A brief review is made of the present situation of hadron-hadron and
hadron-nuclei total elastic and inelastic cross sections at high energiesComment: 7 page

Giacomelli, G.

Giacomelli, R.

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A brief review is made of the present situation of 

hadron-hadron and hadron-nuclei total elastic and inelastic cross-sections at high energies

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IL NUOVO CIMENTO Vol. 24 C, N. 4-5 Luglio-Ottobre 2001Hadron-hadron and hadron-nuclei collisions at high energies(∗)G. Giacomelli and R. GiacomelliDipartimento di Fisica dell’Universita` di Bologna e INFN - I-40127 Bologna, Italy(ricevuto il 28 Ottobre 2000; approvato il 12 Febbraio 2001)Summary.— A brief review is made of the present situation of hadron-hadron andhadron-nuclei total elastic and inelastic cross-sections at high energies.PACS 13.85.Dz – Elastic scattering.PACS 13.85.Fb – Inelastic scattering: two-particle final states.PACS 13.85.Hd – Inelastic scattering: many-particle final states.PACS 01.30.Cc – Conference proceedings.1. – IntroductionIn the 1960’s-1980’s high-quality secondary beams became available at proton syn-chrotrons of increasing energies (PS, AGS, IHEP, FNAL, SPS). The secondary chargedhadron beams contained the six stable or quasi stable charged particles π±, K±, p, p.The main experimental lines of research were: i) total hadron-hadron (hh) cross-sectionmeasurements at high energies (plab > 20 GeV/c); ii) elastic hh scattering measurements;iii) measurements of absorption cross-sections of hadrons in nuclei (as byproducts of hhtotal cross-section measurements); iv) hadron production at forward angles in p-nucleicollisions, and v) inelastic hh collisions [1-5]. In some high-intensity beams many particlesearches were made, which also lead to the study of d, t and He3 production [6].In order to reach higher energies it became necessary to build hadron colliders. Thefirst was the ISR pp and pp collider at CERN, which allowed to reach c.m. energiesbetween 22 and 63 GeV; then the SppS collider at CERN allowed pp collisions from 600to 900 GeV; finally the Fermilab Tevatron collider allowed pp collisions up to 1.8 TeV.The first experiments performed at the ISR were relatively simple dedicated experi-ments, like those for total cross-section and elastic scattering measurements, and singlearm spectrometers for the study of inelastic collisions [7, 8]. Then followed general pur-pose detectors: the SFM at the ISR [9], the general purpose detectors UA1 and UA2 and(∗) Paper presented at the Chacaltaya Meeting on Cosmic Ray Physics, La Paz, Bolivia,July 23-27, 2000.c© Societa` Italiana di Fisica 575576 G. GIACOMELLI and R. GIACOMELLIexperiment UA4 at the SppS collider, and finally the general purpose detectors CDF, D0and the specialized experiments E710, F8 at Fermilab [10].The highest energies were and are still obtainable only with cosmic rays. We shalldiscuss total cross-sections at high energies, the high energy low-pt parameters and somefeatures of inelastic collisions [11,12].2. – Hadron-hadron total cross-sectionsAt fixed target accelerators (AGS, IHEP, FNAL) the total cross-sections were mea-sured with the transmission method, with relative precisions smaller than 1% and sys-tematic scale errors of about 2%. The measurements of the total cross-sections at the ppand pp colliders required the development of new experimental techniques: the scatteringof particles was measured at very small angles, with detectors positioned in re-entrantcontainers (“Roman pots”) located very close to the circulating beams. The combi-nations of statistical and systematic uncertainties are ≥ 10%. Figure 1 summarizes thepresent status of high energy total cross-section measurements: for Ecm =√s > 3.4 GeVall total hh cross-sections decrease, reach a minimum and then increase with increasingenergy (the K+p total cross-section was already increasing at Serpukhov energies [1]).Moreover the differences between the cross-sections xp and xp decrease with increasingenergy [5].There is not a unique interpretation for this rise, though in many QCD-inspiredmodels it seems to be connected with the increase of the number of minijets and thus tosemi-hard gluon interactions.Most of the high energy elastic and total cross-section data have been usually inter-preted in terms of Regge Poles, and thus in terms of Pomeron exchange. Even if thePomeron was introduced long time ago we do not have a consensus on its exact definitionand on its detailed substructure. Some authors view it as a “gluon ladder”.Future experiments on hadron-hadron total cross-sections remain centered at theFermilab Collider (for pp). The near future will rely on the BNL-RICH Collider, andlater, on the LHC proton-proton and heavy-ion Collider at CERN. Large-area cosmicray experiments may be able to improve the data in the ultrahigh energy region [12].3. – Hadron-hadron elastic scatteringThe differential cross-section for the elastic scattering of unpolarized particles fromunpolarized targets has a simple structure in the high energy region. It depends ontwo variables: the energy and an angular variable, which is usually chosen to be thesquare of the four momentum transfer t. The energy dependence is of the ln s type. Theangular distribution may be divided in four regions: i) the Coulomb region for |t| < 0.001(GeV/c)2; ii) the Coulomb-nuclear interference region for 0.001 < |t| < 0.01 (GeV/c)2;measurements in this region yield information on the ratio ρ of the real to the imaginarypart of the forward scattering amplitude; iii) the nuclear diffraction region proper for0.01 < |t| < 0.5 (GeV/c)2; here the most important parameter is the slope B, or theslopes bi, of the diffraction pattern; iv) the large angle region for |t| > 0.5 (GeV/c)2: forEcm ≤ 100 GeV it is characterized by a dip-bump structure which resembles that fromdiffraction from an opaque disc. Most of these features are observed in the pp and ppelastic scattering angular distributions at Ecm = 53, 546 and 1400 GeV, see fig. 2.One usually defines the following high energy scattering parameters: i) the total cross-section, σt; ii) the slope B of the differential elastic nuclear cross-section dσ/dt = AeBt,HADRON-HADRON AND HADRON-NUCLEI ETC. 577Fig. 1. – Compilation of total cross-sections (a) for high-energy hh scattering and (b) for higherenergy pp and pp, including cosmic ray measurements; the solid line is a fit; the uncertaintyregion is delimited by dashed lines.Fig. 2. – Differential elastic cross-sections for pp and pp (a) at 53 and 546 GeV, (b) at 1.8 TeV.578 G. GIACOMELLI and R. GIACOMELLIFig. 3. – Pictorial description of inelastic, small pt processes with characteristic rapidity distri-butions. P indicates Pomeron exchange. (a) Fragmentation of the beam particle a; (b) frag-mentation of the target b; (c) double fragmentation of a and b; (d) central collision.at |t|  0.1 (GeV/c)2; iii) the ratio ρ = (ReA/ImA)t=0; iv) the opacity O = 2σel/σt.At very high energies σt, B and O rise with energy, while ρ is slightly positive. Fromthe behaviour of these parameters there emerges the picture of a proton which becomesbigger (larger B) and more opaque (larger O) as the energy increases. At the highestenergy O  0.48, which is still smaller than the black disk value of 1.4. – Hadron-hadron inelastic processesFigure 3 shows pictorially various inelastic processes at low-pt: single and doublediffraction dissociation and inelastic processes; these are the dominant processes withthe largest cross-sections, concentrated in particular in the very forward angular region:this is the region which is most important for cosmic ray experiments.At high energies the total pp cross-section may be written asσt = σel + σinel = σel + σsd + σsd + σdd + σnd ,(1)where σel is the elastic cross-section, σsd is the single diffractive cross-section when theincoming proton fragments into a number of particles, σsd is the single diffractive cross-section for the fragmentation of the antiproton (at high energies σsd = σsd). σdd isthe double diffractive cross-section, σnd is the non-diffractive part of the inelastic cross-section (fig. 3). The elastic, single diffractive and double diffractive processes give riseto low multiplicity events with particles emitted in the very forward region in the c.m.system. The non-diffractive cross-section is the main part of the inelastic cross-section;it gives rise to high multipliciy events and to particles emitted at all angles. Most of thenon-diffractive cross-section concerns particles emitted with low transverse momentum(low-pt physics) with properties which change slowly with c.m. energy (ln s physics).A small part of the non-diffractive cross-section is due to central collisions among thecolliding particles and gives rise to high pt jets of particles emitted at relatively largeangles (large pt physics). The contribution of jet physics increases with c.m. energy.In fig. 4a, the average charged multiplicities in pp and pp collisions are shown vs.√s.The data may be fitted to a power law of ln s:n = A+B ln s+ C ln2 s  3.6− 0.45 ln s+ 0.20 ln2 s .(2)HADRON-HADRON AND HADRON-NUCLEI ETC. 579Fig. 4. – (a) Average charged multiplicities n for pp and pp collisions vs. Ecm =√s. (b) Averagenumber of π± K±, p and p produced in pp collisions up to Ecm = 63 GeV.At√s = 1.8 TeV are produced on average 40 charged and 20 neutral particles. Figure 4bshows the average number of π±, K±, p and p produced in pp collisions up to√s 100 GeV. Pions are the dominantly produced hadrons. Hadrons are mainly produced atlow transverse momenta. The average pt increases slowly with√s: it is 〈pt〉  0.36 GeV/cin 20 <√s < 100 GeV; then it increases slowly up to  0.46 GeV/c at√s = 1.8 TeV. Thesimplest interpretation of these features is in terms of thermodynamic models: hadronsare emitted from a region with a temperature T  130–200 MeV. QCD, at present,cannot be used to calculate the data at low pt, because the strong coupling constant islarge and perturbative methods cannot be used. Therefore one has to use models. Hardcollisions can instead be calculated by perturbative QCD.5. – Hadron-nucleus and nucleus-nucleus collisionsUsually, as byproducts of hh total cross-section measurements, the absorption cross-sections of π±, K±, p and p on various nuclei (Li, C, Al, Cu, Sn, and Pb) were measuredat incident lab momenta up to 280 GeV/c [2, 4, 11]. Most absorption cross-sectionsdecrease slowly for plab up to  50 GeV/c; for higher plab they are almost constant.The data at each energy were fitted to the simple expressionσa(A) = σ0Aα ,(3)where A is the atomic weight of the target nucleus. Examples are shown in fig. 5a atthree lab momenta for three different incoming hadrons. For all incident particles exceptantiprotons, the value of σ0 increases by up to 10% as the incident plab increases from 60to 280 GeV/c, with the largest increase for K+. For p, σ0 decreases with increasing plab.Figure 5b shows the parameters σ0 and α vs. the corresponding hp total cross-section:σ0 rises monotonically with σhp; the values of α are consistent with α approaching 0.67for large values of σhp as would be expected for an opaque nucleus.580 G. GIACOMELLI and R. GIACOMELLIFig. 5. – (a) Absorption cross-sections vs. atomic weight; the solid lines are fits to eq. (3).(b) The parameters σ0 and α vs. the corresponding hp total cross-sections, σhp.The fragmentation cross-sections of various nuclei were measured at many energiesusing nuclear track detectors, which yield high-resolution measurements of the restrictedenergy loss. This arises from the relatively low energy required to break the polymericbonds of the detectors and because fluctuations due to energetic δ-electrons do not con-tribute to the latent track formation. The radiation damage along the path of an incomingnucleus may be developed to microscope-visible cones by chemical etching. Figure 6ashows the charge distribution obtained with 200 GeV/nucleon S16+ ions and their frag-ments produced in a Cu target [13]: notice the good charge resolution and the absenceof nuclei with fractional charges. The cross-sections in fig. 6b are relative to fragmentsof 158 GeV/nucleon Pb82+ ions in a target with A = 11.5 with a variation of atomicnumber ∆Z = 1–7 with respect to the Z = 82 of the incoming ions.Fig. 6. – (a) Charge distribution of 200 GeV/nucleon S16+ ions and their fragments [13].(b) Cross-sections in a target A = 11.5 of 168 GeV/nucleon Pb82+ ions into nuclear frag-ments for ∆Z ranging from 1 to 7; the open and black points refer to two different computingmethods.HADRON-HADRON AND HADRON-NUCLEI ETC. 5816. – Conclusions. PerspectivesA wealth of experimental information has been obtained since the early 1960’s on high-energy hadron-hadron and hadron-nucleus cross-sections, starting with simple equip-ments and proceeding to more complex apparata and better beams.The higher energy data coming from collider experiments have large systematic uncer-tainties, mainly connected to the poor knowledge of the collider luminosity, the difficultyof measuring with some precision the single and double diffraction cross-sections, etc.Most of the information on hadron-hadron collisions was interpreted in terms of phe-nomenological models. Much more work is needed to interpret and systemize the avail-able data, since only the small part of the cross-section corresponding to large transversemomenta may be interpreted in terms of QCD.Few and not too precise data are available at very low pt and very small angles, whichis the region where more interest lies for cosmic rays. The information is here codified inMonte Carlos, which are becoming progressively more complicated. The Monte Carlosinclude hadron-nucleus collisions (for which the data are much less abundant than forhh collisions); hadron-nucleus effects are mainly interpreted in the context of the Glubermodel [14].Nucleus-nucleus data are even less abundant, and the Monte Carlos have extra com-plications coming from the used models [14].In the near future the RICH collider at BNL should provide data on nucleus-nucleuscollisions. In the future the different experiments at the LHC collider should providedata on hh, hadron-nuclei and nuclei-nuclei collisions at much higher energies.∗ ∗ ∗We thank many colleagues for their collaboration, for many discussions and for ex-planations of Cosmic Ray Monte Carlos. We thank Ms L. De Angelis for typing themanuscript.REFERENCES[1] Allaby J. V. et al., Phys. Lett. B, 30 (1969) 500; Denisov S. P. et al., Phys. Lett. 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Hadron-hadron and hadron-nuclei collisions at high energies

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