europhysics BULLETIN OF THE EUROPEAN PHYSICAL SOCIETY news J.A. Volume 19 Number 11/12 November/December 1988 The EMC Effect P.B. Renton, Oxford (Nuclear Physics Laboratory, University of Oxford) The scattering of high energy muons by nuclei shows an unex­ pected dependence upon nuclear size, suggesting that the con­ stituent quarks and gluons may be shared between nucleons. In our attempts to understand the ele­ ference between the electron and the to describe the many body gas-like mentary structure of matter, the idea of proton or neutron, allows the large dif­ system of nucleons which make up the unravelling successive layers of sub­ ference in the scale of the atom ( 10-10 nucleus. structure has been of central impor­ m) and that of the nucleus (< 10-14 m) to The size of the nucleus (or, more tance. Each new layer corresponds to an be understood. strictly, of its charge distribution) and increasingly smaller distance scale, and Theoretically, electromagnetic inter­ that of the proton have been determined it is assumed that once the physical pro­ actions can be calculated, to remarkable by measuring the elastic scattering of perties of the layer in question are under­ precision, using the relativistic field energetic electrons by them. The me­ stood then those of the previous layer theory of quantum electrodynamics chanism for this process is shown in Fig. can be accounted for. This article is con­ (QED). Because a is small, a perturbative 1. The incident electron interacts with cerned with the subtle interplay bet­ expansion in powers of a can be made the target by the exchange of a photon. ween two layers in this hierarchy: the and only the first few terms need to be The photon in such an interaction is vir­ nucleon structure of the nucleus and the calculated. Knowledge of the detailed tual (i.e. has non-zero mass). If E and P quark structure of the nucleon. structure of the nucleus is unimportant are the energy and momentum of the The main experimental method which in accounting for most atomic proper­ photon respectively, then its relativisti- has been used in probing the sub-struc­ ties. Turning this around, it means that cally invariant mass squared is negative ture of matter is the measurement of the little can be learnt about nuclear sub­ and is given by E2 - P2 = — Q 2, so that scattering angle distribution of a beam structure from the study of atoms. Q2 is a positive quantity. The distance of particles incident on the target being scale down to which the structure of the investigated. If the incident beam is Quark Structure of Matter target is revealed depends on the value composed of electrons, then (at current­ Understanding the nucleus in terms of of Q2. From Heisenberg's Uncertainty ly accessible laboratory energies) the its components as against the atom is Principle, the distance scale resolved is scattering is predominantly by the elec­ much more complicated. The consti­ roughly given by tromagnetic interaction. This interaction tuent protons and neutrons (generically Δz  h /Q2 = 0.2 GeV.fm/ Q2· (1) is well understood and hence the resul­ referred to as nucleons) have similar ting scattering distributions can be con­ masses and the inter-nucleon separa­ Contents verted into a measurement of the charge tion ( 2fm  2x-15 m) is not much density distribution of the target. Histo­ larger than the radius of the nucleon ( The EMC Effect 129 rically, the idea that an atom of atomic 0.8 fm). The nucleus is confined by the Quark Gluon Plasma number Z is composed of a central strong force, which can be envisaged (at Research with Ultra- nucleus of charge +Ze (where e is the least for some purposes) as being due to relativistic Heavy Ions 133 charge of the proton), surrounded by Z the exchange of pions (and other strong­ Particle Accelerators in orbiting electrons each of charge -e, ly interacting particles) between the the Future 137 stems from the classical experiments of nucleons. However, in the region of mo­ Accretion Disks and Rutherford. In the scattering of α-parti- mentum transfers involved in nuclear Magnetic Fields 142 cles (produced by radioactive decays) binding forces, the strong interaction is on thin film targets it was observed that not well understood. The effective Seminar on International many more α-particles were scattered strong interaction coupling constant is Research Facilities 143 through large angles than were expec­ large in this regime, so that perturbative Nobel Prize 1988 143 ted. The relative weakness of the elec­ methods cannot be used. Thus we are New Members of EPS 143 tromagnetic coupling constant (α  left with empirical models, each with a Index for 1988 144 1/137), together with the large mass dif­ somewhat limited range of applicability,

Published by the European Physical Society: 10 issues per year. © 1988. Reproduction rights reserved. ISSN 0531-7479

129 mass energy of the final state hadrons), can easily be shown that then the interaction probability for the x = Q2/(W2 - M2 + Q2), (3) incoming electron can be expressed (to where MN is the nucleon mass. The a good approximation) as variables x and Q2 can be measured for d2 /dQ2dW = α2(K/Q4) F2 (Q2,W) (2) each event from a knowledge of the where K is a known kinematic function. momentum of the incident and scat­ A free photon is massless (i.e. has E = P tered electrons alone. The quark density and so Q = 0), and the 1/Q4 term is a distribution q(x) and its momentum dis­ factor which expresses the suppression tribution xq(x) can thus be built up from which arises when the photon fluctua­ measurements of many such collisions. tes to a mass value of Q. A further surprise was in store when The construction of the two-mile long the results were analysed. The total Fig. 1 — Principal mechanism in the scat­ Stanford Linear Accelerator in the USA momentum fraction carried by the pro­ tering of energetic electrons from nucleons. in the later 1960s extended the upper ton's constituents (the quarks) was range of Q2 which could be explored to found to be only about 0.5. That is, 50% (In eqn. (1) Q2 is measured in GeV2 and about 10 GeV2. From eqn. (1) it can be of the momentum was carried by some units in which h = c = 1 are used.) Thus, seen that this probes the proton down to electrically neutral constituents. We as Q 2 is increased, the structure of mat­ distances of about 0.1 fm, much less now know that these are the gluons; the ter to smaller and smaller distances is than its radius. A study of the distribu­ particles which are responsible for the revealed. The theory of QED specifies tions of scattered electrons in these strong force confining the quarks and precisely the scattering distribution ex­ deep inelastic collisions was carried out. antiquarks inside a hadron. The gluon is pected from a point-like target i.e. one For elastic electron-nucleon scatter­ analogous to the photon in QED, but with no internal structure. Deviations ing the structure function F2 was found whereas the photon carries no electric from these observations can be con­ to fall off rapidly with Q2. A similar be­ charge, the gluon carries the strong verted into a charge density distribution haviour was also found for final states 'charge' (a quantum number arbitrarily for the target. The dependence of the consisting of excited nucleon resonan­ called colour). This leads to an important nuclear radius on the atomic weight A of ces. The experimental result that, for a difference between the theory of colour the target is found to behave roughly as fixed value of W above the 'resonance charges (Quantum Chromodynamics or R = ROA 1/3, where Ro  1.25 fm. Thus, region' (i.e. W  2 GeV), the structure QCD) and QED. The coupling constant in for a copper nucleus (A = 64), R  5 fm. function F2 was essentially independent QCD decreases (increases) as the sepa­ The energy of the incident electron of Q2, was thus a great surprise. The ration of the quarks decreases (increa­ beam used to probe the size of nuclei is discovery of this 'scaling' of the struc­ ses). Alternatively, in terms of the mo­ typically 200 MeV, giving Q2 values of ture function is analogous to that of mentum transfer squared (Q2), the about 10-2 GeV2. The value of Q2 need­ Rutherford more than 50 years earlier; strong coupling constant αs decreases ed to probe the charge radius of a proton only this time it showed that the proton (increases) as Q 2 increases (decreases). target is typically  0.1 GeV2. This mea­ (and neutron) had point-like consti­ At large Q2, or small distances, αs surement is performed using the elastic tuents from which the scattering occur­ becomes small and the quarks become scattering reaction e- +p → e- +p, in red. We now know that these scattering (asymptotically) free. At small Q2, or which the same particles appear in the centres are the quarks which are the large distances, αs becomes large ( 1), initial and final states. building blocks of hadronic matter. and this is believed (although not yet Final states are also formed in which proved) to lead to quark confinement. A schematic diagram of the scattering The interaction mechanisms sketched in an excited state of the target nucleon is process at the nucleon vertex is shown created (e.g. the nucleon resonance A, Fig. 2 can be justified in QCD, at least in Fig. 2. In a Lorentz frame in which the qualitatively. For the initial virtual pho­ which subsequently decays to a nu­ nucleon momentum is large, the motion cleon and a pion, i.e. Δ → N ). As the ton-quark collision at large Q2, say Q2 of the quarks transverse to the virtual > 10 GeV2, αs is small ( 0.2) and QCD available energy transferred to the target photon direction can be neglected. For is increased still further, a new pheno­ interactions at large Q2, the interaction menon is observed. The majority of the time is much shorter than the typical final states is no longer elastic or quasi­ time with which the constituents in­ elastic. The struck proton is observed to teract. Hence the cross-section is just 'break up' and produce many strongly in­ the sum of the incoherent scatterings of teracting particles (i.e hadrons). In these the quarks. One of the nucleon's consti­ inelastic final states at least one of the tuents, carrying a fraction x of the particles produced is either a neutron or energy-momentum four-vector P of the proton (the 'baryon' quantum number is nucleon (Fig. 2a), absorbs the virtual conserved), and the majority of the photon and, in some Lorentz frame, is other relatively long-lived particles pro­ turned around (Fig. 2b). No direct obser­ duced are pions and kaons. vation of these quarks has ever been What happens at the nucleon vertex made in the detectors, however, What (see Fig. 1) can, to a good approxima­ one does observe are collimated 'jets' of jet tion, be expressed in terms of a single, a hadrons; one in the direction of the scat­ priori unknown, function. This so-called tered quark and the other in the direction Fig. 2 — Three stages in the deep inelastic structure function (referred to in the of the incident target. These hadrons ( , scattering process : a) just before collision b) trade as F2) is a function of the two in­ K, p, p etc. and also resonant states) are just after collision c) some time later. The dependent kinematic variables describ­ formed at some later time (Fig. 2c). From quantities, P, xP and q are the energy-mo­ ing the scattering process. Taking these the relativistic kinematics of Fig. 2, it mentum four-vectors of the incident nu­ to be Q 2 and W (W is the total centre of cleon, quark and virtual photon respectively. 130 effects are relatively small. This explains why the Q 2 dependence of the structure Universität Bern Physikalisches Institut function is small (i.e. approximate scal­ Abt. Massenspektrometrie ing). The scattered quark has an in­ und Raumforschung variant mass squared of order Q2 and Assistentin / Assistent can radiate gluons. These in turn can Wir suchen eine Experimentalphysikerin oder einen Experimentalphysiker mit Doktorat produce quark-antiquark pairs or other oder Diplom. Zum Aufgabenkreis gehören die Betreuung einer grossen Eichanlage für gluons. This QCD shower process is Weltraum lonenmassenspektrometer (für deren technischen Unterhalt und Betrieb ein thought to continue until the values of Ingenieur besorgt ist), die Beteiligung am Unterricht (Praktika, Übungen) und die Mitarbeit the momentum transfers involved are an einem Forschungsprojekt aus den Gebieten Sonnenwind, Kometen, Magnetosphäre. small (i.e. αs is large), at which point con­ Erfahrung in den Gebieten lonenoptik, Vakuumtechnik, Elektronik und Informatik ist fined colourless clusters (hadrons) wünschenswert aber nicht unbedingt Voraussetzung. emerge. The hadronisation mechanism Die Dauer der Anstellung ist beschränkt. occurs on a time-scale much longer than that of the initial collision, and so it does Anmeldung an: Prof. H. Balsiger, Physikalisches Institut, not substantially affect the cross-sec­ Uni Bern, Sidlerstr. 5, CH-3012 Bern, Tel. (31) 65 44 11. tion for the complete process. The Latest Surprise 0.6. A sharp rise in the ratio at very large ( 0.6). At small x ( 0.15) the quarks By about 1980 a muon beam, capable x ( 0.8) was also observed, this being (and antiquarks) carry relatively more of producing muons up to 280 GeV and attributable to Fermi motion. At low x momentum in the nuclear target. The in­ Q2 values up to about 100 GeV2 was in the SLAC data showed no sizeable in­ tegrals of F2, over the measured x range, operation at CERN. Muons are easier crease above unity. However, as the are close to zero, showing that there is a than electrons to handle experimentally. minimum x value reached was greater shift in the momentum distribution from The European Muon Collaboration than that where the rise above unity in high to low x in the heavy target, with (EMC), a group comprised of members the EMC data was observed, the results only a fairly small change in the gluon from 13 institutes, was in the process of were not incompatible. distribution. taking data using various targets notably A second experiment, the Bologna - The EMC effect has also been studied hydrogen and deuterium, so that the CERN - Dortmund - Munich - Saclay using incident neutrino beams. Because structure functions on both protons and (BCDMS) Collaboration, was also posi­ the weak interaction cross-section is neutrons could be measured. An iron tioned in the muon beam-line at CERN. small, the resulting event samples are target was also used, the main reason From measurements of the F2 ratios on somewhat smaller than those obtained being to accumulate statistics more N/D and Fe/D, a rise above unity at small with charged lepton beams. However rapidly. Because the Q2 values involved x was confirmed, but not as large as that the results are compatible. were large it was expected that nuclear suggested by the original EMC data. Fur­ effects were negligible, apart from the ther measurements were also carried The Models effects of the Fermi motion of the nu­ out by the EMC using a set-up in which Before considering the detailed mo­ cleons, for which a correction could be the potential systematic errors cancell­ dels which have been proposed, it is applied. Thus, apart from this correction ed directly. The original EMC measure­ worthwhile establishing the approxi­ and the small neutron to proton excess ments were carried out at different mate distance scales involved. If dR is in iron, identical results for the structure times and with different configurations the inter-nucleon separation in the rest function F2 (per nucleon) to those mea­ of the apparatus, so that the resulting frame of the nucleus (dR ~ 1/M, where sured on deuterium were expected. systematic errors on the ratio were M is the pion mass), then in the Lorentz Hence it was yet another surprise in this relatively large. Fig. 3 shows a com­ frame of the collision shown in Fig. 2 subject when it was discovered that this parison of the most accurate data sets (the so-called Breit frame), this distance was not the case. The ratio of F2 on iron produced for nuclei of medium A values is Lorentz contracted to dB  dRMNIP, to deuterium was found to be above uni­ (A = Ca, Fe, Cu). The quantity plotted is where P is the nucleon momentum in ty for small values of x and below unity REMC(x) = FA2(x)/FD2(x), that is, the this frame. From the Uncertainty Princi­ for large x, with a cross-over at about x ratio of the structure function per ple, the wavelength of the quark, anti­ = 0.2. The degree of the surprise can be nucleon on the nuclear target compared quark or gluon (generically known as gauged by the fact that more than 100 to that for deuterium. The data are com­ partons) is   1 (xP), and hence this theoretical papers, attempting to explain patible with a small rise (REMC  1.03) at becomes comparable with the inter­ the effect, have been published since x  0.15. However, there is a turn-over at nucleon separation for a value of x  the discovery was announced in 1983. smaller x, with the ratio again falling 1/(dRMN)   0.15. Although this Confirmation of the effect, which has below unity. This latter effect is seen in argument is rather crude, it illustrates come to be known as the EMC effect, the new EMC data discussed above and the point that partons at low x ( 0.1) soon came from experimenters at SLAC. confirmed by a dedicated study of the can no longer be considered as belong­ Initially data, previously discarded, of in­ small x and Q2 region made with a ing to a specific nucleon. The deuteron teractions in the solid walls of targets special small angle trigger, also by the is, however, loosely bound and, for the were used, but later very precise measu­ EMC. The data shown in Fig. 3 are purpose of this discussion, can be con­ rements, for a whole series of nuclei, averaged over all Q2. Any Q2 depen­ sidered as two (quasi) free nucleons. were carried out. Because of the kine­ dence is fairly small. Two broad classes of model have been matics of the set-up, the most precise Thus a reasonably consistent experi­ developed to explain the region 0.1  x data were at large x. The structure func­ mental picture has become established.  0.7. The first category comprises tion ratio was found to decrease with in­ The quarks in the nuclear target carry a 'conventional' nuclear physics models. creasing atomic mass, going from about smaller momentum fraction (per nu­ In these models a summation is made of 0.9 for C/D to 0.8 for Au/D, both for x  cleon) than those in deuterium at large x the contributions of all possible scatter- 131 ing components of the nucleus. In addi­ tion to the traditional protons and neu­ trons, constituent pions and nucleon re­ sonances (e.g. A) have been considered. More exotic possibilities, such as confin­ ed 'bags' of 6, 9, 12 etc. quarks existing within the nucleus, have also been pro­ posed. There is sufficient flexibility in these models that most can be adjusted to give a plausible fit to the existing data. In the pion models, for example, the pion carriers of the nuclear force provide an additional target of quark-antiquark pairs for the virtual photon. Since the variable x is measured as though the nucleon were the target, this pion contri­ bution suffers a reduction by a kinematic factor M /Mn, and thus appears at small x. This model can thus explain the rise above unity of REMC at x  0.15 and, by Fig. 3 — Compilation of data on the ratio REMC(x) = (x) FD (x) versus x from various experi­ momentum conservation, the depletion ments. The scale in x is logarithmic for x < 0.1 and linear for x  0.1. at larger x. Crudely stated, an iron nucleus in the kinematic regime of the experiments consists of 26 protons, 30 ratio FA(x,Q2)IFD(x,Q2) should follow A2/3. The shadowing process, via this neutrons and about 5 pions. Models the observed pattern of scaling viola­ vector meson dominance mechanism, containing constituents of the nucleus tions. That is, Remc(x) should be less may also be applicable to virtual photons heavier than the nucleon also give a than unity at large x and larger than unity in deep inelastic scattering. It is ex­ depletion at large x. A further, and at small x, with a cross-over at x  0.2. pected that this process is important at related question is the role of Fermi mo­ From Fig. 3 it can be seen that this is the low x ( 0.05), and could explain the tion and nuclear binding energy. How­ case; however, the precise cross-over data shown in Fig. 3. However the model ever, models making a sophisticated point has not yet been established. predicts that the effect dies out rapidly treatment of binding energy do not Although the QCD rescaling model with increasing Q2, and this depen­ predict a rise above unity at x  0.15, uses QCD, it is not required by QCD. It dence is excluded by the data. However and the data cannot be described by has also been argued that the QCD the idea that, at low x, the quarks (and these effects alone. rescaling model and the conventional gluons) extend over more than one nuclear physics approach could be alter­ nucleon, and can recombine in such a In the above models it is assumed that native descriptions of the same underly­ way that their density is changed, can the structure function of a particle in a ing physics. If this is the case, a relation­ explain both the observed x and Q2 de­ nucleus is the same as the free particle ship exists between the QCD constants pendences. structure function. That is, it is assumed which dictate the Q2 evolution and that the internal QCD dynamics of the basic nuclear physics parameters (such The Future nuclear constituents are not influenced as binding energies etc.). The predicted Prior to the discovery of the EMC by the nuclear environment. A different relationships are indeed roughly satis­ effect the structure of the nucleus was approach is taken in the second model, fied. All these models have limited thought to be unimportant in the inter­ the so-called QCD rescaling model. Here ranges of applicability, however. The pretation of deep inelastic scattering it is assumed that the internal QCD QCD model does not explain the rapid phenomena. This is no longer the case. dynamics are indeed modified in the (Fermi motion) rise at large x, and none This subject has proven to be a most fer­ nuclear environment, and that it is these of these models predicted the turn-over tile interdisciplinary area for both the changes which give rise to the observed for x  0.05. nuclear structure and the elementary effects. In QCD, the Q2 dependence of Studies with real photons have shown particle physics communities. the structure functions, but not the that the total cross-section per nucleon Further experimental investigation is functions themselves, can be predicted varies with A as roughly A2/3. These in progress or is planned. Discrimination (in a perturbative expansion). The between the various models may be observations can be understood as possible by a detailed study of the Q2 predicted pattern that, as Q2 increases, follows. The incident photon undergoes dependence. Indeed, preliminary results there is a fall in the structure function at quantum fluctuations to quark-anti­ quark pairs (this is required by QED). suggest that many models will have dif­ large x and a rise at small x has been ficulty in accommodating it. The ulti­ verified for targets of different A values. These pairs have the same quantum mate goal is, however, an understanding In the rescaling model, the evolution numbers as the vector mesons ( , , ), of the nucleus in terms of QCD. This may with Q2 of FA(x,Q2) is taken to be the J/ etc.), and it is assumed that they well be some way off, but the existing same as FD(x,Q2), but from a different transform into virtual states of these particles. Since the mean free path of a and planned data on the EMC effect pro­ starting point in Q2. Thus the Q2 value vide valuable clues in this quest. at which a nucleon in an iron nucleus has strongly interacting particle in nuclear the same properties as a free nucleon is matter is small (typically a few fermis), Further Reading not the same (roughly Q2   (Q2)Q2, the interaction with a nucleus is mainly a A detailed review of the experiments with   2 for A = Fe). Hence, for a surface effect. Thus the other nucleons and models can be found In Berger E.L. given Q2, the heavy target structure are in the shadow of the surface nu­ and Coester F., Annual Review of Nu­ functions are more evolved, so that the cleons, and one expects  ~  R2 ~ clear Science 37 (1987) 463. 132