Hard scattering and jets--from p-p collisions in the 1970's to Au+Au collisions at RHIC

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by  M. J. Tannenbaum

EPJ manuscript No.
(will be inserted by the editor)
Hard scattering and jets—from p-p collisions in the 1970’s to
Au+Au collisions at RHIC.
M. J. Tannenbaum a
Brookhaven National Laboratory
Upton,NY 11973-5000 USA
5
0 Received: date/ Revised version: date
0
2 Abstract. Hardscatteringinp-pcollisions,discoveredattheCERNISRin1972bythemethodofleading
particles,provedthatthepartonsofDeeplyInelasticScatteringstronglyinteractedwitheachother.Further
n
a ISR measurements utilizing inclusive single or pairs of hadrons established that high pT particles are
J producedfrom stateswith tworoughly back-to-backjetswhich aretheresult ofscattering ofconstituents
ofthenucleonsasdescribedbyQuantumChromodynamics(QCD),whichwasdevelopedduringthecourse
5
of these measurements. These techniques, which are the only practical method to study hard-scattering

1 andjetphenomenainAu+Aucentralcollisions,arereviewed,withapplicationtomeasurementsatRHIC.
v
2
0 1 Introduction systemas a function of the transversemomentum p and
T
0 c.m. energy √s has a characteristic shape (Fig. 1). There
01 In 1998,at the QCD workshopin Paris,Rolf Baier asked is an exponential tail (e−6pT) at low pT, which depends
5 me whether jets could be measured in Au+Au collisions very little on √s. This is the soft physics region, where
0 because he had a prediction of a QCD medium-effect on the hadrons are fragments of ‘beam jets’. At higher pT,
/ color-chargedpartonstraversingahot-dense-mediumcom- there is a power-law tail which depends very strongly on
x
posed of screened color-charges [1]. I told him [2] that √s.This is the hard-scatteringregion,where the hadrons
e
- there was a generalconsensus [3] that for Au+Au central
cl collisions at √sNN = 200 GeV, leading particles are the
u only way to find jets, because in one unit of the nomi-
n nal jet-finding cone, ∆r = p(∆η)2+(∆φ)2, there is an 2]) 102 CDF 1800 GeV
v: estimated π 1 dET 375 GeV of energy !(!) /c (a) 630 GeV
Xi The good×n2eπwsdηwa∼s that hard-scattering in p-p col- GeV 10 UA1 950000 GGeeVV
ar ltihseiomnsethhaoddboefelenaddiinscgopvearretdiclaets,tbheefoCreEtRhNea1dSvRen[t4o,5f,Q6C] bDy, mb/( 1 200 GeV
STAR 200 GeV
anditwasprovedbysingleinclusiveandtwo-particlecor- [
relation measurements in the period 1972-1982 that high 3p 10 -1 ISR 53 GeV
pT particles are produced from states with two roughly /d 23 GeV
-2
back-to-backjetswhicharetheresultofscatteringofcon- 3sd10
stituents ofthe nucleonsasdescribedbyQCD,whichwas
E
-3
developed during this period. The other good news was
10
that the PHENIX detector had been designed to make
suchmeasurementsandcouldidentifyandseparatedirect -4
10
single γ and π0 out to p 30 GeV/c.
T
≥ -5
10
h++ h-
-6
2 Systematics of single particle inclusive 2
10
production in p-p collisions.
0 2 4 6 8
Inp-pcollisions,theinvariantcrosssectionfornonidenti-
p (GeV/c)
fiedcharge-averagedhadronproductionat90◦ inthec.m. T
a Research supported by U.S. Department of Energy, DE- Fig. 1. Ed3σ/d3p vs. pT at mid-rapidity as a function of √s
AC02-98CH10886. in p p collisions.
−
2 M. J. Tannenbaum:Hard scattering—from p-pcollisions in the1970’s to Au+Aucollisions at RHIC
are fragments of the high p QCD jets from constituent- thatit tookquite sometime for x scalingwiththe value
T T
scattering. of n = 5.1 0.4, consistent with QCD, to be observed
±
The hard scattering behavior for the reactionp+p at the CERN-ISR [12]. This was due to the so-called ‘in-
→
C+X is easy to understand from general principles pro- trinsic’transversemomentum of partons,the “k effect”,
T
posed by Bjorken and collaborators [7,8] and subsequent which causes a transverse momentum imbalance of the
authors [9,10]. Using the principle of factorization of the outgoing parton-pairs from hard-scattering, making the
reactionintopartondistributionfunctionsfortheprotons, jets not exactly back-to-back in azimuth. This was dis-
fragmentation functions to particle C for the scattered covered by experimenters [13] and clarified by Feynman
partons and a short-distance parton-parton hard scatter- and collaborators [14]. The “k -effect” acts to broaden
T
ing cross section, the invariantcross section for the inclu- the p spectrum, thus spoiling the x -scaling at values
T T
sive reaction,where particle C has transversemomentum of p 7.5 GeV/c, at the ISR, and totally confusing the
T
≤
p nearmid-rapidity,wasgivenbythegeneral‘x -scaling’ issueatfixedtargetincidentenergiesof200–400GeV[15,
T T
form [9], where x =2p /√s: 16]duetothetherelativelysteepp spectrum(seeFig.1),
T T T
whichresults ina relativelystrongbroadeningeffect.It is
d3σ 1 2p 1 also evident from Fig. 1 that hard-scattering, which is a
T
E = F( )= G(x ). (1)
dp3 pn √s √sn T relativelysmallcomponentofthepT spectrumat√s 20
T ∼
GeV, dominates for p 2 GeV/c by nearly 2 orders of
T
≥
The cross section has 2 factors, a function F (G) which magnitude at RHIC c.m. energies compared to the soft
‘scales’, i.e. depends only on the ratio of momenta; and a physics e−6pT extrapolation [17].
dimensioned factor, p−n (√s−n), where n gives the form The status of theory and experiment, circa 1980, is
T
ofthe force-lawbetween constituents.For QEDor Vector summarizedbythefirstmodernQCDcalculationandpre-
Gluon exchange [8], n = 4, and for the case of quark- diction for high p single particle production in hadron-
T
meson scattering by the exchange of a quark [9], n=8. hadron collisions, in agreement with the data. The calcu-
When QCD is added to the mix [10], pure scaling breaks lation by Jeff Owens and collaborators [18] included non-
down and n varies according to the x and √s regions scaling and initial state radiation under the assumption
T
used in the comparison, n n(x ,√s). that high p particles are produced from states with two
T T
→
roughly back-to-back jets which are the result of scatter-
ing of constituents of the nucleons (partons). The overall
22 p+p hard-scattering cross section in “leading logarithm”
10 CDF 1800 GeV
pQCDisthesumoverpartonreactionsa+b c+d(e.g.
(b) 630 GeV →
2]V/c)1020 UA1 952000000 GGGeeeVVV egn+ergqy→√sˆg=+√qx)1xat2sp.arton-parton center-of-mass (c.m.)
e 18
G10
mb/(1016 ISSTRAR 2 0503 GGeeVV dx1dxd23dσcosθ∗ = 1s Xfa(x1)fb(x2)π2αx2s1(Qx22)Σab(cosθ∗)
3 [ 23 GeV ab (2)
p 14
d10 where f (x ), f (x ), are parton distribution functions,
/ a 1 b 2
the differential probabilities for partons a and b to carry
3s
Ed1012 momentum fractions x1 and x2 of their respective pro-
tons (e.g. u(x )), and where θ∗ is the scattering angle in
3 2
6.eV)1010 tchesespaanrtgounla-pradritsotnricb.umti.osnyss,teΣma.b(Tchoesθc∗h)a,raacntdertihsteiccsouubpplirnog-
/Gs 108 h++ h- cdoicntsitoannst,ofαQs(CQD2)[1=9,122205π].ln(Q2/Λ2), are fundamental pre-
( 2
6 The difficulty in finding jets in 4π calorimetersat ISR
10
energies or lower gave rise to many false claims, creating
-3 -2 -1 skepticism during the period 1977-82 [21], although jet
10 10 10 1
effectsaresimply anddirectly visibleusing 2-particlecor-
x
T relations of high p particles. A ‘phase change’ in belief-
T
in-jetswasproducedbyoneUA2eventatthe1982ICHEP
Fig. 2. √s(GeV)6.3 Ed3σ/d3p vsxT =2pT/√s. inParis[22],which,togetherwiththefirstdirectmeasure-
× ment of the QCD constituent-scattering angulardistribu-
tion, Σab(cosθ∗) (Eq. 2), using two-particle correlations,
We now know that the characteristic √s dependence presented at the same meeting (Fig. 3), gave universal
of the high p tail is simply explained by the x scal- credibility to the pQCD description of high p hadron
T T T
ing of the spectrum (with n = 6.3, valid in the range physics[23,24,25].The measurementofjets andjet prop-
0.01 x 0.1 relevant to the early RHIC measure- erties via 2-particle correlations was a key element in un-
T
≤ ≤
ments (see Fig.2)) [11]. However,it is worthwhile to note derstanding the details of high p production.
T
M. J. Tannenbaum:Hard scattering—from p-pcollisions in the1970’s to Au+Aucollisions at RHIC 3
Fig. 3. a) (left 3 panels) CCOR measurement [22,26] of polar angular distributions of π0 pairs with net pT < 1 GeV/c at
mid-rapidity in p-p collisions with √s=62.4 GeV for 3 different values of ππ invariant mass Mππ. b) (rightmost panel) QCD
predictions for Σab(cosθ∗) for theelastic scattering of gg,qg,qq′, qq, and qq with αs(Q2) evolution.
3 Almost everything you want to know about measured. In Fig. 4a,b, the azimuthal distributions of as-
jets can be found with 2-particle correlations. sociated charged particles relative to a π0 trigger with
transversemomentump >7GeV/careshownforthree
Tt
Many ISR experiments provided excellent 2-particle cor- intervals of associated particle transverse momentum pT.
relation measurements [27]. The CCOR experiment [28] In all cases, strong correlation peaks on flat backgrounds
wasthefirsttoprovidechargedparticlemeasurementwith are clearly visible, indicating the di-jet structure which
is contained in an interval ∆φ = 60◦ about a direction
±
towards and opposite the to trigger for all values of asso-
ciated p (> 0.3 GeV/c) shown. The width of the peaks
T
about the trigger direction (Fig. 4a), or opposite to the
trigger (Fig. 4b) indicates out-of-plane activity from the
individualfragmentsofjets.Thefactthatthewidth(∆φ)
oftheawaypeak(Fig.4b)doesnotdecreaseinproportion
to j /p , where j is the mean transverse momen-
T T T
∼h i h i
tumofjetfragmentation,isindicativeofthe factthatthe
angular width of the away peak is dominated by the jet
acoplanarityduetok ,andnotbythetransversemomen-
T
tum of fragmentation, j .
T
The same side peak shows the important property of
“trigger bias” [29] on which the method of leading parti-
cles is based: due to the steeply falling power-law trans-
verse momentum spectrum of the scattered partons, the
inclusive single particle (e.g. π) spectrum from jet frag-
mentation is dominated by fragments with largez, where
z = p /p is the fragmentation variable. The trigger
Tπ Tq
biaswasdirectlymeasuredfromthesedatabyreconstruct-
ing the trigger jet from the associated charged particles
Fig. 4. a,b) Azimuthal distributions of charged particles of with p 0.3 Gev/c, within ∆φ= 60◦ from the trigger
transverse momentum pT, with respect to a trigger π0 with T ≥ ±
particle,usingthealgorithmp =p +1.5 p cos(∆φ),
pTt 7 GeV/c, for 3 intervals of pT: a) for ∆φ = π/2 rad Tjet Tt P T
≥ ± where the factor 1.5 correctsthe measured chargedparti-
about the trigger particle, and b) for ∆φ = π/2 about π
± cles for missing neutrals. The measured z = p /p
radians (i.e. directly opposite in azimuth) to the trigger. The trig Tt Tjet
distributions for 3 values of √s (Fig. 5) show the “unex-
trigger particle is restricted to η < 0.4, while the associated
| | pected”[30]propertyofx scaling.Thejetproperties,j
charged particles are in the range η 0.7. T T
| |≤ andk were also measuredfromthese data [31], with the
T
resultthat j is a constant,independent of p and√s,
h Ti Tt
full anduniformacceptance overthe entireazimuth, with asexpectedforfragmentation,butk increaseswithboth
T
pseudorapidity coverage 0.7 η 0.7, so that the jet p and √s, suggestive of a radiative origin, rather than
− ≤ ≤ Tt
structure of high p scattering could be easily seen and an ‘intrinsic’ origin due to confinement.
T
4 M. J. Tannenbaum:Hard scattering—from p-pcollisions in the1970’s to Au+Aucollisions at RHIC
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