Manifestations of minimum-bias dijets in high-energy nuclear collisions

1.4 MB·

by  Thomas A. Trainor

Version 1.2
Manifestations of minimum-bias dijets in high-energy nuclear collisions
Thomas A. Trainor
CENPA 354290, University of Washington, Seattle, Washington 98195
(Dated: January 30, 2017)
Dijets observed near midrapidity in high-energy nuclear collisions result from large-angle scat-
tering of low-x partons (gluons) within projectile hadrons as a signature manifestation of QCD.
Withinthesamecollisionsithasbeenclaimedthathydrodynamicflows(radial,ellipticand“higher
harmonic” flows) carried by a dense QCD medium or quark-gluon plasma (QGP) dominate the
observed hadronic final state. The flow-QGP narrative is imposed a priori on primary particle
data, and of all possible analysis methods a subset A that seems to support that narrative is pre-
ferred. The present study explores an alternative minimum-bias (MB) jet narrative – quantitative
correspondence of MB dijet manifestations in the hadronic final state with measured isolated jet
properties. The latter incorporates a different set of methods B that emerge from inductive study
7 of primary particle data without a priori assumptions. The resulting system of methods and data
1 manifestations is represented by a two-component (soft + hard) model (TCM) of hadron produc-
0 tion. A survey of methods reveals that type A tends to discard substantial information carried by
2 primary particle data whereas type B retains almost all information in both primary particle data
from nuclear collisions and from isolated jets. The main goal of the present study is a review of
n
MB dijet contributions to high-energy collisions in small and large systems relative to measured
a
isolated-jet properties. Representative analysis methods from types A and B are compared in the
J
context of MB jet manifestations. This study suggests that at least some data features commonly
6
attributed to flows actually result from MB dijets and thereby challenges the flow-QGP narrative.
2

PACSnumbers: 12.38.Qk,13.87.Fh,25.75.Ag,25.75.Bh,25.75.Ld,25.75.Nq
]
h
p
- I. INTRODUCTION that most hadrons emerge from “freezeout” of a locally-
p thermalized, flowing dense medium [8]. Hadron p is di-
t
e
videdintoseveralintervalswithspecificphysicalinterpre-
h This study reviews manifestations of minimum-bias
tations: thermalization and flows for p < 2 GeV/c [9],
[ (MB) dijets in the hadronic final state of high-energy t
high-p jet phenomena for p > 5 GeV/c [10] and an in-
nuclear collisions in the context of claimed collectivity t t
1 termediate region where production mechanisms are de-
(flows) in the same systems. There is widespread belief
v
bated[11,12]. Suchassumptionsprovideapreferredcon-
6 that hydrodynamic flows play a dominant role in high-
text for analysis and interpretation of high-energy data.
6 energy collisions wherein a dense medium (quark-gluon
8 plasma or QGP) is formed that supports a collective Forexample,transverse-momentumpt spectramaybe
7 velocity field manifested by features of hadron distribu- fitted with a monolithic model function interpreted to
0 tions [1]. However, it is possible that at least some data reflect a thermodynamic context and to measure radial
.
1 features attributed to flows may relate to MB dijets [2]. flow [9]. Two-dimensional (2D) angular correlations are
0 In order to clarify such ambiguities MB dijets should be projectedontoperiodic1Dazimuthφandrepresentedby
7 understood in p-p, p-A and A-A collisions in relation to FourierserieswhereineachFouriertermisinterpretedto
1 eventwise-reconstructed (isolated) jets derived indepen- represent a type of transverse flow [13]. Charge and pt
:
v dently from e+-e− and p-p¯collisions over a broad range fluctuationsareaddressedwithstatisticalmeasuresmoti-
i of collision energies. That is the main goal of this study. vatedbythermodynamicassumptionsincludingsomede-
X
Flows and QGP are intimately related by the assump- gree of local thermalization of a bulk medium. Intensive
r
a tionthatadense,strongly-interactingmediumdeveloped ratiosorratiosofratiosarepreferredoverextensivemea-
during nucleus-nucleus (A-A) collisions should respond sures of collision observables such as integrated charge
to initial-state energy- and matter-density gradients by multiplicitynch orintegratedPt withinsomeangulardo-
developing a velocity field (various flows) whose conse- main [14, 15]. Jet contributions are acknowledged only
quences may be observed in the hadronic final state [3]. within restricted pt intervals including a small fraction
Observation of flow manifestations and a causal relation of all hadrons, and assumed jet properties are based on
toA-Ainitial-stategeometryissoughtaprioriandinter- conjecture rather than actual jet measurements [10, 16].
preted to imply that a QGP has been established [4–6]. In contrast, the properties of eventwise-reconstructed
Flow-QGPclaimsthenrelyonassignmentofcertaindata dijets,theirfragmentmomentumdistributions(fragmen-
features to flows and may refer to others as “nonflow” tationfunctions or FFs)[17–19] andjet (leading-parton)
withoutfurtherelaboration[7]. Theflow-QGPnarrative energy spectra [20–22] measured over thirty years pre-
formsthebasisforotherdataanalysisandinterpretation, dict quantitatively certain manifestations of MB dijets
andMBjetcontributionsmaybeminimizedbypreferred that appear in high-energy collision data [23]. Predic-
analysis methods and interpretation strategies. tions from isolated-jet measurements [as opposed to per-
Theflownarrativeisrelatedtodatabyanassumption turbative QCD (pQCD) theory with its limitations] are
2
inconsistent with much of the flow narrative and its pre- be assumed. SP densities are defined on p as p spectra
t t
sumed basis in measurement as discussed below. and on (η,φ) as angular densities.
In this study I examine the process of measure design Two-particle(pair)densitiesdefinedon6Dmomentum
in several critical areas and compare competing analy- space (p ,η ,φ ,p ,η ,φ ) or a subspace may reveal
t1 1 1 t2 2 2
sis methods. I demonstrate how measured properties of certain pair correlations identified with physical mech-
isolated jets predict certain data features from nuclear anisms. 2Dpairdensitieson(x ,x )maybeprojected by
1 2
collisions corresponding to MB dijets and how analysis averaging onto difference variables x = x −x to ob-
∆ 1 2
methodsmotivatedbytheflownarrativemayleadtoat- tainajoint angular autocorrelationonthereducedspace
tributionofthesamefeaturestoflows. Ishowhowatwo- (p ,p ,η ,φ ) [24] which can be further reduced by
t1 t2 ∆ ∆
component (soft + hard) model (TCM) of hadron pro- integration over p bins or the entire p acceptance. In
t t
duction in high-energy collisions emerges naturally from discussing2Dangularcorrelationsitisconvenienttosep-
inductive analysis of p-p spectrum and correlation data, arateazimuthdifferenceφ intotwointervals: same-side
∆
is not imposed a priori, and how the TCM is manifested (SS, |φ |<π/2) and away-side (AS, |φ −π|<π/2).
∆ ∆
in other contexts. A number of examples are presented. Charge multiplicity and particle p may be integrated
t
Iconcludethatwhendatafeaturesarereexaminedinthe over some angular acceptance (∆η,∆φ) or multiple bins
contextofisolated-jetmeasurementslittlesubstantialev- withinanangularacceptancetoobtainn andP asex-
ch t
idence remains to support the flow narrative. tensive eventwise random variables (RVs) whose fluctua-
Thisarticleisarrangedasfollows: SectionIIdiscusses tions may be of interest [24, 25]. Uncorrected (observed)
preferredanalysismethods. SectionIIIintroducesatwo- chargemultiplicitiesdenotedbynˆ arerelevanttoPois-
ch
componentspectrummodelforp-pcollisions. SectionIV son statistics, for instance in determining void probabili-
reviews the measured properties of reconstructed jets. ties defined below. n then denotes corrected values.
ch
Section V describes MB jet contributions to p-p spectra. Secondary observables may be defined as combina-
SectionVIpresentsMBjetcontributionstoA-Aspectra. tionsofprimaryobservables,forinstanceeventwisemean
Section VII reviews MB jet contributions to two-particle (cid:104)p (cid:105) = P /n as an intensive RV [15], event-ensemble-
t t ch
charge correlations. Section VIII presents MB jet con- mean p¯ = P¯/n¯ characterizing a collision system [14],
t t ch
tributions to p fluctuations and p angular correlations. spectrumratioR astheratioofacentralA-Ap spec-
t t AA t
Sections IX and X present discussion and summary. trum to a p-p spectrum [26], and v (p ) also as a ratio
2 t
of distinct hadron spectra [27]. Fluctuation and pair-
correlation measures (variances and covariances) may be
combined with other statistics in sums, differences or ra-
II. PREFERRED ANALYSIS METHODS
tios to define secondary statistics. SP and pair momen-
tum spaces may be partitioned (possibly based on a pri-
For some aspects of data analysis alternative meth-
oriassumptions),forinstancedefiningcertainp intervals
t
ods may give significantly different results and support
within which specific physical mechanisms are expected
different physical interpretations. The overall interpre-
to dominate collision data according to some narrative.
tation of high-energy nuclear collisions then depends on
a sequence of method choices. How should such choices
be made to establish an overall result that best reflects
B. Competing analysis methods
reality? Onepossiblecriterionisthefractionofinforma-
tioncarriedbyprimaryparticledatathatisretainedbya
Analysis methods are generally not unique. A spe-
method for hypothesis testing. MB dijet manifestations
cificcombinationofmethodscontributingtoapublished
in nuclear collisions compared to measured properties of
analysis may comprise a subset of available methods de-
isolated jets may provide a basis for evaluation.
termined by a sequence of choices among alternatives,
possibly guided by a preferred narrative. In a given con-
text(e.g.SPspectraorpairangularcorrelations)alterna-
A. Primary and secondary observables
tiveselectionsmayleadtosignificantlydifferentphysical
interpretations of collision data. For instance, each of
All analysis methods are based on primary particle extensive measures P and n or their ensemble means
t ch
data. A charged-particle detector (e.g. time-projection P¯ and n¯ may reveal certain data trends inconsistent
t ch
chamber) determines the primary hadron single-particle with a temperature hypothesis but supporting an alter-
(SP)observablesinhigh-energynuclearcollisions: trans- native hypothesis whereas fluctuations of intensive even-
verse momentum p , pseudorapidity η, azimuth angle twise (cid:104)p (cid:105) or systematics of ensemble p¯ may be seen as
t t t
φ, charge sign and possibly hadron species via particle reflecting local temperature variations of a conjectured
ID, in which case η → y (longitudinal rapidity) and bulk medium. Critical extensive trends may be sup-
z
(cid:112)
p → m = p2+m2 (transverse mass) with m a pressed by cancellations within intensive ratios.
t t t h h
hadron mass. Transverse rapidity y ≡ln[(p +m )/m ] Hadronpaircorrelationsfromhigh-energynuclearcol-
t t t h
provides superior visual access to SP spectrum structure lisionsprojectedonto1Dazimuthexhibitstrongnonuni-
at lower p . For unidentified hadrons the pion mass may formities (literally “azimuthal anisotropy”) that may
t
3
oMcanaoorncnoiBmtidglsmyiomnFadtaboortitojuytneeeprltryiaysef.wrrF[io2nhcom8taouHe]te.rroffiipisewteArrcsveeinvepetsyereenhadrrty,ildesoiasitspfcshtah(treFlyhisbosySetuirn)ceait.oargizmnoliTinmnyhsmm,ue“oetaconcahanuhsanispsasleeonbwrartietisrsioiyomtoddhpmnesiisccmca“irazTnefliiztbcmhoirlemewyuuddu”ts[hieietn.xhcaeigs--l., (1/n) dn/ydyschtt1111111000100001112468024 11.5 [1/n(nˆ)] N(y,nˆ)schtch 0001....46812 Dh = 1N0
-2
anisotropy] is called elliptic flow” [29] reflects a common 10-4 nˆch = 1 0.2 A B C
assumption. Alternative modeling of azimuth distribu- 1100-6 Dh = 1 S0 0
tions may favor a different physical interpretation. 1 2 3 4 0 1 2 3 4
y y
This study emphasizes manifestations of MB dijets t t
from high-energy nuclear collisions within several con-
FIG.1: Left: y spectrafromtencharge-multiplicityclasses
texts (e.g. yields, spectra, correlations, statistical fluctu- t
of 200 GeV p-p collisions (points) compared to fixed refer-
ations) and their relation to selection of specific analysis enceSˆ (y )(thinsolidcurves)[30]. Right: Runningintegrals
0 t
methods: How are MB dijets, consistent with measured
N(y )ofnormalized(andextrapolated)y spectraintheleft
t t
isolated-jet properties, revealed or concealed by method panel for ten multiplicity classes (solid curves) compared to
choices,andwhatcriteriawouldinsureconsciousandun- runningintegralN (y )offixedreferenceSˆ (y )(dash-dotted
0 t 0 t
biased choices that lead to meaningful interpretations? curve).
III. TWO-COMPONENT SPECTRUM MODEL dence lies within interval B as the running integral of a
peaked spectrum component with amplitude ∝n .
ch
The limiting case N (y ) is modeled by the running
In Ref. [30] a detailed analysis of p spectra was ap- 0 t
t
integral of a unit-normal L´evy distribution on m [31]
pliedtotenmultiplicityclassesof200GeVp-pcollisions. t
No a priori assumptions about spectrum structure were A(T ,n )
imposed. The main goal was to understand systematic Sˆ0(mt) = [1+(mt−m0 h)0/n0T0]n0, (1)
variation of spectrum shape with n in terms of alge-
ch
braic models inferred from data alone: given available where T ≈ 145 MeV controls the function mainly in
0
spectrum data what is the most efficient algebraic de- interval A and n ≈12.8 controls the function mainly in
0
scription? For reasons given in Sec. II this analysis is intervalC.TheJacobianfactorfromm toy isp m /y .
t t t t t
presented in terms of transverse rapidity y . The resulting Sˆ (y ) model inferred directly from data
t 0 t
trends can be subtracted to reveal the peaked spectrum
(hard) component residing mainly within interval B.
A. Spectrum data and soft component
B. Spectrum hard component
Figure 1 (left) shows y spectra for ten p-p multiplic-
t
ity classes normalized by soft-component multiplicity n
s
(points)anddisplacedupwardfromeachotherbysucces- Figure 2 (left) shows the normalized spectrum data in
sivefactors40relativetothelowestspectrum(theterms Fig.1(left)withfixedmodelSˆ (y )inferredfromEq.(1)
0 t
“soft” and “hard” are interpreted below) [30]. Empir- subtracted to reveal peaked distributions (points and
ically, all spectra are observed to coincide at lower y dashed curves) centered on interval B with amplitudes
t
if normalized by n ≈ n −αn2 for some α ≈ 0.01. increasing approximately ∝ n . With a few exceptions
s ch ch ch
The definition of n in terms of n is refined further in discussed below the distributions are well described by a
s ch
Sec. IIIB. two-parameterGaussianfunction(solidcurves). Thatre-
Figure1(right)showsrunning integralsofthetennor- sult suggests that the peaked hard component H(y ,n )
t ch
malized spectra in the left panel. The spectra have been has the factorized form H(y ,n )/n ∝n Hˆ (y ).
t ch s ch 0 t
extrapolated to yt = 0 (note that yt spectra are nearly Figure2(right)showsdataintheleftpanelrescaledby
constantatloweryt). Therunningintegralisameansto soft-component multiplicity ns (rather than nch) (solid)
enhance a long-wavelength signal (spectrum shape) over compared with a fixed Gaussian model in the form
short-wavelength (statistical) noise. Different behavior αHˆ (y ) with centroid y¯ ≈ 2.7 and width σ ≈ 0.45
0 t t yt
is observed in each of yt intervals A, B and C (spanning (dashed) and with coefficient α ≈ 0.006 determined by
the detector acceptance). In interval A the integrals ap- thedata-modelcomparison. Insummary, aTCMforp-p
proximately coincide. In interval B the integrals diverge y spectra is inferredinductivelyfrom p-p spectrum data
t
substantially. In interval C the integrals are nearly con- alone as
stant, and those constant values increase approximately
dn
linearly with n . The limiting case for n → 0 is de- ch = S (y ,n )+H (y ,n ) (2)
ch s y dy pp t ch pp t ch
scribed by function N (y ) (dash-dotted curve) defined t t
0 t
below. Those results indicate that the main n depen- = n (n )Sˆ (y )+n (n )Hˆ (y ),
ch s ch 0 t h ch 0 t
4
-2 tainty for each y value. That format differs from more-
10 t
-dn/ydy S(y)chtt0t00000...000..0012323555 H(ynt,snˆch) B 2(1/n) H(y,nˆ)stch1100---543 Aa H0(yt)B C ctfgrohaoivrmnaetvlneoetwsnetsetrrtiroaonnnengvdadlealeynrrpdtisrvumeecpsdruepinltfrtetreiraopsitmslaii.corinfietOsstieitndisinnuttgathheloeEsrsmqreai.tsgfi(hotl3ostf)wsdathearoroetuasyvp/ltdame.lcubotEeerdssuerpmelfeojrceradicatatpileotaldyas-
n) s 0.01 10 Dh = 1 (solid points) and to the TCM described above (open
(1/0.005 10-6 points) compared to the fixed value n0 = 12.8 for the
TCM itself. The variation descends from values exceed-
0
2 2.5 3 3.5 1 2 3 4 ing the TCM soft-component value for lower nch to val-
y y uesconsistentwiththejet-relatedTCMhardcomponent
t t
for larger n as dijet production increases ∝ nˆ2 per
ch ch
FIG. 2: Left: Normalized yt spectra in Fig. 1 (left) mi- Ref. [33].
nus unit-normal reference Sˆ (y ) (points) [30]. The vertical
0 t
dottedlinesencloseintervalBpreviouslydefined. Right: Dis-
tributions H(n ,y )/n2 (solid curves, data in the left panel
ch t s 22
rescaledbyn )comparedtofixedreferenceαH (y )(dashed). a n
s 0 t t 30
√ da 20 21= nˆch 1280 potwoe dra-ltaaw fit:
wfohretrheentcwhoasnpdecyttrutrmencdosmhpaovneebnetes.nTfahcetroeriazreedtswepoaerxacteeply- fit) / 10 453 1146 totw fiox-ecdo mmpoodneelnt
tions: (a) Significant systematic deviations from Hˆ0(yt) -ata 0 12 fixed model
d
aterme aotbiscerdveevdiaftoirontshearloewaelsstonocbhsecrlavsesdesf.or(ba)llSnmcahllcelrassysess- N (evt--2100 power law 180
near the upper limit of the y acceptance. Both excep- yt 6
t √ 2 3 4 0 2.5 5 7.5 10 12.5
tionswerereconsideredinRef.[32]andincorporatedinto y nˆ
t ch
anextendedTCMdescribingspectrumdataoverthefull
range of collision energies (see Sec. VB).
FIG. 3: Left: Relative residuals from power-law fits to p
t
More-detailed analysis [33] shows that the relation spectra in Fig. 1 [30]. The hatched band represents the ex-
nh = αn2s is required by data, with α ≈ 0.006 for 200 pectedstatisticalerrors. Right: Exponentsnfrompower-law
GeV p-p collisions [32] (and see Fig. 9, left). Adding the fits to data (solid points) and to corresponding TCM fixed-
condition n = n +n defines n (n ) and n (n ) in model functions (open circles) compared to the fixed-model
ch s h s ch h ch
terms of corrected total multiplicity nch (as opposed to value n0 ≈12.8 (hatched band).
detected nˆ ≈n /2). The resulting SP spectrum TCM
ch ch
with fixed parameters and functional forms describes p-p
spectra accurately over an n interval corresponding to
ch It could be argued that the TCM for p spectra is
t
10-fold increase in the soft component and 100-fold in-
simply one of several competing spectrum models and
crease in the hard (dijet) component. There was no re-
that the power-law model should be preferred as requir-
quirement for physical interpretation of the TCM com-
ing only two parameters compared to five for the TCM.
ponents as the model was inferred from spectrum data.
However, the TCM is not a simple fitting exercise ap-
plied to a single data spectrum. Ref. [30] established
that a spectrum TCM inferred inductively from the n
ch
C. Alternative spectrum models
dependence of p spectra without any a priori assump-
t
tions is necessary to describe consistently an ensemble
The TCM derived inductively from spectrum data re- of high-statistics p spectra over a large n range (e.g.
t ch
quires five fixed parameters to describe p-p spectra for factor10). Separationofp-pspectrumdataintotwocom-
anyeventmultiplicitywithinalargeinterval[32,33]. Al- ponents does not depend on an imposed model. Specific
ternative spectrum models could be proposed with free model functions were introduced only after resolution of
parameters determined for each event class by fits to data spectra into two components based on n trends.
ch
data. Onesuchmodelistheso-called“power-law”(n)or
Tsallis (q) distribution that is similar in form to Eq. (1) Incontrast,whatemergesfrompower-lawfitsistwenty
parameter values to describe ten multiplicity classes as
A opposed to five for the TCM. The large penalty for poor
P(x ) = , (3)
t [1+x /nT]n fits in Figure 3 (left) is even more determining. The
t
dramaticvariationofpower-lawparameternintheright
where x is p [34, 35] or m [36] and n↔1/(q−1). panelhasnoaprioriexplanation,whereasinaTCMcon-
t t t
Figure 3 shows the result of fitting the spectrum data text the variation occurs because an inappropriate (soft)
fromFig.1(left)withEq.(3). Ontheleftarefitresiduals model attempts to accommodate quadratic increase of
for ten multiplicity classes in units of statistical uncer- the jet-related (hard) spectrum component with n .
ch
5
IV. EVENTWISE-RECONSTRUCTED JETS Figure 4 (left) shows ISR and Spp¯S jet spectrum data
(points) with the jet spectra rescaled vertically by factor
Jets may be reconstructed eventwise from final-state (∆yb)2 and parton rapidity ymax rescaled horizontally
hadrons within the full hadron momentum space in- to u assuming Emin ≈ 3 GeV. All spectrum data for
cluding scalar momentum and angular correlations rel- p-p¯ collision energies below 1 TeV fall on the common
ative to an inferred leading-parton four momentum. locus0.15exp(−u2/2σu2)(solidcurve). Theparametrized
This section emphasizes scalar-momentum dependence parton spectrum conditional on p-p beam energy is then
of reconstructed jets and jet fragments. A joint
d2σ 1
dsceanlsairtyfradgismtreinbtutmioonmoenntupmartpofnrag(jecta)nebneergfayctEorjieztedanads dymaxjdη = 0.026∆yb2(cid:112)2πσu2e−u2/2σu2, (7)
P(E ,p ) = P(E )P(p |E ), where condi-
jet frag jet frag jet
(cid:112)
tional distribution P(p |E ) → Dh(p |E ) is a where 0.026/ 2πσ2 = 0.15 and σ ≈ 1/7 is determined
frag jet p frag jet u u
fragmentation function (FF) for parton type p fragment- empirically from the data. All jet production over nine
√
ing to hadron type h, and P(E ) → dσ /dE is the decades is then represented by parameters s ≈ 10
jet j jet 0 √
jet energy spectrum for a given dijet source (e.g. p-p¯col- GeV, E ≈ 3 GeV and σ ≈ 1/7. Endpoints s
min u 0
lisions). Inthissectionsimpleandaccurateparametriza- andE arecloselyrelatedbykinematicconstraintson
min
tions of isolated-jet data for e+-e− and p-p¯collision sys- fragmentationtochargedhadronsfromlow-xgluons[37].
tems are based on logarithmic rapidity variables, with
EjAetA↔Q.CpDpt--tproeljaaecttecdo(smcemanteotrdegrayetedd-esppoaemrntedoecnno)cneveeninsetrtigoyynpaicslpanleloycttaortafiotnh.e 2shy) d / du dmaxj1111110000001------654321 966550334000060 UUUUUAAAAAU11211A1/UA2/R807 h / dpd (mb/GeV)jt11111111000000001---------987654321 17 UA1/UA2/R890070
ttfoiicornmesnilenorggt(yeQrms/cQsa0loe)f.wraAhpeirddeietsyQcr0viaprrteiiapobnrelesoefyntf=rsalsgnom[m(epen+tcahEtaio)r/namctfuer]nic≈s-- 2DD(1/y)(1/b111000-1---0987 bea2 m 0603 e nUReA8r01g7y (GeV) 2sd1111100000----11113210 minijebtes4a3m en6er3gy2 (0G0eV50)0
ln(2p/m )asinRef.[17]ispresentedinthenextsubhsec- 10 0 0.2 0.4 0.6 0.8 1 10 102
h u pt (GeV)
tion. A jet spectrum near midrapidity for p-p collision
√
energy s can be written in terms of a jet “rapidity” by
FIG. 4: Left: Jet energy spectra from p-p¯collisions for sev-
eral energies [20–22] rescaled by factor ∆y2 and plotted vs
d2σ d2σ b
p j = j , (4) normalized jet rapidity u. Within uncertainties the data fall
tdp dη dy dη onthecommonlocus0.15exp(−25u2). Right: Thesamedata
t max
plotted in a conventional log-log format. Dashed and dotted
where ymax ≡ln(2Ejet/mπ) was first defined in Ref. [17] curves through thedataarederivedfrom the universaltrend
in connection with fragmentation functions as summa- (solid curve) in the left panel as described in the text.
rized in the next subsection and E → p as noted
jet t
above. Figure 4 (right) shows ISR and Spp¯S spectrum data
Studyofjet-relatedyields,spectraandangularcorrela- from the left panel plotted vs p ↔ E in a conven-
t jet
tionsin200GeVp-pcollisionsrevealsthatthejet-related tional log-log format. The curve for each beam energy
(hard-component) density dnh/dη (and presumably jet is d√efined by Eq. (7). The dotted curve corresponds
production dnj/dη) scales with the soft-component den- to s = 630 GeV [21]. The model curves extend to
sity as dnh/dη ∝ (dns/dη)2. Giv√en that relation and u = 0.9 corresp√onding to partons with momentum frac-
dns/dη ∝ log(s/s0) ≡ 2∆yb (with s0 ≈ 10 GeV) near tionx=2Ejet/ s≈2/3beyondwhichthep-pcollision-
midrapidity[32]thenumberofMBdijets(dominatedby energy constraint should strongly influence the spectra.
lowest-energyjets)appearingnearmidrapidityinp-pcol-
lisions should vary with collision energy as [32, 33, 37].
B. Fragmentation functions
d2σ
j ∝ ∆y2 near some E . (5)
dy dη b min
max Dijet formation depends on parton energy scale Q =
√Kinematic constraints impose√the upper limit 2Ejet < 2Ejet with rapidity y = ln[(E +p)/mπ] (for an uniden-
s (y < y ) with y = ln( s/m ). Evidence from tified hadron fragment with scalar momentum p) and
max b b π
jet[20]andSP-hadron[23]spectrasuggestsalowerlimit maximum rapidity ymax as defined below Eq. (4) to de-
Ejet > Emin (ymax > ymin) with Emin ≈ 3 GeV. A scribee+-e− FFswithD(y|ymax)=2dnch,j/dy,thefrag-
normalized jet rapidity variable can then be defined by ment rapidity density per dijet. The FF parametriza-
tion is D(y|y ) = 2n (y )β(u;p,q)/y , where
max ch,j max max
y −y log(E /E ) β(u;p,q) is a unit-normal (on u) beta distribution, u =
u = max min = √jet min ∈[0,1]. (6)
yb−ymin log( s/2Emin) (y −ymin)/(ymax −ymin) ∈ [0,1] is a normalized frag-
6
ment rapidity, and parameters p and q (for each parton- missing from reconstructed p-p¯ FFs. This comparison
hadron combination) are nearly constant over a large is dominated by quark jets, but quark and gluon FFs
jet energy interval [17]. The total fragment multiplicity convergenearE ≈3GeVwheremostMBjetsappear.
jet
2n (y )(fromtwojets)isinferredfromtheshapeof
ch,j max
β(u;p,q) (and therefore parameters p and q) via parton 8
(djiejFte)tigeeunnreeerrg5gyie(slceof[nt1)s8e,srh1voa9wt]isoexnmt.eenadsuinrgeddFowFns (tpoovinetrsy)lfoowr tfhrarege- D(y|y)ppmax 567 1 10p5E (7dG3ijee GtV 1=e0/cV0) D / Dppee 000...7891 78 GeV
ment momentum (less than 100 MeV/c). When plotted 0.6 E = 573 GeV
4 dijet
on fragment rapidity y the FFs show a self-similar evo- 78 CDF 0.5
3 0.4
lution with maximum rapidity y . The solid curves
max 2 0.3
showthecorrespondingFFparametrizationdevelopedin 6 0.2
1
Ref. [17] based on the beta distribution as noted above. 0.1
0
0 2 4 6 8 0 2 4 6 8
2 dn/dych 678 √s =e+-e- dn / duch, j12..272.5255 FerIgGie.s6(:poiLnetfst):fFrormagmp-ep¯ntcaotliloisyniofnusnacttio1n.8sTfoerVse[3v8er].alTdhijeetsoelniyd-
45 44 91 OGPeVAL y) max1.12.55 pcuarrvaemserterpizraesteionntainp-[p¯17p]a.raTmheetrdiazsahtieodncduerrviveesdshfroowmtthheeee++--ee−−
3 14 n(ch, j 1 parametrizationitselffortwoenergiesforcomparison. Right:
2 TASSO ymax 1/ 00.7.55 e+-e- jets TtiohnesraDtiovofspfr-ap¯gFmFesnDtrpapptiodictoyrrsehsopwoinndginsygsete+m-ea−tipcadriaffmereetnrcizeas-:
1 14, 44 GeV 0.25 14, 44, 91 GeV acommeoenstrongsuppressionbelowy=4(p≈4GeV/c)for
0 2 4 6 00 0.2 0.4 0.6 0.8 1 all parton energies and substantial reduction at larger frag-
y u
ment rapidities for parton energies with E >80 GeV.
dijet
FIG. 5: Left: Fragmentation functions for three dijet ener-
giesfrome+-e−collisions[18,19]vshadronfragmentrapidity Figure 6 (right) shows the ratio of p-p¯FF data in the
y as in Ref. [17] showing self-similar evolution with parton left panel to the e+-e− FF parametrization for each jet
rapidityymax. Right: Thesamedatarescaledtounit-normal energy (points), revealing systematic differences. The
distributionsonnormalizedrapidityu. Thereisabarelysig- solid curve is tanh[(y − 1.5)/1.7] which describes mea-
nificant evolution with parton energy. The rescaling result sured p-p¯ FFs relative to e+-e− FFs for dijet energies
providesthebasisforasimpleandaccurateparametrization.
below 70 GeV. FF parametrizations for quark and gluon
jets used for p-p collisions in the present study are the
Figure 5 (right) shows the self-similar data in the left e+-e− parametrizationsofRef.[17]andFig.5multiplied
panelrescaledtounitintegralandplottedonscaledfrag-
by the same tanh factor for both quark and gluon FFs.
ment rapidity u with y ≈0.35 (p≈50 MeV/c). The
min
solid curves are corresponding beta distributions with
parameters p and q nearly constant over a large jet en-
V. JET CONTRIBUTIONS TO p-p SPECTRA
ergy interval. The simple two-parameter description is
accurate to a few percent within the E interval 3 GeV
jet
The MB dijet contribution to p spectra and other
(y ≈ 3.75) to 100 GeV (y ≈ 7.25) [17]. FF data t
max max
momentum-space measures should consist of all hadron
forlight-quarkandgluonjetsareparametrizedseparately
fragments from all dijets emerging from a given collision
but the parametrizations for gluon and light-quark jets
systemandappearingwithinacertainangularandp ac-
converge near E = 3 GeV. All minimum-bias jet frag- t
jet
ceptance. Given the jet spectrum and FF parametriza-
ment production can be described with a few universal
tions in the previous section the resulting MB fragment
parameters via introduction of logarithmic rapidities.
FFsforisolateddijetsderivedfrome+-e−collisionsare distributioncanbeobtainedfromaconvolutionintegral.
quitedifferentfromFFsderivedfromp-p¯orp-pcollisions
asnotedbelow. Minordifferencesmightarisefromalter-
native jet reconstruction algorithms, but larger observed A. Minimum-bias fragment distributions
differences suggest that the concept of universality may
not apply to FFs from distinct collision systems. The midrapidity η density of MB dijets from non-
Figure6(left)showsFFsfortendijetenergiesfrom78 single-diffractive (NSD) p-p collision is estimated by
to 573 GeV inferred from 1.8 TeV p-p¯collisions (points)
using eventwise jet reconstruction [38]. The solid curves 1 dσ
f = j ≈0.028 at 200 GeV (8)
are a parametrization. Comparison with the e+-e− FF NSD σ dη
NSD
data in Fig. 5 (left) (e.g. dashed curves in this panel for
2E =6and91GeV)revealsthatasubstantialportion given σ ≈ 36.5 mb [39] and dσ /dη ≈ 1 mb [20, 37]
jet NSD j
of e+-e− dijet FFs at lower fragment momenta may be atthatenergy. Theensemble-meanfragmentdistribution
7
for MB dijets is defined by the convolution integral The apparent difference between calculated and mea-
suredjetspectrafallswithinthesystematicuncertainties
1 (cid:90) ∞ d2σ of Ref. [20]. On the other hand the FF parametriza-
D¯ (y) ≈ dy D (y|y ) j ,(9)
u dσj/dη 0 max pp max dymaxdη tion from Fig. 6 extrapolated down to Ejet < 10 GeV
(y < 5) may overestimate the fragment yield there
max
wheresubscriptudenotesunidentified-hadronfragments. substantially. In any case the measured spectrum hard
GiventhataspectrumhardcomponentH(y )represents component from 200 GeV NSD p-p collisions is quanti-
t
hadron fragments from MB dijets it can be expressed as tativelyconsistentwithadijetcontributionderivedfrom
y H(y ) ≈ (cid:15)f D¯ (y), where (cid:15)(∆η,∆η ) ∈ [0.5,1] is eventwise-reconstructedjets[20,37,40]. Giventhespec-
t t NSD u 4π
the average fraction of a dijet appearing in detector ac- trumhard-componentmodenearpt =1GeV/cthiscom-
ceptance ∆η compared to effective 4π acceptance ∆η parison also establishes that a parton (jet) spectrum ef-
4π
(whichdependsoncollisionenergy). At200GeV(cid:15)≈0.6 fective lower limit Emin = 3.0±0.2 GeV is required by
within detector acceptance ∆η = 2. The spectrum hard 200GeVp-pspectrumdata. Extrapolatingthe(≈power-
component so defined represents the fragment contribu- law) jet spectrum significantly below 3 GeV (e.g. as in
tion from MB scattered parton pairs into acceptance some Monte Carlos) would result in a large overestimate
∆η. It is assumed that for midrapidity jets yt ≈ y (i.e. of H(yt) for fragment momenta below 1 GeV/c.
collinearity) except for low-momentum fragments (e.g.
p <0.5 GeV/c).
t
Fig. 7 (left) shows a surface plot of the Eq. (9) B. Measured spectrum hard components
integrand—D (y|y )d2σ /dy dη—incorporating
pp max j max
p-p¯ FFs from Fig. 6 (left) and the 200 GeV jet pt ThecomparisoninFig.7providesconvincingevidence
(→ ymax) spectrum from Fig. 4 (right). The p-p¯ FFs from a specific 200 GeV NSD p-p SP spectrum that its
are bounded below by ymin ≈ 1.5 (p ≈ 0.3 GeV/c). TCM hard component does indeed represent a MB jet
The jet-spectrum effective lower bound is Emin ≈ 3 fragmentdistribution. Amore-recentstudyrevealswhat
GeV. The z axis is logarithmic to show all distribution canbelearnedfromn andcollision-energydependence.
ch
structure. Figure 8 (left) shows the n evolution of a revised
ch
TCM spectrum hard-component model as derived in
y 5678 D(y), S(y)upmax11010-1 e Du 1 pb (GSeVp/c) 10 RfmorfoeoRfmd.ee[fR3.n2ee[]f3a.0rb[]3ays3sthe].=dowT2onh.n7einrivseacFareiilnagrett.ai2ohdniy(grbhaige-pshlpottawa)tr.ietsWnhtitechishnearsterphdaees-cctetorhamuremlpymoddnoaaedntteaatl
4 shapewasinitiallyheldfixedindependentofn toretain
3 ey), t10-2 simplicity, the revised TCM of Ref. [32] accocmh modates
H(
2 yt -3 all significant variation of spectrum data. Shape varia-
01 (1/f) 10-4 yStpH(y(myta)x/)f trieolantsebde.loIwntaenrpdreatbeodveinthaejmeto-dreelaatreedevciodnetnetxltytthigehtrleyvicsoerd-
0 2 4 6 8 10
2 3 4 5 6 model suggests that as larger event multiplicities are re-
y y
max b quired the underlying jet spectrum is biased to more-
energetic jets with larger fragment multiplicities.
FIG. 7: Left: (Color online) Argument of the pQCD convo-
lutionintegralon(y,y )basedonin-vacuump-p¯ FFs[23]. It is important to note that while the p-p TCM hard
max
The z axis is logarithmic. Right: The spectrum hard com- component was initially modeled by a simple Gaussian
ponent for 200 GeV NSD p-p collisions [30] in the form on yt [30] subsequent detailed analysis of p-p and A-A
y H(y )/f (cid:15) (solid points) compared to calculated mean spectrum data combined [41] revealed that an exponen-
t t NSD
fragment distribution D¯u(y) (dashed) with yb = yt, y or tial tail for the Gaussian on yt is required for the hard-
ymax [23]. The jet spectrum that generated D¯u(y) is defined component model. The corresponding power-law trend
by Eq. (7) rescaled by factor 2/3 (dash-dotted curve). The
on p required by data for 200 GeV p-p collisions is then
t
open boxes are 200 GeV p-p jet-spectrum data [20]. ≈1/p7 as indicated by the dashed line in Figure 8 (left).
t
The power-law exponent evolution with collision energy
Fig. 7 (right) shows the corresponding mean fragment in Figure 8 (right) [32] is compatible with jet spectrum
distribution(cid:15)D¯ (y)asaprojection(dashed)describedby measurements [37]. In contrast, the “power law” of soft
u
Eq. (9) and compared to hard-component data from 200 componentSˆ (m )correspondingto≈1/p13 at200GeV
0 t t
GeVNSDp-pcollisions(solidpoints[30,33])intheform appears to be unrelated to jet physics.
y H(y )/f correspondingtotheirrelationinthetext Figure 8 (right) shows spectrum hard components for
t t NSD
just below Eq. (9). The open boxes are 200 GeV p-p¯jet- arangeofp-pcollisionenergiesfromSPStotopLHCen-
spectrum data from Ref. [20]. The dash-dotted curve S ergies based on the analysis in Ref. [32]. The main vari-
p
is Eq. (7) reduced by factor 2/3 so D¯ (y) from Eq. (9) ation is reduction of the power-law exponent describing
u
(dashed) best accommodates the p-p SP spectrum data the distribution high-p tail (note dashed lines at right)
t
(solid points). which can be compared with the jet-spectrum evolution
8
H(y;n)0tch1100--32 n = 1,n2 = 7 n = 1-7 rH(p) / ts111000---321 0.2 TeV 13 TeV1/pt5.6 n / nhs 0.1 200 GeV p-p p (GeV/c)t0.04.55 200 GeV p-p
a 10-4 1/pt7 10-4 17.3 GeV
-5 0.05 0.4
200 GeV p-p 10
-5 NSD p-p eikonal trend
10 -6
n = 1 10
-6 10-7 1/pt8.5 00 5 10 15 20 25 0.350 5 10 15 20 25
10 2 3 4 1 10 n / Dh n / Dh
y p (GeV/c) s s
t t
FIG. 9: Left: Hard/soft multiplicity ratio n /n (points) vs
h s
FIG. 8: Left: Evolution of the hard-component model over
soft component n consistent with a linear trend (line) [43].
s
seven multiplicity classes of 200 GeV p-p collisions [32] that
Assuming that n represents the density of small-x partici-
s
exhaustsallinformationinhigh-statisticsspectrumdatafrom
pant partons (gluons) and n represents dijet production by
h
Ref. [33]. Right: A survey of spectrum hard components
parton scattering, an eikonal model of p-p collision geometry
for NSD p-p collisions over the currently accessible energy
(analogoustotheGlaubermodelofA-Acollisions)wouldpre-
range from threshold of dijet production (10 GeV) to LHC
dictann1/3 trendfortheratio(dashedcurve). Right: Thep¯
top energy (13 TeV). The curves are defined by parameters s t
trendpredictedbythep-pspectrumTCM(line)andasdeter-
from Table III of Ref. [32] except for the 200 GeV fine solid
mined by direct spectrum integration (points). The hatched
curvesobtainedfromtheTCMcurvesony intheleftpanel.
t bandrepresentstheuncertaintyinsoftcomponentp¯ (dashed
The points are from Refs. [33] (200 GeV) and [32] (13 TeV). ts
line) from extrapolating p spectra to zero momentum.
t
shown in Fig. 4 (right). The close correspondence be-
sityρ¯ welldescribedbyaconstantpluslinearterm. The
tween TCM spectrum hard components and jet spectra s
solid line is a TCM for that quantity derived from the
providesadditionalsupportforinterpretationofthehard
spectrum TCM of Eq. (2). Given the evidence in this
component as a MB jet fragment distribution.
section one may conclude that p¯ variation with ρ¯ is
t s
determined entirely by the jet-related hard component.
C. Hadron yields and p¯ vs p-p multiplicity
t
VI. JET CONTRIBUTIONS TO A-A SPECTRA
TCM analysis of differential spectrum structure as de-
scribed above can be supplemented by statistical mea-
Thep-pTCMprovidesanimportantreferenceforA-A
sures, e.g. integrated yields n or mean angular densi-
x collisions. Itisreasonabletoexpectmore-peripheralA-A
ties ρ¯ within some angular acceptance and ensemble-
x collisions to be described by the same basic model el-
meanp¯. GivenTCMsoftandhardcomponentsinferred
t ements modulo the Glauber model of A-A collision ge-
from differential p spectra the integrated multiplicities
t ometry – dependence on number of participant nucle-
n and n and ensemble means p¯ and p¯ can be com-
s h ts th ons N and N-N binary collisions N , with ν ≡
part bin
puted. Figure2(right)showsaninitialcomparisonfrom
2N /N as the mean number of binary collisions per
bin part
Ref. [30] suggesting a quadratic relation between n and
h participant. However, it has been established that jets
n . A study of recent high-statistics p-p spectrum data
ch arestronglymodifiedinmore-centralA-Acollisions. The
from Ref. [33] establishes more accurate relations.
TCM hard-component model should then be altered to
Figure 9 (left) shows ratio n /n vs soft-component
h s accommodate such changes.
meandensityρ¯ =n /∆ηfortenmultiplicityclasses[42].
s s
n is the integral of hard-component H(y ) appearing
h t
differentially in Fig. 2 (left) and as a running integral in
A. Identified-hadron spectrum evolution
Fig. 1 (right) (excesses above unity at right). The lin-
ear trend for n /n confirms the relation ρ¯ ∝ ρ¯2 [33].
h s h s The TCM for p-p spectra can be extended to describe
Soft-componentdensityρ¯ maybeinterpretedasaproxy
s data from A-A collisions (and identified hadrons) as in
for the density of low-x gluons released from projectile
Ref. [41]. The TCM reference for A-A collisions corre-
nucleons in a p-p collision. p-p spectrum data then re-
sponding to Glauber linear superposition (GLS) of iso-
veal that the number of midrapidity dijets ∝ ρ¯ varies
h lated N-N collisions is based on the p-p result in Eq. (2)
quadratically with number of participant gluons. But in
evaluated for inelastic N-N collisions as represented by
an eikonal collision model the number of gluon-gluon bi-
narycollisionsshouldvaryasthedashedcurverepresent-
ρ¯ (y ) ≈ S (y )+H (y ). (10)
0 t NN t NN t
ingρ¯ ∝ρ¯4/3 asfortheGlaubermodelofA-Acollisions.
h s
Thep-pdataappearinconsistentwiththeeikonalmodel. By hypothesis the TCM soft component in A-A colli-
Figure9(right)showsp¯ vssoft-componentmeanden- sions should scale with N /2 and the hard component
t part
9
shouldscalewithN leadingtotheA-AspectrumTCM more-centralcollisionsasinferredfromconventionalratio
bin
measureR [26]. However, substantialenhancementat
AA
ρ¯0(yt,b) ≈ (Npart/2)SNN(yt)+NbinHAA(yt,b) lower pt is a new feature not revealed by RAA data.
2
ρ¯ (y ,b) ≈ S (y )+νH (y ,b), (11)
Npart 0 t NN t AA t pNN10-2 pions NNp10-2 protons
wAvah-rAeyresc-1uetnbhtsertasaolniftttyiacloblymutapntohdneeinsjtetthi-seranelsaastu1pem0dr-ie1nhdcaitrpodablceoobimnjvepcaotrnioaefnnstttwmudiatyhy. r-(2/N) Sppart011110000----6543 nH 2H0NA0N AGeV2 p0-0p GeVA Aeu-5-.A5 uyt r-(2/N) Spart0p11110000----6543 nH HNANA 200 GeVA A eu-5-A.0yut
)10 )
(ypt10-2 (yppt 10-2 1 pt (GeV/c) 10 10-7 10-7
rN) 0ppart1100--43 HNN rN) part0 1100--43 SNN HNN 2 3 4 yt(p5) 2 3 4 yt(p5)
(2/10-5 200 GeV p-p (2/ 10-5 GLS FIG.11: (Coloronline)Left: Thehardcomponentsofpiony
t
10-6 pions 10-6 protons spectraintheformνHAA(solid)comparedtotwo-component
10-7 200 GeV Au-Au SNN 10-7 200 GeV Au-Au S reference νHNN (dotted). The spectrum hard component
NN forunidentifiedhadrons(80%pions)fromNSDp-pcollisions
2 3 4 5 2 3 4 5 (points) is included for reference. Right: The hard compo-
yt(p ) yt(p ) nentsofprotonytspectraintheformνHAA(solid)compared
to two-component reference νH (dotted). In either case
NN
FIG. 10: (Color online) Summary of pion (left) and proton H (dashed)isthereferenceN-N (≈p-p)hardcomponent,
NN
(right) per-participant-pair single-particle spectra from Au- and dotted curves νH represent a GLS reference.
NN
Aucollisionsat200GeVandfivecentralities[41]. H isthe
NN
hard component (minimum-bias transverse parton fragmen-
The structure of the proton hard component is a sur-
tation)andS isthesoftcomponent(longitudinalnucleon
NN prise. ThemodeforN-N (≈p-p)collisionsappearsnear
fragmentation), both inferred for N-N collisions. The solid
p = 1 GeV/c as for pions but the peak width is sub-
pointsintheleftpanelrepresenttheNSDp-pspectrum[30]. t
stantially less, and there is a significant difference in the
“power-law” slope at high y as described below. How-
Figure 10 shows identified-pion and -proton spectra t
ever, it is most notable that hard-component maximum
(solid curves) for five centrality classes of 200 GeV
values are essentially the same for protons and pions in
Au-Au collisions plotted vs rapidity y (π) with pion
t contrast to the soft components. The similarity of two
mass assumed [41]. The rapidity variable is used in
hardcomponentsonp isthemainmotivationforadopt-
this case simply as a logarithmic momentum variable t
ing y (π)≈ln(2p /m ) as the independent variable [41].
y ≈ln(2p /m ) but with well-defined zero. That choice t t π
t t π
is explained below. Also plotted with the pion spectra is
the unidentified-hadron spectrum for 200 GeV NSD p-p
collisions(points)[30]. TheTCMsoftcomponentsS B. Spectrum ratios for identified hadrons
NNx
(dotted)aredefinedasthelimitsofnormalizedspectrum
dataasN →0,equivalenttothedefinitionforp-pcol- Figure12showsratiosr =H /H forpionsand
part AA AA NN
lisions. The pion soft component is consistent with the protonsfromfivecentralityclassesof200GeVAu-Aucol-
p-p soft component inferred from unidentified hadrons. lisions(curvesofseverallinestyles). Alsoplottedarep-p
The pion hard component H is also consistent with hard-componentdatainratiotothepionH reference
NN NN
the p-p analysis. The proton soft and hard components (points). Several features are notable. The peripheral
havethesamealgebraicstructure,butmodelparameters pion and proton data for 60-80% central collisions indi-
are adjusted to accommodate peripheral Au-Au data as cate no jet modification (r = 1), a result consistent
AA
described below. The dash-dotted curves are GLS refer- with the observation from jet-related 2D angular corre-
ence spectra for ν =1 and 6 (A-A limiting cases). lations that below a sharp transition (ST) in jet charac-
Figure 11 shows data hard components for identified teristics near 50% of the total cross section jets remain
pions and protons (solid) from five centrality classes of unmodified in 200 GeV Au-Au collisions [44].
200GeVAu-AucollisionsintheformνH perEq.(11). AbovetheSTthereisincreasingsuppressionathigher
AA
Also plotted are the hard component for unidentified p , with a saturation value ≈0.2 for both pions and pro-
t
hadrons from 200 GeV NSD p-p collisions (points) and tons in central Au-Au collisions as observed with con-
hard-component models H (dashed). The dotted ventional ratio parameter R . However, because R
NNx AA AA
curves are GLS references corresponding to the five cen- as defined is a ratio of entire spectra including soft com-
trality classes assuming that H = H (i.e. linear ponents the evolution of jet-related H below p = 3
AA NN AA t
scaling with factor ν). Relative to those reference curves GeV/c (y ≈ 3.75) is visually inaccessible. In con-
t
the data exhibit substantial suppression at higher p for trast, ratio r including only hard components reveals
t AA
10
N N
/ HAN10 0-122%00 GeV pAiuo-nAsu / HAN10 200 GeVp rAouto-Ansu rr / pp 1 200 GeV Au-Au rr / pp 1 Hp/Hp 0-12%
A A 0-12%
H H 0-12%
= 200 GeV p-p =
A A
rA 1 rA 1 60-80%
60-80% 60-80%
60-80%
Sp/Sp
-1 -1 -1 -1
10 10 10 10
2 3 4 5 2 3 4 5 0 5 10 2 3 4 5
y y pt (GeV/c) yt
t t
FIG. 13: Left: Proton/pion spectrum-ratio data vs p
FIG. 12: Hard-component ratios r (y ) for five centrali- t
AA t
for 0-12% central (solid points) and 60-80% central (open
tiesof200GeVAu-Aucollisions(curves)forpions(left)and
points) 200 GeV Au-Au collisions [45] compared to curves
protons (right) [41]. Also shown are NSD p-p data (points,
(solid and dashed respectively) generated by the correspond-
unidentified hadrons) compared to hard component H .
NN
ing spectrum TCMs for identified hadrons described above
and in Ref. [41]. The curves were not fitted to those data.
Right: Curves from the left panel plotted vs y (bold solid
large enhancements of jet-related hadron yields at lower t
and dashed) compared to ratios determined separately from
p tightly correlated on centrality with suppressions at
t soft components (bold dotted) common to both centralities
higher pt. But whereas enhancement for pions extends and hard components (dash-dotted) for the individual cen-
below0.5GeV/c(yt =2)enhancementforprotonspeaks tralities.
near 2.5 GeV/c (y ≈ 3.6), and below p = 1 GeV/c the
t t
protondataforallcentralitiesremainconsistentwiththe
N-N reference(r =1)withinthedetectoracceptance. ratio data reveals that the data peak is dominated by
AA
These jet-related hard-component trends have impor- the jet-related hard component. In contrast, the ratio
tant consequences for other (e.g. ratio) measures and for peak for peripheral collisions is dominated by the soft
the flow narrative. In particular, whereas conjectured component; the hard component only influences the pe-
radial flow should boost all hadron species to higher p ripheralratioabove7GeV/c. Notethattheratioofhard
t
proportional to hadron mass the trends in Fig. 12 show to soft hadron production in Au-Au collisions increases
that while protons appear boosted to higher p relative withcentralityaccordingtoparameterνwithnojetmod-
t
tothep-phard-componentmodepionsmovetolowerp . ification (5-fold increase) and by an additional factor 3
t
Figure13(left)showsaconventionalratiocomparison due to jet modification [46]. Thus, from peripheral to
ofprotonandpionspectra–theproton-to-pionratio–for central Au-Au collisions the hard/soft ratio increases by
twocentralitiesof200GeVAu-Aucollisions(points)[45]. about 3×5 = 15-fold. Although peaks in the left panel
The curves are derived from a TCM for Au-Au spectra appear similar and suggest a common mechanism this
including hard-component modification in more-central TCM analysis reveals that they represent distinct soft
collisions [23] that describes the spectrum evolution in and hard hadron production mechanisms. Comparisons
Fig. 11. Those curves were not fitted to the ratio data. of spectrum ratio data with in-vacuum e+-e− FFs and
Figure 13 (right) shows the curves in the left panel re- nonjet(soft)recombinationorcoalescencehadronization
plotted on y to improve visibility of the low-p region. models as in Ref. [45] are likely misleading.
t t
Since the TCM soft and hard components contributing
to those spectrum ratios are known their ratios can be
plotted separately (dotted and dash-dotted curves re- C. Hadron yields and p¯t vs A-A centrality
spectively). The soft component by hypothesis does not
vary with A-A centrality. The hard-component ratio for Justasforp-pcollisionsdifferentialp spectrumstruc-
t
peripheralA-A(andthereforeN-N)collisionsisunityat tureforA-Acollisionscanbesupplementedbytrendsfor
the mode (y = 2.7, p ≈ 1 GeV/c). It falls off on either integrated spectrum yields and p mean values. For in-
t t t
side of the mode because of the peak width difference stance,hadronyieldsvsp-pmultiplicitywerediscussedin
but increases for larger y because the proton power-law Sec. VC where observed dijet production appears incon-
t
exponentissmaller(thespectrumhigh-p tailisharder), sistent with the eikonal approximation. The centrality
t
all consistent with the discussion of Fig. 11 above. dependence of p -integral hadron yields (or mean angu-
t
The hard-component ratio maximum for central colli- lar densities) in A-A collisions is similarly of interest.
sionshasasubstantiallylargervalueandthemodeonp Figure 14 (left) shows integrated unidentified-hadron
t
shiftsupto3GeV/c. Protonsarestronglyenhancedrela- densities in the form (2/N )dn /dη (solid points) re-
part ch
tivetopionsabovetheN-N modebutpionsarestrongly constructed from spectrum data in Fig. 10 [41]. Due to
enhanced relative to protons below the mode, a feature multiplicity fluctuations the most-central point of such
concealed by the conventional R ratio and plotting a trend is typically high by an amount controlled by the
AA
format. Comparison with the solid curve matching the detectorangularacceptance: theexcessislessforalarger