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 3. e.g. see Proc. Int’l Wks. Quark Gluon Plsama Signatures, eds. V.Bernard, et al., (Editions Frontieres, Gif-sur-Yvette, France, 1991). 4. F. 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