmath91  @xcite , a centrality trend that , modulo the is eccentricity , _ increases much faster than the dijet production rate_.    a non - zero value @xmath92 from eq .  ( [ loglog ] ) extrapolated to  collisions agrees with a  qcd color - dipole prediction  @xcite . as one aspect of the present  correlation study we confirm extrapolation of the  nj quadrupole centrality trend to   collisions and 
   determine the  dependence of  @xmath93 . 
   nj quadrupole systematics may help clarify the concept of  centrality : is an is eccentricity relevant for  collisions ; if so how does it vary with ? 
   the two - component ( soft+hard ) model ( tcm ) of hadron production in high energy nuclear collisions has been reviewed in refs . 
   @xcite for  collisions and refs . 
   @xcite for   collisions . 
   the tcm serves first as a mathematical framework for data description and then , after comparisons with theory , as a basis for physical interpretation of data systematics . 
   the tcm has been interpreted to represent two main sources of final - state hadrons : longitudinal projectile - nucleon dissociation ( soft ) and large - angle - scattered ( transverse ) parton fragmentation ( hard ) . in 
   collisions the two processes scale respectively proportional to @xmath44 ( participant nucleons @xmath43 ) and @xmath45 (  binary encounters ) . 
   analogous scalings for  collisions were considered in ref . 
   @xcite . 
   the ( soft + hard ) tcm accurately describes most fs hadron yield and spectrum systematics  @xcite , whereas there is no significant manifestation of the nj quadrupole in yields and spectra  @xcite . 
   in contrast , the nj quadrupole plays a major role in   2d angular correlations and is measurable as such even for  collisions ( per this study ) . 
   the tcm previously applied to yields and spectra must therefore be extended to include the nj quadrupole as a third component of all high - energy nuclear collisions . 
   an effective tcm should be complete and self - consistent , capable of describing all aspects of data from any collision system . 
   the joint single - charged - particle 2d ( azimuth integral ) density on @xmath1 and @xmath2 is denoted by @xmath95 . 
   the @xmath2-averaged ( over @xmath37 )  spectrum is @xmath96 . 
   the @xmath1-integral mean angular density is @xmath97 averaged over acceptance @xmath37 ( @xmath2 averages are considered in more detail in sec . 
   [ etadensity ] ) . 
   the @xmath5 dependence of  @xmath1 spectra was determined in ref . 
   @xcite , and mb spectra were decomposed into soft and hard components according to the tcm .    in  collisions soft and hard spectrum components 
   have fixed forms but their relative admixture varies with @xmath5  @xcite . 
   the relation of the hard component to pqcd theory was established in ref . 
   @xcite . in  collisions the soft component retains its fixed form but 
   the hard - component form changes substantially with centrality , reflecting quantitative modification of jet formation  @xcite . 
   identification of the hard component with jets in  and more - peripheral  collisions is supported by data systematics and comparisons with pqcd theory  @xcite . in more - central  collisions a jet interpretation for the tcm hard component has been questioned  @xcite . 
   the two - component decomposition of  @xmath1 spectra conditional on uncorrected @xmath98 integrated over angular acceptance @xmath37 within @xmath36 azimuth is denoted by  @xcite [ ppspec ] |_0(y_t;n_ch ) & = & s(y_t;n_ch ) + h(y_t;n_ch ) + & = & |_s(n_ch ) s_0(y_t ) + |_h(n_ch ) h_0(y_t ) , where @xmath99 and @xmath100 are corresponding @xmath2-averaged soft and hard components with corrected @xmath101 ( see sec . 
   [ etadensity ] ) . 
   the inferred soft and hard @xmath1 spectrum shapes [ unit normal @xmath102 and @xmath103 are independent of @xmath98 and are just as defined in refs . 
   @xcite . the fixed hard - component spectrum shape @xmath104 ( gaussian plus power - law tail ) is predicted quantitatively by measured fragmentation functions convoluted with a measured 200 gev minimum - bias jet spectrum  @xcite . 
   figure [ fig1a ] ( left ) shows @xmath1 spectra for several @xmath98 classes . 
   the spectra ( uncorrected for tracking inefficiencies ) are normalized by corrected - yield soft component @xmath105 . 
   a common @xmath1-dependent inefficiency function is introduced for comparison of this analysis with corrected spectra in ref . 
   @xcite , indicated below @xmath106 by the ratio of the two dash - dotted curves representing uncorrected @xmath107 and corrected @xmath102 soft - component models . 
   the data spectra are represented by spline curves rather than individual points to emphasize systematic variation with @xmath98 . 
   left : normalized  spectra for six multiplicity classes of 200 gev  collisions ( @xmath108 see table  [ multclass ] ) . 
   @xmath102 is the soft - component model function for corrected ( upper dash - dotted ) and uncorrected ( lower dash - dotted ) data . 
   @xmath105 is the soft - component multiplicity assuming @xmath109 ( see text ) . 
   the spectra are averaged over acceptance @xmath110 . 
   right : spectrum hard components in the form @xmath111 from eq . 
   ( [ ppspec ] ) compared to hard - component model function @xmath112 ( dashed ) . 
   bars and carets are omitted from the figure labels . 
   , title="fig:",width=158,height=153 ]   left : normalized  spectra for six multiplicity classes of 200 gev  collisions ( @xmath108 see table  [ multclass ] ) . 
   @xmath102 is the soft - component model function for corrected ( upper dash - dotted ) and uncorrected ( lower dash - dotted ) data . 
   @xmath105 is the soft - component multiplicity assuming @xmath109 ( see text ) . 
   the spectra are averaged over acceptance @xmath110 . 
   right : spectrum hard components in the form @xmath111 from eq . 
   ( [ ppspec ] ) compared to hard - component model function @xmath112 ( dashed ) . 
   bars and carets are omitted from the figure labels . 
   , title="fig:",width=158,height=153 ]    figure [ fig1a ] ( right ) shows normalized spectra from the left panel in the form @xmath113 / \bar \rho_s \approx \alpha \hat h_0(y_t)$ ] with @xmath114 . from ref . 
   @xcite we infer @xmath115 . 
   given that empirical relation and @xmath116 as simultaneous equations we can obtain @xmath117 , @xmath105 and @xmath118 for any @xmath98 and @xmath37 ( see details in sec . 
   [ etayt ] ) . 
   note that although the data hard - component shapes for the lowest two @xmath98 values deviate significantly from the @xmath112 model the integrals on  remain close to the value @xmath119 . 
   the amplitude 0.33 of unit - normal @xmath120 corresponds to the maximum of the dashed curve @xmath121 . 
   these spectrum results are consistent with those from ref . 
   @xcite with @xmath122 ( see sec . 
   [ etadep ] ) .      in ref . 
   @xcite the tcm spectrum hard - component yield @xmath123 within @xmath122 was observed to vary as @xmath124 , with uncorrected @xmath125 . 
   a refined analysis provided the more precise density relation @xmath126 . 
   as noted , the tcm soft - component density @xmath105 is then defined by the simultaneous equations @xmath127 , and @xmath128 for some @xmath129 , consistent with pqcd plus ref . 
   @xcite . in ref . 
   @xcite @xmath105 is associated with the number of _ participant low-@xmath3 partons _ ( gluons ) and dijet production , proportional to the number of participant - parton binary encounters , 
   is then observed to scale @xmath130 . 
   based on a dijet interpretation for the hard component we define @xmath131 , where @xmath132 is the dijet frequency per collision and per unit @xmath2 , @xmath133 $ ] is the average fraction of a dijet appearing in acceptance @xmath37 , and @xmath134 is the mb mean dijet fragment multiplicity in @xmath135 . 
   dijet fraction @xmath136 should be distinguished from initial - state eccentricity @xmath137 associated with the nj quadrupole . 
   we also distinguish among number of dijets , number of jets , dijet mean fragment multiplicity and jet mean fragment multiplicity ( their values integrated over @xmath135 vs within some limited detector acceptance @xmath37 ) . 
   the definition of @xmath118 above separates factors @xmath138 $ ] and @xmath139 that were combined in previous studies . 
   the @xmath139 values estimated here are thus approximately a factor 2 ( i.e.  @xmath140 ) larger than previous estimates  @xcite .    for 200 gev nsd  collisions with @xmath141 and dijet mean fragment multiplicity @xmath142 derived from measured jet systematics 
   the inferred jet frequency @xmath143 is inferred from  spectrum data within @xmath122 . that value can be compared with the pqcd prediction @xmath144 for 200 gev  collisions  @xcite based on a measured jet spectrum and nsd cross section corresponding to mean - value  parton distribution functions . 
   thus , the observed nsd  spectrum hard - component yield @xmath123  @xcite is quantitatively consistent with measured dijet systematics derived from event - wise jet reconstruction  @xcite .    if a non - nsd  event sample with arbitrary mean @xmath98 is selected we employ empirical  trends consistent with ref .  @xcite and having their own pqcd implications , as discussed in ref . 
   we assume for the present study that the dijet frequency varies with soft multiplicity as [ nj1 ] f(n_ch ) & & 0.027 ^2 with @xmath145 for 200 gev  collisions . 
   we define @xmath146 as the _ dijet number _ within some angular acceptance @xmath37 . 
   for the @xmath98 range considered in this study the fraction of hard hadrons @xmath147 is not more than about 15% . 
   the  final state is never dominated by hard processes but mb dijet production does play a major role , especially for @xmath148 ( @xmath149 gev / c ) where _ most jet fragments appear_.      mb two - particle correlations have been studied extensively for nsd  collisions  @xcite and  collisions  @xcite . 
   a correspondence between jet - related correlations and @xmath1-spectrum hard components has been established quantitatively in refs . 
   angular - correlation structure is consistent with extrapolation of the centrality systematics of angular correlations from  collisions  @xcite . 
   both correlations on transverse rapidity @xmath150 and 2d angular correlations on @xmath38 from  collisions are described by the tcm . 
   @xmath150 correlations for 200 gev  collisions are fully consistent with the sp  spectrum results described above and in ref . 
   the hard component corresponds ( when projected onto 1d @xmath1 ) to the hard component of eq . 
   ( [ ppspec ] ) . 
   figure  [ ppcorr ] ( left panel ) shows @xmath150 correlations for 200 gev approximately nsd  collisions . 
   the logarithmic interval @xmath151 $ ] corresponds to @xmath152 $ ] gev / c . 
   the two peak features correspond to tcm soft and hard components . 
   the 2d hard component with mode near  = 2.7 ( @xmath153 gev / c ) corresponds quantitatively to the 1d sp spectrum hard component modeled by @xmath104 in ref . 
   the soft component ( us pairs only ) is consistent with longitudinal fragmentation ( dissociation ) of projectile nucleons manifesting local charge conservation . 
   ( color online ) ( a ) minimum - bias correlated - pair density on 2d transverse - rapidity space @xmath150 from 200 gev  collisions showing soft ( smaller ) and hard ( larger ) components as peak structures . 
   ( b ) correlated - pair density on 2d angular difference space @xmath38 . 
   hadrons are selected with @xmath154 gev / c ( @xmath155 ) . 
   nevertheless , features expected for dijets are observed : ( i ) same - side 2d peak representing intrajet correlations and ( ii ) away - side 1d peak on azimuth representing interjet ( back - to - back jet ) correlations  @xcite . 
   , title="fig:",width=158,height=134 ] ( -85,92 ) * ( a ) *   ( color online ) ( a ) minimum - bias correlated - pair density on 2d transverse - rapidity space @xmath150 from 200 gev  collisions showing soft ( smaller ) and hard ( larger ) components as peak structures . 
   ( b ) correlated - pair density on 2d angular difference space @xmath38 . 
   hadrons are selected with @xmath154 gev / c ( @xmath155 ) . 
   nevertheless , features expected for dijets are observed : ( i ) same - side 2d peak representing intrajet correlations and ( ii ) away - side 1d peak on azimuth representing interjet ( back - to - back jet ) correlations  @xcite . 
   , title="fig:",width=158,height=134 ] ( -85,92 ) * ( b ) *    figure  [ ppcorr ] ( right panel ) shows 2d angular correlations on difference variables @xmath38 . 
   the hadron  values for that plot are constrained to lie near 0.6 gev / c ( just above  = 2 ) , corresponding to the saddle between soft and hard peaks in the left panel . 
   although the hadron  is very low the structures expected for jet angular correlations are still clearly evident : a ss 2d peak at the origin representing intrajet correlations and a 1d peak on azimuth at @xmath156 corresponding to interjet correlations between back - to - back jet pairs . 
   the volume of the ss 2d peak corresponds quantitatively to the hard component of the total hadron yield inferred from @xmath1 spectrum data and to pqcd calculations  @xcite . 
   the soft component , a narrow 1d gaussian on @xmath73 including only us charge pairs , is excluded by the @xmath157 gev / c cut  @xcite . 
   angular correlation systematics have been compared to the qcd monte carlo pythia  @xcite , and general qualitative agreement is observed  @xcite . the correlation measure @xmath55 proportional to the number of correlated pairs per final - state hadron 
   @xcite is analogous to ratio @xmath158 given @xmath159 correlated - pair number . in the present study we extend the  results by measuring systematic variations of 2d angular correlations with parameter @xmath98 . 
   ( -120,115 ) * ( a ) *   ( -120,115 ) * ( b ) *   ( -120,115 ) * ( c ) * +   ( -120,115 ) * ( d ) *   ( -120,115 ) * ( e ) *   ( -120,115 ) * ( f ) * 
   two - particle angular correlations are obtained with the same basic methods as employed in refs . 
   @xcite . data for this analysis were obtained from a mb sample of  collisions at @xmath160  gev . 
   charged particles were detected with the star time projection chamber ( tpc ) . 
   the acceptance was @xmath36 azimuth , pseudorapidity @xmath161 , and @xmath24  gev / c . 
   the _ observed _ ( uncorrected ) charge multiplicity within the @xmath2 acceptance is denoted by @xmath98 , whereas the efficiency - corrected and @xmath6-extrapolated _ true _ event multiplicity in the acceptance is denoted by @xmath5 with corrected mean angular density @xmath162 within acceptance @xmath37 . 
   seven event classes indexed by the observed charged - particle multiplicity are defined in table  [ multclass ] . 
   the range of corrected particle density @xmath163 is approximately 2 - 20 particles per unit @xmath2 . 
   this analysis is based on 6 million ( m ) events , compared to 3 m events for the @xmath6-spectrum study in ref . 
   @xcite . 
   .multiplicity classes based on the observed ( uncorrected ) multiplicity @xmath98 falling within acceptance @xmath161 or @xmath110 . 
   the efficiency - corrected density is @xmath162 . 
   event numbers are given in millions ( m = @xmath164 ) . 
   tcm parameters include @xmath109 and @xmath165 . 
   [ cols="^,^,^,^,^,^,^,^",options="header " , ]     alteration of the ss 2d peak is also notable . visually the peak appears to narrow dramatically on @xmath39 with increasing . 
   however , 2d model fits reveal that the fitted peak width decreases only slightly . 
   the _ apparent _ narrowing is due to superposition of the nj quadrupole component onto the 2d peak structure . 
   the change from left to right panel is dominated by the ten - fold increase of curvature ratio @xmath166 , as indicated in fig . 
   [ curvature ] ( right ) .      in ref . 
   @xcite the systematics of 2d angular correlations derived from 62 and 200 gev  collisions were extrapolated first to peripheral  collisions ( as a proxy for nsd  collisions ) and then to 7 tev for comparisons with cms  data . 
   the question posed : are ss 2d peak , as dipole and nj quadrupole systematics at and below 200 gev consistent with those at 7 tev and especially with the emergence of a ss `` ridge '' structure for certain conditions imposed at that energy ? as to  estimates , at 200 gev the nsd  values of @xmath167 and @xmath168 from the present study are numerically consistent with the  extrapolation to  collisions . 
   the value of @xmath169 for 200 gev  collisions was overestimated by a factor 2 by addition of a conjectured quadrupole contribution from the as 1d peak modeled as a 1d gaussian . 
   according to the present study the as peak for  collisions is actually well described by a single dipole element . 
   it was demonstrated that dijet production at 7 tev is consistent with extrapolation from 200 gev using factor @xmath170 ( derived from comparison of 62 and 200 gev data ) interpreted to describe the increase of participant low-@xmath3 gluons with increasing collision energy . 
   that factor applies to the _ per - particle _ 
   ss 2d peak amplitude @xmath167 ( intrajet correlations ) , whereas increase of as dipole amplitude @xmath168 ( jet - jet correlations ) is considerably less ( consistent with no amplitude increase from 62 to 200 gev  @xcite . 
   nj quadrupole measurements at rhic suggest that @xmath169 also increases by factor 2.3 .    as to multiplicity trends for  collisions , in the present study the corrected charge density for multiplicity 
   class @xmath171 is @xmath172 , 5.5 times the mb value 2.5 , whereas at 7 tev the cms @xmath173 multiplicity class corresponds to corrected @xmath174 , 4.8 times the mb value 5.8 . in this 
   study the @xmath171 class corresponds to measured four - fold increase of @xmath168 and @xmath167 and fifteen - fold increase of @xmath169 over their mb values .    as to responses to  cuts 
   we note that about half of all mb jet fragments appear below the mode of the 200 gev spectrum hard component at 1 gev / c  @xcite . 
   in contrast , the mode of @xmath175 on  is close to 3 gev / c  @xcite . 
   the cms cut @xmath176 $ ] gev / c is effectively a lower limit at 1 gev / c , since the hadron spectrum falls rapidly with . 
   we thus expect that a  lower limit imposed at 1 gev / c should reduce the as dipole substantially more than the nj quadrupole . 
   we have reduced @xmath168 by factor 1/2 and @xmath169 by factor 2/3 to estimate the effect of  cuts . 
   table  [ table ] summarizes the various estimates . 
   the first two rows report results from the present study and the curvature ratios shown in fig . 
   [ curvature ] . 
   as noted in the text the 7 tev mb values are obtained by multiplying @xmath167 and @xmath169 by 2.3 and @xmath168 by 1.4 . 
   the values for @xmath177 are obtained with factors 4 and 15 applied as for the 200 gev values for @xmath171 ( ignoring the small difference in ratios to mb multiplicities between rhic and lhc energies ) . 
   the effect of the  cut is estimated by factors 1/2 and 2/3 as noted above . 
   results from the present study describe the reported cms 7 tev 2d angular correlations quantitatively and are generally consistent with ref . 
   @xcite but also provide insight into the physical origins of the reported ss `` ridge . '' 
   the large collision - energy increase combined with imposed @xmath6 and multiplicity cuts increases the  nj quadrupole amplitude eight - fold relative to the as 1d jet peak , changing the ss curvature sign and producing an apparent ss ridge . in effect , the ss azimuth curvature functions as a comparator , switching from valley to ridge as one amplitude increases relative to another . 
   a quantitative curvature change is transformed to a qualitative shape change ( mis)interpreted as emergence of a novel phenomenon at a higher energy . 
   several open issues for high - energy  collisions were summarized in sec .  [ issues ] : ( a ) the role of  collision centrality , ( b ) the definition and nature of the  underlying event or ue , ( c ) the systematics of mb dijet production and ( d ) confirmed existence and characteristics of a nj quadrupole component in  angular correlations . 
   we return to those points in light of results from this study . 
   the measured hard components of  spectra , @xmath2 densities and 2d angular correlations presented in this study complete a unified experimental and theoretical picture of mb dijet production ( no  cuts ) established previously for  collisions  @xcite . 
   there were no previous measurement of a nj quadrupole component for  collisions . 
   the combined dijet and quadrupole results from the present study convey important implications for claims of  collectivity ( flows ) ,  centrality , ue studies and the mechanism of the cms ridge . 
   the term `` collective '' or `` collectivity '' ( e.g.  as recently applied to small collision systems at the lhc ) is ambiguous , since jet formation is a form of `` collectivity '' as is the nj quadrupole whatever its production mechanism . introducing the term `` collectivity '' as synonymous with `` flow '' may produce confusion . 
   there are certainly collective aspects of  collisions although it is unlikely that hydrodynamic flow ( in the sense of fluid motion resulting from particle rescattering ) plays a role . 
   dijet production and the nj quadrupole amplitude follow characteristic trends on @xmath105 precisely over a large range of amplitudes ( 100-fold for dijets , 1000-fold for quadrupole as correlated - pair numbers ) while the underlying particle ( participant - gluon ) density varies 10-fold . 
   how can a small collision system with extremely low particle density support a hydrodynamic phenomenon that conspires to follow the same trends over such a large density interval ?      the notion of centrality ( impact parameter ) for  collisions is ambiguous in principle . concerning  centrality 
   several questions arise : what does `` is geometry '' mean for  collisions ? is an impact parameter relevant ? how are total , triggered dijets , transverse low-@xmath3 parton ( gluon ) density and  centrality correlated ? how do those factors relate to measured ensemble - mean pdfs , _ event - wise _ participant - parton distributions on @xmath3 and initial momentum transfer ? 
   there are certainly large event - wise fluctuations in soft - hadron and dijet production , but whether those correspond to fluctuations of  is transverse geometry or some other collision aspect is in question . 
   the need for comprehensive study of the  dependence of  angular correlations in relation to  centrality was one motivation for the present study . 
   results from this study support two arguments against a major role for a  centrality concept : ( a )  dijet production scales as @xmath178 but the eikonal approximation implies binary - collision scaling as @xmath179 ( as for   collisions ) . 
   the observed dijet trend is consistent with encounters between all possible participant - gluon pairs in each collision , not a smaller subset determined by an impact parameter . 
   ( b ) the nj quadrupole amplitude scales as @xmath180 over a large  range consistent with _ 
   part _ of the @xmath181 trend observed for   collisions , but there is no significant reduction with a decreasing  eccentricity . 
   the combined trends suggest that  is geometry is not a determining factor for either phenomenon . instead 
   , the event - wise depth of penetration on momentum fraction @xmath3 of the projectile wave function may be the main source of variation for soft , hard and quadrupole components .      as noted in sec . 
   [ issues ] ue studies rely on several assumptions : ( a ) concentration of low-@xmath3 gluons at small radius in the proton ( inferred from dis data ) provides a correlation among  centrality , soft hadron production and dijet production , ( b ) the conventionally - defined tr on azimuth includes no contribution from a triggered dijet and ( c ) multiple - parton interactions ( mpi ) may occur in jet - triggered  collisions . the integrated tr yield denoted by @xmath10 
   is observed to increase with increasing jet - trigger  condition and is interpreted to represent a soft background increasing with  centrality . 
   reference  @xcite addressed part of that narrative with simulations based on the tcm for hadron production from  collisions . 
   it concluded that most dijets ( what would result from an applied trigger at lower ) emerge from _ low_-multiplicity collisions . 
   spectrum studies already indicated that higher - multiplicity collisions do produce dijets at higher rates but are few in number and so contribute only a small fraction of the -triggered event population . 
   a @xmath182 condition can not significantly alter the soft component or  collision centrality ( if relevant ) . 
   the present study adds the following new information : ( a ) 2d angular correlations confirm a strong contribution from mb dijets _ within the tr_. ( b ) the dijet production trend @xmath130 suggests that the eikonal approximation is invalid and that centrality is not a useful concept for  collisions . 
   ( c ) monotonic increase of the nj quadrupole @xmath183 over a large  range also suggests that  centrality , as manifested in a varying is eccentricity , is not a useful concept . 
   those factors confirm the conclusions of ref . 
   @xcite and lead to the following scenario for @xmath10 variation with a  trigger : as the trigger condition is increased from zero the integrated spectrum soft component increases @xmath10 from zero to a plateau on @xmath11 . 
   the hard - component ( jet ) contribution to @xmath10 is similarly integrated up to a plateau . 
   @xmath10 thus has both soft and hard components exhibiting plateau structures slightly displaced from one another on @xmath11 . 
   almost all events satisfying an increased trigger condition contain a dijet ( are hard events ) but remain characteristic of a mb population with smaller soft multiplicity , not the expected more - central population with larger soft multiplicity . 
   given the observed -dependent structure of  2d angular correlations we arrive at three conclusions : ( a ) all dijets include a large - angle base that strongly overlaps the tr . 
   that base dominates minimum - bias jets but may persist within all higher - energy 
   ( e.g.  -triggered ) dijets . 
   ( b ) the region with a minimal dijet contribution that might suffice for ue studies is defined by @xmath184 and @xmath185 ( see fig .  [ quadcomp ] ) . 
   an immediate example of novel ue structure that might be discovered there is provided by the cms `` ridge , '' a manifestation of the nj quadrupole that was not expected in  collisions . 
   ( c ) the likelihood of multiple dijet production in -triggered events ( which retain a low soft multiplicity as noted ) is small whereas the likelihood of multiple dijets in high - multiplicity events approaches unity . 
   the usual interpretation of @xmath10 trends in terms of mpi may be misleading . 
   arguments against the tcm have been presented since commencement of rhic operation . 
   it has been noted that the hijing monte carlo  @xcite ( based on pythia  @xcite ) fails to describe rhic and lhc   data . 
   that failure as been expressed as `` too slow increase '' of hadron production with centrality and energy  @xcite . 
   hijing is assumed to represent the tcm and its failure is then confused with failure of the tcm itself , of which hijing is only a specific theory implementation . the problems with hijing are traceable to the eikonal - model assumption included in default pythia  @xcite 
   . such arguments typically rely on data from a centrality range covering only the more - central 40 - 50% of the   cross section  @xcite . 
   the critical centrality region extending from  or  collisions to the _ sharp transition _ in jet formation  @xcite is not considered . 
   alternative models that seem to describe the more - central data are actually falsified by more - peripheral data  @xcite . 
   an alternative argument is based on assuming that tcm agreement with data is accidental , that a _ constituent - quark _ model ( soft only , excluding jets ) is more fundamental and describes data as well  @xcite , but that argument is questionable  @xcite . 
   the tcm invoked in this study is based on previous analysis of  spectrum @xmath5 and centrality dependence  @xcite ,  fluctuations and correlations  @xcite , transverse - rapidity @xmath150 correlations  @xcite and minimum - bias 2d number angular correlations  @xcite . in each case model elements were determined quantitatively by systematic analysis without regard to physical mechanisms . only after the tcm was so established were connections with theory and physical interpretations introduced . in the present study 
   we extend the tcm to describe the  dependence of 200 gev  @xmath2 densities and 2d angular correlations . in the latter we observe for the first time a significant nj quadrupole component and its  dependence as a novel nonjet phenomenon within the ue . 
   we find that the extended tcm remains fully self - consistent and provides accurate and efficient representation of a large body of data . 
   we report measurements of the charge - multiplicity dependence of single - particle ( sp ) densities on transverse rapidity  ( as  spectra ) and pseudorapidity @xmath2 and 2d angular correlations on @xmath186 from 200 gev  collisions . 
   the sp densities are described accurately by a two - component ( soft + hard ) model ( tcm ) of hadron production . 
   the inferred -spectrum tcm is consistent with a previous study . 
   the result for @xmath2 densities newly reveals the distribution on @xmath2 of minimum - bias ( mb ) jet fragments . 
   2d angular correlations are fitted with a multi - element fit model previously applied to data from 62 and 200 gev  collisions . 
   fit residuals are consistent with statistical uncertainties in all cases 
   .    trends for several 2d correlation model parameters are simply expressed in terms of tcm soft - component multiplicity @xmath187 or mean density @xmath188 ( @xmath37 is a detector acceptance ) . 
   correlated - pair numbers for soft component ( projectile dissociation ) scale @xmath189 , for hard component ( dijet production ) scale @xmath130 and for nonjet ( nj ) quadrupole scale @xmath183 . 
   the nj quadrupole amplitude is quite significant for higher - multiplicity  collisions . 
   the dijet production trend is inconsistent with an eikonal approximation for  collisions ( which would require dijets @xmath190 ) , and the monotonically - increasing nj quadrupole trend is inconsistent with an initial - state eccentricity determined by  impact parameter . 
   the two trends combined suggest that centrality is not a useful concept for  collisions . 
   fluctuations may instead depend on the event - wise depth of penetration on momentum fraction @xmath3 of the projectile wave functions and in turn on the number of participant low-@xmath3 partons . 
   2d angular - correlation data are in conflict with assumptions relating to the  underlying event ( ue , the complement to a triggered dijet ) . the azimuth transverse region ( tr ) bracketing @xmath191 is assumed to contain no contribution from a triggered dijet , but minimum - bias dijets are observed to make a strong contribution there . 
   the region with minimal jet contribution is defined by @xmath184 near the azimuth origin that excludes the same - side 2d jet peak and most of the away - side 1d jet peak . 
   the presence of a significant nj quadrupole component and its multiplicity trend have several implications : ( a ) initial - state transverse geometry does not appear to be a useful concept for  collisions as noted above , ( b ) the appearance of a nj quadrupole component in a small system with negligible particle density contradicts the concept of a hydro phenomenon based on particle rescattering and large energy / particle density gradients and ( c ) the same - side `` ridge '' observed in  collisions at the large hadron collider ( lhc ) , interpreted by some to suggest `` collectivity '' ( flows ) in small systems , results from an interplay of the jet - related away - side 1d peak and the nj quadrupole that together determine the curvature on azimuth near the origin . when that curvature transitions from positive to negative ( depending on collision energy and other applied cuts ) a same - side `` ridge '' appears .    in a hydro narrative 
   the nj quadrupole component interpreted as elliptic flow should represent azimuth modulation of radial flow detected as a modification of sp  spectra . 
   but no corresponding modification is observed in  spectra despite precise differential analysis . 
   t.  a.  trainor , d.  t.  kettler , d.  j.  prindle and r.  l.  ray , j.  phys . 
   g * 42 * , no . 2 , 025102 ( 2015 ) . 
   d.  t.  kettler , d.  j.  prindle and t.  a.  trainor , phys . 
   c * 91 * , 064910 ( 2015 ) . 
   d.  t.  kettler ( star collaboration ) , eur . 
   j.   c * 62 * , 175 ( 2009 ) . 
   d.  kettler ( star collaboration ) , j.  phys . 
   .  ser .   * 
   270 * , 012058 ( 2011 ) . 
   t.  a.  trainor and d.  t.  kettler , phys . 
   c * 84 * , 024910 ( 2011 ) . t.  a.  trainor , phys . 
   d * 87 * , no . 5 , 054005 ( 2013 ) . 
   t.  a.  trainor , mod . 
   a * 23 * , 569 ( 2008 ) . 
   t.  a.  trainor , int . 
   j.  mod . 
   e * 17 * , 1499 ( 2008 ) . 
   t.  a.  trainor , phys . 
   c * 80 * , 044901 ( 2009 ) . 
   g.  agakishiev , _ et al . _ 
   ( star collaboration ) , phys . 
   c * 86 * , 064902 ( 2012 ) . 
   t.  a.  trainor and d.  t.  kettler , phys . 
   c * 83 * , 034903 ( 2011 ) . 
   s.  gavin , l.  mclerran and g.  moschelli , phys . 
   c * 79 * , 051902 ( 2009 ) . 
   t.  a.  trainor , phys . 
   c * 91 * , no . 4 , 044905 ( 2015 ) . 
   b.  z.  kopeliovich , a.  h.  rezaeian and i.  schmidt , phys . 
   d * 78 * , 114009 ( 2008 ) . 
   cms  collaboration , jhep * 1009 * , 091 ( 2010 ) . 
   t.  a.  trainor , phys . 
   c * 90 * , no . 2 , 024909 ( 2014 ) t.  a.  trainor , phys . 
   c * 92 * , no . 2 , 024915 ( 2015 ) . 
   j.  adams _ et al . _ 
   ( star collaboration ) , phys . 
   c * 73 * , 064907 ( 2006 ) . 
   j.  adams _ et al . _ 
   ( star collaboration ) , phys . 
   b * 634 * , 347 ( 2006 ) . 
   t.  a.  trainor , r.  j.  porter and d.  j.  prindle , j.  phys . 
   g * 31 * , 809 ( 2005 ) . 
   r.  j.  porter and t.  a.  trainor ( star collaboration ) , acta phys . 
   b * 36 * , 353 ( 2005 ) . 
   t.  a.  trainor , phys . 
   d * 89 * , no . 9 , 094011 ( 2014 ) . 
   t.  a.  trainor , j.  phys . 
   g * 37 * , 085004 ( 2010 ) . 
   t.  a.  trainor , phys . 
   c * 81 * , 014905 ( 2010 ) . ya . 
   i.  azimov , yu .  l.  dokshitzer , v.  a.  khoze , s.  i.  troyan , z. phys . 
   c * 27 * , 65 ( 1985 ) , z. phys . 
   c * 31 * , 213 ( 1986 ) . 
   g.  wolschin , phys . 
   c * 91 * , 014905 ( 2015 ) . t.  a.  trainor , j.  phys . 
   g * 40 * , 055104 ( 2013 ) . 
   t.  a.  trainor , d.  j.  prindle and r.  l.  ray , phys . 
   c * 86 * , 064905 ( 2012 ) . 
   m.  b.  de kock , h.  c.  eggers and t.  a.  trainor , phys . 
   c * 92 * , no . 3 , 034908 ( 2015 ) 
   . b.  i.  abelev _ et al . _ 
   ( star collaboration ) , phys . 
   c * 80 * , 064912 ( 2009 ) . 
   t.  a.  trainor , j.  phys . 
   g * 39 * , 095102 ( 2012 ) m.  gyulassy and l.  mclerran , nucl . 
   a * 750 * , 30 ( 2005 ) 
   . b.  b.  back _ et al . _ 
   ( phobos collaboration ) , phys . 
   b * 578 * , 297 ( 2004 ) . 
   d.  kharzeev and e.  levin , phys . 
   b * 523 * , 79 ( 2001 ) . 
   s.  s.  adler _ et al . 
   _ ( phenix collaboration ) , phys . 
   c * 89 * , no . 4 , 044905 ( 2014 ) .
summary: an established phenomenology and theoretical interpretation of @xmath0-@xmath0 collision data at lower collision energies should provide a reference for @xmath0-@xmath0 and other collision systems at higher energies , against which claims of novel physics may be tested . 
   the description of @xmath0-@xmath0 collisions at the relativistic heavy ion collider ( rhic ) has remained incomplete even as claims for collectivity and other novelties in data from smaller systems at the large hadron collider ( lhc ) have emerged recently . in this study 
   we report the charge - multiplicity dependence of two - dimensional ( 2d ) angular correlations and of single - particle ( sp ) densities on transverse rapidity @xmath1 and pseudorapidity @xmath2 from 200 gev @xmath0-@xmath0 collisions . 
   we define a comprehensive and self - consistent two - component ( soft + hard ) model ( tcm ) for hadron production and report a significant @xmath0-@xmath0 nonjet ( nj ) quadrupole component as a third ( angular - correlation ) component . 
   our results have implications for @xmath0-@xmath0  centrality , the underlying event ( ue ) , collectivity in small systems and the existence of flows in high - energy nuclear collisions .