Nuclear physics at large Q2

Nuclear Physics A478 (1988) 29c-45c North-Holland, Amsterdam

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NUCLEAR PHYSICS AT LARGE Qa D. VON HARRACH .eidelberg, Federal Republic of Germany and CERN, Geneva, Max-Planck Institut JEW Kernphysik, N Switzerland

fi. Introduction QCD tells us that the fundamental ingredients of all hadrons, including nuclei, are quarks andgluons. This fact is confirmed by a vast class of high-energy physics experimentssuch as deep inelastic lepton scattering, massive lepton pair production, e+e- annihilation into hadrons and large-pT phenomena in hadron collisions. Nuclear physics experiments on the contrary have successfully been interpreted by assuming "elementary" nucleons interacting by relatively weak phenomenological nuclear forces . At larger momentum transfer, corresponding to shorter distances probed, thepictureis enriched by mesons, baryon resonances andtheir antiparticles. It is not clear whether these ingredients are to be identified with the free physical particles and how many of them,with what momentum distribution, are to be taken into account in a given experiment . Therefore there is nothing like a conventional or standard nuclear model. The discoveryofthe EMC effect') hasdemonstrated that them ylear environment changes the quark parton structure of the nucleon. More recent experiments, which I am going to review, have refined and extended the original observation. Models are developing whichtell us howto relate observations at large momentum transfer to nuclear degrees of freedom . I will compare the predictions of some of these models to the available data, and show that we are still lacking important experimental information to sort out the correct models. I hope that the new field of nuclear physics at large momentum transfer will help to establish the important effective degrees of freedom in the nucleus and determine the role of quarks and gluons in the nucleus. I will begin with a short description of the basic tools to reveal the parton structure of hadrons. 2. Deep inelastic scattering and the parton model Deep inelastic lepton scattering is probably the most direct and best explored way to access the parton structure of nuclei and the nucleon. In the following I will concentrate on charged lepton scattering. The inelastic scattering of electrons or muons is described by the emission and absorption of a virtual photon y* . The properties of this probe are entirely determined by the charged lepton kinematics 0375-9474/88/$03 .50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

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D. wn Harrach / Nuclear physics at large Qa

(fig . 1) . The photon energy is v = E,, - Ew and its invariant mass is -4EE' sine 10= -Q2.

q2

=

Scattered

Fin41 State Hadrons Fig. 1 . Kinematics of deep inelastic muon scattering.

The massive virtual photon can be longitudinally or transversely polarised, consequently there are two independent absorption cross sections. The photon is highly virtual and has a finite lifetime -r-1/Q in its rest frame. In the laboratory frame this corresponds to a space-time extension ®t =®z = yT = (v1 Q) x (1/Q) = v/Q2 . If the virtual photon is absorbed by partons with vanishing transverse momentum and mass then at large v and Q2 (but Q2/ v finite) kinematics require p+=-q+ . p+ and q'" are the partons and the photons respective light cone momenta p+ = po+p3, 2 q+ =qo +q3 =-Q /2v. The light cone momenta are equivalent to the momenta in an infinite momentum frame. If p+ represents a fraction x (0, x,1) of the targets light cone momentum (P+ =M for a target at rest) then the absorption condition reads as x = Q2/2Mv. We see that by fixing theratio Q2/ vwe notonly determine the momentum fraction of the absorbing parton but also the space-time interval in which a coherent interaction of the photon with hadronic cuvrents can occur. In a more rigorous formulation 2.3) this leads to the notion that inclusive deep inelrstic scattering measures the light cone correlation function of the target. We will later make use of this complementary of x with spatial dimensions probed in the target. The structure functions areobtained from the inclusive deep inelastic crosssection after dividing out the Mott point cross section and kinematical factors. Structure functions, as functions of x and Q2 (instead of v and Q2), are interpreted as the probability to find a parton with momentum fraction x in the target. If partons are identified with spin-2 quarks andtheir ::ansverse momenta aresmall, thelongitudinal cross section vanishes and we are left with one structure function which can be

D. von Harrach / Nuclearphysics at large Qz

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written as a sum of the contribution of the different flavours of gf weighted with the fractional quark charges of squared . F2(x, Q2)=x

E ef2(gr(x, Q 2)+4r(x, Q2 ))

=x E ei(gt(x, Q2) - 4f(x, Q2))+2x E ei4t(x, Q2)=xq',+xq,

The structure function can be decomposed in a sea and a valence contribution . Since there are three valence quarks we have fto qdx = 3 (with QCD corrections 3(1-a,/ar) . Fig. 2 shows the valence and the sea contribution and their sum for the nucleon structure function in iron measured in neutrino and muon scattering experiments. The sea contribution to the structure function becomes negligible for x>0.3 .

Fig. 2. The nucleon structure function (iron) and its sea andvalence components. The sea component in our notation is xq,.

Integrals over structure functions determine the momentum fraction carriedby a given quark type . It turns out that the integral of the structure function F2 , i.e. all charged partons, is 0.49±0.01 (stat.) ±0.04 (syst.) at Q2 =15GeV2 [ref. `)] which means that only about one half of the momentum is carried by charged partons. The rest is carried by gluons which do not couple to photons. 3. Recent data on the EMC effect Fig. 3a,b summarises the present charged lepton scattering data for the structure function ratio r= F2A/ F2 of A= Fe or Cu formuon and electron scattering data 5'$).

D. von Harrach / Nuclear physics at large Qz

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Fig. 3. Comparison of structure function ratios on Fe or Cu to deuterium (a) BCDMS (1987) Fe, (b) electron data from SLAC E139 and E61, (c) preliminary (1986) EMCdata on Cu and deuterium .

D. vonHauach / Nuclear physics at large Qx

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The overall agreement of the data in the low-x region is nowgood with the exception of the SLAC E139 6) experiment. Data in the region of x-0.15 fail to reproduce the (4.5 t0.5)% enhancement observed in the muon scattering experiments",') and also in the SLAC E61 5) electron experiment. The crossing at x .-0.05 which was seen in the same experiment is now also seen in preliminary EMC data at much higher Q2 =-3-6GeV2. For the lowest experimental x-value of x=0.015 the ratio has a value of r= 0.87:1:0.05. The nonconfirmation of the original EMC data') in the region x<0.2, whichhas led to some disappointment of theearly modelbuilders, does not mean that the nuclear effects in the structure functions have disappeared. Their maximum of ^-20% is reached at about x=0.65. The slope of the almost straight section in between 0.2
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D. von Hauach / Nuclear physics at large Qz

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be constructed from v, v scattering on the proton. A comparison ") shows that nuclear effects in the deuteron in the range 0.05
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hasbeen obtained.This meansthat thepartition of the momentum carried by quarks and gluons respectively, is not signficantly different in Fe/Cu and D. In order to account for the depression of the ratio at x-values smaller than 0.1, a reduction of the sea component is needed since the valence contribution goes to zero at x=0. There are two alternatives ; either the sea contribution xg,(x) has the same x-dependence and consequently a reduced integral or the sea component xg,(x) changes the shape by a decrease at low x and an increase at larger x. Fits to the structure functions and their ratios ") cannot distinguish between the two alternatives, that is (i) a decrease of the seaby 20% and accordingly its contribution to the momentum sum rule, (ii) a hardening of the sea contribution keeping the momentum of the sea quarks constant. Evolution equations propose that the sea quark distribution is roughly proportional to the gluon distribution. In view of the observed conservation of the gluon momentum it would be surprising if the momentum carried by the sea quarks has to be reduced significantly. QCD fits of scaling violations including the non-singlet (sea) structure functions give constraints on the gluon distribution . Fig. 5 shows a comparison of gluon distributions extracted in this way. There is a strong tendency forthegluondistributions for Fe to be considerably harder than for hydrogen. This is however, in contradiction with an increase for the incoherent (inelastic) J/0 production from Fe by a factor of 1.45±0.12 (stat.) 10.22 (syst.) in the range 0.03 < x < 0.08 relative to H2/ D2 observed by the EMC collaboration ' 8). In the framework of the photon gluon fusion model ") this observation can be related to a relative increase of the gluon distribution. A recent experiment measuring the A-dependence of incoherent and coherent J/ 0 production by real photons at Fermilab zo) reaches the opposite conclusion. T1ie incoherent cross sections can be parameterised as v;_=v°,c =A°- with t= ;_= 0.94±0.02±0.03. This corresponds to a decrease of 20% of the cross section per nucleon from H/D to Fe . Recent new measurements ofJ/ 0 production on nitrogen from theEMCcollaboration, which are still under evaluation, indicate some inconsistences with earlier data on Fe . The experimental problem of removing the coherent production may

0

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X Fig. 5 . Gluon distributions extracted from scaling violations in iron and hydrogen . (BCDMS data from ref. ")) . have caused a problem . In fact the Fermilab experiment found the coherent production to rise with a_,,=1 .40±0.06±0.04 . Neutrino experiments, which at least conceptually, are best suited to determine the relative importance of sea and valence distributions are inconclusive. The CDHS experiment"), see fig. 6a, extracted the ratio 2(d+û+2s)F./(d+s)H from antineutrino cross sections at large y = (E - E')/ E. If the plausible assumption û = d is made this should correspond to the ratio of the sea contributions. The result of 1.10±0.11 (stat.) ±0.07 (syst.) is consistent with unity. The bubble chamber experiment WA25/59 [ref. 22)] fig. 6b, measuring v and v scattering on deuterium and Ne presents the results on the sea by simultaneous fits to the four cross sections. The fits at Q 2 >4.5 GeV2 seem to favour a decrease of the sea by (14±11)% and essentially no change of its shape. The fits are made with an ansatz for the valence part of the structure function as xq,(x)=Ax°(1-x)"

f'

with A fixed by the sum rule q dx = 3 and fit parameters a and P. If the ratio of the variations da and dß are kept constant as da/dß=a/(ß-1)=0 .13 then the momentum carried by the valence sea quarks is constant. The value of ,1ß essentially

D. von Harrach / Nuclear physics at large Q2

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determines the slope of the structure function ratio at x=0.5 . Fits forthe VVA25/59 data prefer values of dß = 0.46 t0.22 and da/d,8=0.20'-0. 11. Consequently the momentum cttrtied by the valence quarks increases in these fits. If the gluon momentum would be strictly conserved, the increase of the valence quark momentum is an inevitable consequence of an overall lowering of the sea. Unfortunately the systematic errors of the momentum sum rule still leave some room for a relative change of the sea momentum of about 10% while keeping the valence quark momentum constant . Although the overall shape of the EMC effect is now well established, important questions remain to be solved which are related to the sea-to-valence ratio in the region x < 0.3 . There is no guaranteethat there is a general loss of momentum from the valence quark distribution and an increase of the momentum carried by the sea as has been proposed earlier. The changes of the gluon distribution inferred from the QCD fits propose that the sea distributions are also harder in nuclei so we can escape from the necessity of a reduction of the sea momentum.

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D. von Harrach / Nuclear physics at large Q2

4. The

Q2

dependence of the EMC effect

All measurements of the EMC effect have been unable to see any significant Q 2 8.22) in fig. 7, are not precise enough to see Q2 dependence. However, the data dependences dlog(F2/F2 )/dlog Q2 as low as one percent. In the framework of perturbative QCD the Q2 dependence of a structure function at x>0.3 is predictable from the structure functions themselves . Predictions are of the order of a few per mille or less except for very large values of x where a few percent changes are expected 23). If however, higher twist contributions, which essentially contain the final state interaction of the struck quark and the nuclear debris, contribute to the nuclear structure functions the expectations could change significantly ') since the Q2 dependence of higher twist contributions follows inverse powers of Q2. The accuracy of present data is not yet sufficient to draw any conclusion on this point. S. The A dependence of the EMC effect The first result on the A-dependence of the EMC effect in the range 0.1
Jx

dyfA(y)FZ(xly)

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D. von Harnich / Nuclear physics at large Q2

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Fig. 9. Preliminary EMC (1986) data") on the A-dependence of structure function ratios Qwloo parameterized as a'w/o'p=c A° at low x and SLAC E139 °) data.

Taking more than one cluster type into account leads to the sum over the relevant clusters . The validity of the ansatz has been discussed') and found to be arguable. Incoherence of the cluster with spectators has to be assumed as well as the absence of final state interaction of the debris of the cluster with the spectator system . Recently the importance ofantisymmetrisation on the quarklevel wasdemonstrated . Such an effect, which cannot be described by a convolution ansatz, can lead to nuclear effects of the observed order of magnitude 2° ). The cluster models with the minimal input are the "binding plus Fermi-motion" models 26.2') assuming nucleons to be bound by nuclear forces . By assuming negligible final state interaction of the hit nucleon with the surrounding nuclear matter, they derive a rescaling of the nucleon mass by m->m(1 -jej) where (ej is the mean separation energy per nucleon. In order to fit the data these models need mean separation energies of about 50-60MeV, considerably larger than thevalues derived from ee'p experiments ") whichprefer l e 25 MeV. In addition themean separation energies determined in quasifree ee' scattering' °) show no significant A-dependence

I-

42C

D, von Harnich / Nuclear physics at large QZ

beyond A-24, after correction fortrivial initial and final state Coulomb interaction of the electron "). The failure to obtain the correct A-dependence is demonstrated in ref. 211) where separation energies were taken from Hartree-Fock calculations reproducing e.g . nuclear masses correctly. The binding models give rise to a momentum deficit. Only a fraction 1-isI/nip of the nucleus momentum is carried by thenucleons, i .e . we would expect areduction of the momentum carried by the valence quarks of the same order Jel/mP--5-6% . Recently the binding model was criticised 28). The inclusion cf an additional relativistic term almost cancels the binding effect. The models which include w-mesons 32 .33) attribute the momentum lost by the nucleons to the momentum carriedby extrapionswhich mediate the nuclearbinding forces. These models usethefree pion structure function as determined in Drell-Yan experiments 3° ) . There are however, different prescriptions for the number and momentum distribution function of the pionswithin the nucleus.Themodels succeed in reproducing the observed A-dependence since the number of extra pions is assumed to be proportional to the average two-nucleon density. Different versions of this model predict different amounts of sea enhancement 35). The models also predicta loss ofmomentum from thevalence quarks . The depression of thestructure function at x<0.1 is not yet reproduced by the pion models which all predict an enhancementof about 10% at x-0.1 . With apion structure function strongly peaked at x-0 it is difficult to see how this can be cured. There are more versions of cluster models with conventional and unconventional ingredients which inevitably have more freedom to fit data since their input is less restricted by experiments.Fordiscussion thereader is referred to recent reviews 33.35) . There are two types of models for nuclear effects which do not have to resort to convolution ideas . The rescaling models 36.37) assume a modification of the nucleon properties which can be summarised in a change of one important scale which is indentified with the confinement radius . It is argued that this scale change is equivalent to a change in Q2. Roughly speaking the models predict that structure functions of nuclei should look like the nucleon structure function at larger Q2, thus, assuming an increase of the confinement radius . The model 33) predicts a loss of momentum from the valence quarks in iron by about 7% (Q2-20) corresponding to roughly doubling Q2. All models presented explain the softening of the valence distribution by mechanisms which reduce the total momentum carried by valence quarks by 5-7% i .e. by 1.7 to 2.5% of the total momentum . This means that these models are incompatible with a decrease of the sea momentum. If the momentum carried by gluons were constant they would require a sea momentum increase of -11-16% . The rescaling model also predicts a softening of the sea and gluon distributions . In fact, it predicts an enhancementof J/ 1P production at low x - 0.05 of about 15% [ref. 35)]. A particular feature of the model is the prediction of an EMC effect of r=1 at x-0.15, here the scaling violations are experimentally found to vanish . The amount of rescaling is determined in this model by the probability

D. von Harrach / Nuclear physics at large Qz

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that two nucleons come close i.e. the two-nucleon density. This model can, as the pion model, reproduce the observed A-dependence. Obviously the model fails to describe the low and high x behaviour of the data and has to be supplemented by additional mechanisms. Nevertheless the idea of a scale change of the bound nucleon relative to the free one, which reproduces a major feature of the data,has inspired newunconventional questions as is indicated by the general title of the session: Do hadrons keep their free identity in nuclei? The othermodelwhichis basedon QCD and addressesitself to the low-x region, is thegluon recombinationmodel 3g"°°). It is now experimentally beyond doubt that the structure function ratios drop below one at x< 0.05 andthis featurepersists up to large values of Q2 ~ 6-10 GeV2 . It is clear that the classical vector dominance explanations of shadowing are no longer valid at this Q2 [ref. ")]. As has been shown before, partons of low x interact with the photon over long distances dl -I/mx. For dl larger than the average distance of two nucleons, which is of order2 fm or equivalently x G 0.1, correlations involvingtwo nucleons are expected to be seen. At even smaller x, x :G 0.015 correlations over the whole diameter of an A - 100 -nucleus are seen. In the gluon recombination models the probability of the recombination of two soft gluons into one harder gluon, is calculated as a function of the two-gluon density. The natural consequences of this picture are: - the depletion of G(x) at low x since gluon densities are large and thecorrelation length is large (screening); -since the total gluon momentum is conserved in the recombination process, a harder gluon distribution is expected, leading to a compensation of the depletion at larger x (antiscreening). In an early version of the model 38) the transition point between the screening and antiscreening effect is predicted to be at x- 0.15A- ' I3 , which corresponds to x-0.04 for A-60. A recent evaluation 42) finds the transition for Fe at x m 0.03 and predicts maximum screening of r=F2/F°=0.9 at x<0.01 and maximum antiscreening at x-0.1 of r=1 .05. Obviously this model reproduces qualitatively the complex features found at x<0.3. However, the model is in conflict with the pion models which explain the enhancement at low x by the presence of additional pions. Whether a dual description can be found similar to the one which has been proposed 37), to account forthealternative descriptionofthevalence quark depletion at large x, is an open question . Summarising the comparison of theory and experiments we state that there is presently no model which explains all observed features of the structure function ratios in a unified way. All models (except the gluon recombination model) need a reduction of the momentum carried by the valence quarks: by 5-6% (binding, pions) or 7% (rescaling). This is in conflict with the WA25/59 neutrino data (on neon) by at least 1.5-1 .8tr even if themaximum possible increase of themomentum

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D. von Hauach / Nuclear physics nr large QZ

carried by gluons, compatible with the error limits of the new sum-rule evaluation, are used . 7. Summary A new series of measurements of nuclear effects in structure function ratios has now established the following features : There is now clear evidence of an enhancement of FZ`/F° at x0 .15. The existence of nuclear shadowing, i.e . a depression of Fz°/ F° below 1 at x<0.05 at large values of Q2 = 3-10 GeV2 is seen for the first time . The partition of the total momentum into glue and quarks within small errors is unchanged going from deuterium to iron. Probably the glue in iron is harder than in deuterium and hydrogen. This needs experimental confirmation. The WA25/59 neutrino experiment finds no evidence foran enhancement of the momentum carried by the sea. This also needs experimental confirmation. Q2 has shown itself to be a rich field . Considerable Nuclear physics at large experimental efforts are still required to solve the essential question of the nuclear dependence of thesea-to-valence ratio, the shape of the gluon distribution in nuclei and the behaviour at very small x and large Q2 . Iwish to thankK. Rith,R. Voss, H.J. Pimerand Y. Mizuno for valuable discussion and advice. References EMC, J.J. Aubert et al., Phys . Lett. 123B (1983) 275 C.H . Llewellyn-Smith, Nucl . Phys . A434 (1985) 35c R. :,. Jaffe, MIT preprint 1261 (1985) EMC, J.J. Aubert er al, Nucl. Phys. B272 (1986) 158 S . Stein er al, Phys. Rev. D12 (1975) 1884 R .G. Arnold et al., Phys. Rev. Lett. 52 (1984) 722 P.R. Norton, Proc. XXIII Int. Conf. on High energy physics, Berkeley 1986 A.C. Benvenuti et al., CERN-EP/87-13; G. Bari et al, Phys . Lett. 163B (1985) 282 9) A. Bodek et al., Phys. Rev . D20 (1979) 1471 10) EMC, J.J . Aubert et al., Phys. Lett . 123B (1983) 275 11) R. Voss, private communication 12) S. Dasu er al., Univ. of Rochester preprint UR-958 13) M. Glück, E. Hoffmann and E. Reya, Z. Phys. C13 (1982) 119 14) A. Bodek and A. Simon, Univ. of Rochester preprint UR-906 15) G. West, Phys. Rev. Lett. 16ßB (1986) 400 16) Y . Mizuno, private communication 17) V. Gibson, Rutherford and Appleton Laboratory preprint RAL-T.035 18) EMC, J .J. Aubert et al., Phys. Lett. 152B (1985) 433 19) M. Glück anti E . Reya Phys. Lett. 83B (1975) 98 20) M.D. Sokoloff et al., Phys . Rev. Lett. 57 (1986) 3003 21) H. Abramovicz et al., Z. Phys. C25 (1984) 29 1) 2) 3) 4) 5) 6) 7) 8)

D. von Harrach / Nuclear physics at large Q2

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22) J. Guy et al., CERN -EP/86-217 23) R.P. Bickerstaff and G.A. Miller, Phys. Rev. D34 (1986) 2890 24) E.V. Shuryak, Proc. XI Europhysic Divisional Conf. on Nuclear physics with electromagnetic probes, Paris 1985 p.259c 25) P. Hoodbhoy and R.L . Jaffe, Phys. Rev. D35 (1987) 113 26) S .V. Akulinichev et al., Phys. Lett. 15813 (1985) 485 Phys . Rev . Lett . 55 (1985) 2239 27) B .L. Birbiair et al, Phys. Lett. 1668 (1986) 119 28) M.I . Strikman and L .L. Frankfurt, Leningrad preprint 1197 29) S. Frullani and J . Mougey, Adv. in Nucl . Phys. 14 (1984) 1 30) E.J. Monitz et al., Phys . Rev . Lett . 26 (1971) 445 31) R. Rosenfelder, Ann . of Phys. 128 (1980) 188 32) M. Ericson and A. Thomas, Phys. Lett. 14813 (1984) 191 33) E.L. Berger and F. Coester, ANL-HEP-PR-87-13, ANL-PHY-4967 (1987) submitted to Ann. Rev. Nucl . Part. Sci. ; E.L. Berger et al., Phys. Rev . D29 (1984) 398 34) J. Badier et al, Z . Phys . C26 (1984) 281 35) R.P. Bickerstaff, M .C . Birse and G .A. Miller, Phys. Rev. D33 (1986) 3228 36) O. Nachtmann and H.J . Pinter, Z . Phys. C21 (1984) 277 37) F. Close et al, Phys. Lett. 1248 (1983) 346; Phys . Rev. D31 (1985) 1004 ; Phys. Lett. 16813 (1986) 400; 18313 (1987) 101 38) N .N. Nikolaev and V.I. Zakharov, Phys. Lett. 5513 (1975) 397 39) L. Gribov, E . Levin and M . Ryskin, Phys . Reports 100 (1984) 1 40) A.H. Mueller and J. Qiu, Nucl. Phys. 8268 (1986) 427 ; J. Qiu, Columbia Univ. preprint CU-TP-361 41) J.D. Bjorken, Springer Tracts in Mod. Phys . vol . 108 (1986) 17 42) E.M . Levin, Leningrad preprint 1147 (1985)