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SLAC-PUB-
January 1991
T/E
NOVEL TESTS OF QUANTUM CHROMODYNAMICS IN ELECTRO- PRODUCTION*
Stanley J. Brodsky and Paul Hoyer**
Stanford Linear Accelerator Center, Stanford University, Stanford, California 94309
ABSTRACT
We discuss a number of ways in which single arm and coincident measurements of
electroproduction on proton and nuclear targets can test fundamental QCD phenom-
ena and provide constraints on hadronic wavefunctions. The topics include tests of color
transparency, predictions for charm production at threshold, formation zone phenomena,
and non-additive nuclear effects. We particularly emphasize the need for measurements
which probe the short-range structure of hadronic and nuclear wave functions. In ad-
dition to the “extrinsic” gluonic and sea-quark contributions associated with radiation
from single partons, perturbative QCD predicts an “intrinsic” hardness of the high-mass
fluctuations of the wave function. These contributions can dominate heavy particle pro-
duction at large z in the target fragmentation region and can be further enhanced in
nuclear target reactions. Intrinsic hardness can also provide a possible explanation of
the anomalous nuclear phenomena referred to as “cumulative production”.
INTRODUCTION
A common goal of both particle and nuclear physics is to understand the struc-
ture of the nucleon and nucleus in terms of their fundamental quark and gluon degrees
of freedom. The quark and gluon wavefunctions of hadrons play a role in virtually
every aspect of high energy and electro-weak phenomenology. For example, detailed
knowledge of these wavefunctions is crucial for the accurate calculations of weak de-
cay amplitudes. The processes underlying strong and nuclear forces, color confinement,
and jet hadronization in QCD all require an understanding of the coherent bound-state
structure of hadrons.
The definitive probe of hadronic and nuclear structure is lepton scattering-not
only the classic single-arm inclusive measurements of deep inelastic structure functions,
but also coincidence lepto-production measurements of hadronic exclusive and semi-
inclusive final states. The combination of elastic and inelastic lepton scattering is still
the best “microscope” for probing the fundamental structure of the nucleon. Existing
* Work supported by the Department of Energy contract DE-AC03-76SF00515.
*+ Work supported by the Academy of Finland. Permanent address: Department of Higk Energy Physics, University of Helsinki, Finland Invited talk presented by S. J. Brodsky at the
Second European Workshop on Hadronic Physics with Electrons Beyond 10 GeV
Dourdan, France, October 8-12, 1990
measurements at SLAC, Fermilab, and CERN have provided many constraints on the quark and gluon distributions that constitute the proton, but much remains unknown.
The focus of this talk will be on new opportunities for studying fundamental QCD phenomena in high energy electroproduction, particularly the opportunities made pos- sible by a high-duty factor facility such as the PEGASYS experiment at SLAC, which proposes to make hermetic 47r measurements of the final state produced on polarized or
unpolarized gas jet targets in the PEP eF beams with Elob < 15 GeV, and a new high-
intensity high-duty-factor electron machine in Europe which would access coincident electroproduction at higher energies. We will also mention some exciting physics oppor-
tunities which are possible using the unique high energy 50 GeV highly-polarized SLC
beam at SLAC in single or double-arm deep inelastic lepton scattering experiments. The energy and momentum transfer range of all of these facilities are high enough such that the leading twist electron-quark scattering subprocess can dominate the cross section and that charm production near and above threshold can be studied. At much higher energies, colliding electron-proton beams at HERA can test QCD evolution in the domain of very low 2 where gluon saturation and new types of higher twist contributions begin to dominate the structure functi0ns.l Observing the fast fragments from the fast proton beam at HERA will permit another range of unique elec- troproduction experiments. For example, by detecting the forward proton in diffractive events ep + e’p’X one can study the QCD structure of the Pomeron (and the “Odd-
eronn 2 in the case of exclusive channels where X = ~“,~o, etc.). The production of
high SF particles and heavy quark systems in the proton fragmentation region even at low Q2 can test QCD short-distance effects in the proton wavefunction. The traditional focus of electroproduction experiments has been the tests of the perturbative QCD predictions for the logarithmic evolution of the deep inelastic struc- ture functions due to gluonic radiation from the struck quark. However, it has not been possible to completely test the QCD predictions for structure function evolution because of the persistent discrepancies between the present EMC, BCDMS, and SLAC measurements. A 50 GeV high precision experiment using the SLAC SLC beam would be ideal for removing these experimental conflicts. Just as important, at moderate val- ues of momentum transfer there remain important questions and ambiguities concerning the magnitude and origin of higher twist corrections, the behavior of R = UL/CTT, the origin of quark spin correlations, the shape of heavy quark structure functions, and the properties of the gluon distribution. Predictions for the Regge behavior of non-singlet structure functions have not been checked to high precision. In addition, recent lepton scattering experiments have claimed intriguing violations of QCD sum rules, anomalous spin correlations, unexpected charm particle effects, and significant non-additive nuclear corrections. These measurements all require confirmation and further investigation with
a high energy, high intensity polarized beam such as the SLC 50 GeV beam at SLAC.
It is also important to extend measurements of the proton and neutron elastic and transition form factors to larger momentum transfer. These exclusive processes test QCD scaling laws and provide essential constraints on the “distribution amplitude” $~(xl, x2,53, Q) -the fundamental covariant wave function describing the correlations
l Jet Fragmentation Studies: Confirm^ QCD^ predictions^ for^ jet^ fragmentation^ at
the leading and next-to-leading twist level; test predictions8 for dominant l/Q contributions to jet fragmentation at z N 1. The recent extended factorization theorem of Sterman and Qiug makes it imperative that one search for the these higher twist longitudinal current contributions since they are directly connected to contributions seen in large z meson induced Drell-Yan reactions. l Intrinsic Charm: confirm the anomalous components of the charm structure func- tions of the proton seen at large ZBj. Study charmonium and open charm produc- tion in the target fragmentation region. We will discuss this important physics in more detail in the following section. l Photo-and electroproduction of charmonium states: provide constraints on the gluon distribution of the proton in the photon-gluon fusion model; use the nuclear dependence to find non-additive gluon effects and determine a+~. a Nuclear-bound quarkonium: study electroproduction just below the threshold in 7A -+ vcA reactions to identify nuclear-bound charmonium states such as qc - 3He, novel bou nd states formed by the attractive QCD van der Waals gluonic exchange potential. l Intrinsic Hardness: test PQCD predictions for high transverse momentum pair correlations in proton and nuclear intrinsic momentum wave functions. l Cumulative Efiect in 7A + HX : measure the production of fast hadrons in the backward direction well beyond the kinematic limit for a proton target; identify anomalous short-range correlations predicted by PQCD. l Quark-diquark structure of the proton: study correlations of final state hadrons in the target fragmentation region. l Prompt photon emission: study anomalous soft-photon production as a clue to hadronization mechanisms and final state quark scattering. l Diflractive electroproduction such as 7p + p p and yp + J/G p on proton or nuclear targets: probe Pomeron coupling to systems of variable size and measure multi-gluon exchange form factors. l Difiractive ?r and 7 photoproduction: identify and probe the QCD “Odderon’ -odd C contribution to high energy scattering from three gluon exchange, etc. l Exclusive channels, such as ep --t eN* at large Q2: measure the fundamental distribution amplitudes of the proton and baryonic resonances; extend meson form factor measurements; test PQCD scaling laws for yp + MN reactions. l Exclusive nuclear amplitudes such as 7d + np : test PQCD “reduced amplitude” predictions. l Virtual Compton scattering at high momentum transfer 7p ---) yp : check pertur- bative QCD predictions. l Compton scattering on nuclei such as 7D -t 7D: search for “hidden color” multi-quark resonances predicted by QCD which could dominate the large angle reaction.
a Electron-positron asymmetry in ep --f e‘yX: measure fractional charges of quarks and a new type of valence structure function. l Spin-one structure functions for electroproduction on a deuteron target: test PQCD predictions for high spin structure functions lo requiring multi-quark coherence. l Anomalous spin correlations: study the spin structure functions and helicity effects in the final state, including spin correlations of strange hadrons.
COLOR TRANSPARENCY
One of the most interesting QCD phenomena that can be tested in electropro-
duction is “color transparency.” l1 The basic measurement requires the observation of quasi-elastic nearly-coplanar electron-proton scattering in a nuclear target without extra hadronic production. A basic feature of perturbative QCD is the assertion that a hadron can only scatter through large momentum transfer and stay intact if its wave- function is in a fluctuation4 which contains only valence quarks at small transverse separation bl - l/Q. QCD then makes the remarkable prediction that the cross section for large momentum transfer quasi-elastic scattering such as ep + ep in a nucleus will be unaffected by final-state absorption corrections, since the scattering is dominated by a configuration of the valence-quark wave-function of the proton which has a small color dipole moment. (By definition, quasi-elastic processes are nearly coplanar, integrated over the Fermi motion of the protons in the nucleus. Such processes are nearly exclusive in the sense that no extra hadrons are allowed in the final state.) Thus, at large mo- mentum transfer and energies, quasi-elastic exclusive reactions are predicted to occur uniformly in the nuclear volume, unaffected by initial or final state multiple-scattering or absorption of the interacting hadrons. This remarkable phenomenon is called color transparency reflecting the transparency of the nucleus to small color-singlet configura- tions. There are many tests of color transparency in electroproduction in addition to quasi-elastic ep scattering, such as baryon resonance production, 7p + ~+n,7n -+ K-p, 7*p + pp at high transverse momentum or at high photon mass. In each case one can test for the dominance of hard-scattering dominance of the exclusive reaction. The ability to isolate photoproduction on neutrons provides further checks on QCD predic- tions for the underlying subprocesses. In the case of high energy J/lc, photoproduction, the initially formed cZ can propagate freely through the nucleus as a small color-singlet forming the charmonium state outside of the nuc1eus.l’ As emphasized by Pire and Ralston,12 the nucleus filters out the non-perturbative soft-contributions. There are two conditions which set the kinematic scale where PQCD color trans- parency should be evident and quasi-elastic scattering cross section will be additive in proton number in the nuclear target. First, the hard scattering subprocess must occur at a sufficiently large momentum transfer so that only small transverse size wavefunction components $(zi, bl N l/Q) with small color dipole moments dominate the reaction. Second, the state must remain small during its transit through the nucleus. The ex- pansion distance is controlled by the time in which the small Fock component mixes with other Fock components. By Lorentz invariance, the time scale r = ~EF/AM~
processes to occur additively throughout the nuclear volume.12 Experimentally, a strong enhancement of ANN is observed at the threshold for strange particle production, which is again consistent with the dominance of the J = L = S = 1 partial wave helicity amplitude. The large size of ANN observed at both the charm and strange thresholds is striking evidence of a strong effect on elastic amplitudes due to threshold production of fermion-antifermion pairs.
If the above explanation of the ANN and color transparency anomalies is correct then one can identify the effect of heavy quark thresholds in hadron collisions by studying their elastic scattering at large angles. Through unitarity, even a threshold cross section
of only 1 pb for the production of open charm in pp collisions will have a profound
influence on the pp --$ pp scattering at J3; - 5 GeV, because of its very small cross section at 90’. The production of charm at threshold implies that there is a contribution with massive, slow-moving constituents to the pp elastic amplitude which can modify the ordinary PQCD predictions, including dimensional counting scaling laws, helicity dependence, angular dependence, and especially the “color transparency” of quasi-elastic pp scattering in a nuclear target. Note that this effect would not affect the onset of color transparency in quasi-elastic ep scattering, but it could appear in other color transparency tests in electroproduction such as eA + e’?rn(A - 1).
PHOTOPRODUCTIONANDELECTROPRODUCTIONOFNUCLEARBOUNDQUARKONIUM
In general one expects that heavy quark systems produced near threshold will expe- rience strong final state interactions since there is a long time for the system to interact strongly. Thus one expects enhancements to open charm and charmonium in electropro- duction at threshold beyond that expected from photon-gluon fusion from both initial state intrinsic charm components in the wavefunction (see the next section) and multi- gluon exchange contributions. The situation could be even more interesting in a nuclear target. For example, consider the reaction 7 3He + 3He(cZ) where the charmonium state is produced nearly at rest. At the threshold for charm production, the produced particles will be slow (in the center of mass frame) and will fuse into a compound nucleus because of the strong attractive nuclear force. The charmonium state will be attracted to the nucleus by the QCD gluonic van der Waals force. One^ thus^ expects^ strong^ final^ state interactions near threshold. In fact, it is argued in Ref. 19 that the ci? system could bind to the 3He nucleus. It is thus possible that a new type of exotic nuclear bound state will be formed: charmonium bound to nuclear matter. Such a state should be observable at a distinct 7 3He center of mass energy, spread by the width of the charmonium state, and it will decay to unique signatures. The binding energy in the nucleus gives a measure of the charmonium’s interactions with ordinary hadrons and nuclei; its hadronic decays will measure hadron-nucleus interactions and test color transparency starting from a unique initial state condition. In &CD, the nuclear forces are identified with the residual strong color interactions due to quark interchange and multiple-gluon exchange. Because of the identity of the quark constituents of nucleons, a short-range repulsive component is also present (Pauli- blocking). From this perspective, the study of heavy quarkonium interactions in nuclear
matter is particularly interesting: due to the distinct flavors of the quarks involved in the quarkonium-nucleon interaction there is no quark exchange to first order in elastic processes, and thus no one-meson-exchange potential from which to build a standard nuclear potential. For the same reason, there is no Pauli-blocking and consequently no short-range nuclear repulsion. The nuclear interaction in this case is purely gluonic and thus of a different nature from the usual nuclear forces.
The production of nuclear-bound quarkonium would be the first realization of hadronic nuclei with exotic components bound by a purely gluonic potential. Furthermore, the charmonium-nucleon interaction would provide the dynamical basis for understanding
the spin-spin correlation anomaly in high energy pp elastic scattering.” In this case, the interaction is not strong enough to produce a bound state, but it can provide an
enhancement at the heavy-quark threshold characteristic of an almost-bound
system.
THE HEAVY QUARK CONTENT OF NUCLEONS
One of the most intriguing unknowns in nucleon structure is the strange and charm quark structure of the nucleon wavefunction. The EMC spin crisis measurements indi- cate a significant ss content of the proton, with the strange quark spin strongly anti- correlated with the proton spin. Just as striking, the EMC measurements of the charm structure function of the proton at large xgj N 0.4 appear to be considerably larger than that predicted by the conventional photon-gluon fusion model, indicating an anomalous charm content at large values of z. 21 The^ probability^ of intrinsic^ charm^ has been esti- mated 21 at 0.3%. In the following sections we discuss the QCD physics of hadronic wavefunctions and the basis for understanding intrinsic heavy quark states and other high mass components of the hadronic and nuclear wavefunctions. Coincidence measurements of strange and charmed particles in high energy electroproduction to test these anomalies are important and challenging experiments. One of the most interesting areas of investigation are the exclusive charm channels, e.g., 7*p --t DA,, to test predictions of possibly enhanced cross sections near threshold. Such measurements of constrained charmed meson and charmed baryon final states could provide a definitive measurements of charmed baryon decay branching ratios. One of the major uncertainties in the present determinations of the charmed baryon production cross sections in hadron collisions is the large uncertainty in the branching fractions for the A,. Complete measurements of the heavy quark content of protons and nuclei will re- quire a high energy high duty factor electron facility, such as the European facility discussed at this meeting. Initially, the PEGASYS facility at SLAC together with a 47r detector such as the Mark II or TPC, would provide an ideal laboratory for large acceptance coincidence electroproduction experiments on polarized or unpolarized gas jet targets, including studies of charm production near and above threshold. In addi- tion the 9 GeV electron ring which could be available at a high intensity asymmetric B-factory would permit higher luminosity coincident electroproduction measurements. A PEGASYS-type facility at a B-factory could provide a sensitive probe of fundamental
tributions are suppressed by two or more inverse powers of the heavy quark mass. Nev- ertheless, these contributions can still be important and dominate in certain kinematic regions, particularly large 2. The^ intrinsic^ contributions^ have^ a number^ of^ remarkable properties which we return to below.
It is particularly convenient to use the Fock expansion to describe the interactions
of a hadron moving at large momentum P (although the results are frame independent
when light-cone quantization is used.) For example, to describe ep scattering in the CM or HERA colliding beam configuration we consider the Fock expansion of the proton in
&CD, lp) = Iuud) + juudg) +... + IuudQQ) +...
where q(Q) re ers tof a light (heavy) quark and g to a gluon. At high energies, most scattering processes in electroproduction only involve states of the proton that were formed long before the collision takes place. The individual Fock components in (1)
have “lifetimes” At (before mixing with other components) which can be estimated from
the uncertainty relation AEAt - 1. At large hadron energies E the energy difference
becomes small,
AEx
Fock components for which l/AE is larger than the interaction time have thus formed
before the scattering and can be regarded as independent constituents of the incoming wave function. At high energies only collisions with momentum transfers commensurate
with the center of mass energy, such as deep inelastic lepton scattering (Q2 N 2mv) and
jet production with pi w O(Ecm) produce states with lifetimes as short as the scattering time. The above arguments show that a typical scattering process is essentially determined by the mixture of incoming Fock states, i.e., by the^ wave functions^ of the^ scattering^ par- ticles. This is true even for collisions with very heavy quarks or with particles having very large pi in the final state, provided only that the momentum transferred in the collision is small compared to EC,,,. The cross sections for such collisions are thus de- termined by the probability of finding the corresponding Fock states in the beam or target particle wave functions; cf. Eq. (1). A n example of this is provided by the Bethe- Heitler process of e+e- pair production in QED. A high energy photon can materialize in the Coulomb field of a nucleus into an e+e- pair through the exchange of a very soft photon. The creation of the massive e+e- pair occurs long before the collision and is associated with the wave function of the photon. The collision process itself is soft and does not significantly change the momentum distribution of the pair. Similarly, heavy quark production in hadron collisions or electroproduction at any Q2 at high energies (E,, >> mQ) is governed by the hard (far off energy-shell) components of the hadronic wave functions.
THE STRUCTURE OF INTRINSICALLY HARD STATES
The leading extrinsic contribution to heavy quarks in a hadronic wave function is one gluon splitting into a heavy quark pair, G + Q& (Fig. la). We call this contribution extrinsic since it is independent of the hadron wave function, except for its gluon content. The extrinsic heavy quarks are, in a sense, “constituents of the gluon”. The extrinsic heavy quark wave function has the form
IEe=trinsic(q~Q~)^ =^ l-G TH(G^ +^ 98)^ &^ (3)
The square of the gluon amplitude TG gives the ordinary gluon structure function of the hadron. The gluon splitting amplitude TH is of order Jm, and AE is the energy difference (2). The integral of the extrinsic probability I\EeztrinJic12 over p$Q
for mQ 2 O(mQ) b rin g s a factor^ of^ m$.^ Hence^ we see that^ the^ probability^ of finding
extrinsic heavy quarks (or large pi) in a hadronic wave function is actually independent of the quark mass (or pi). This is related to the quadratic divergence of the quark loop in Fig. lb. The production cross section of the QB pair is still damped by a factor l/m& this^ being^ the^ approximate^ transverse^ area of the^ pair.
w-90 (4 (b) 6764Al
Figure 1. (a) Gluon splitting gives rise to extrinsic heavy quarks in a hadron wave function. The pointlike coupling to the gluon implies that all quark masses and all transverse momenta are generated with equal probability. (b) In the squared amplitude, this is seen as a quadratic divergence of the quark loop.
Intrinsic heavy quark Fock states2’ arise from the spatial overlap of light partons. Typical diagrams are shown in Fig. 2. The transverse distance between the participating light partons must be 5 O(l/mQ) for th em to be able to produce the heavy quarks. The wave function of the intrinsic Fock state has the general structure
Here I’ij is the two-parton wave function, which has a dimension given by the inverse hadron radius. T~(ij -+ Qv) is the amplitude for two (or, more generally, several) light partons i,j to create the heavy quarks, and AE is the energy difference (2) between the heavy quark Fock state and the hadron. A^ sum^ over^ different^ processes,^ and^ over
small, of O(l/m6). Th e extrinsic^ heavy^ quarks^ are^ produced^ by^ a single^ (pointlike) gluon (Fig. l), w hereas the intrinsic mechanism is more peripheral (Fig. 2). This means that rescattering and absorption effects for intrinsic states produced on heavy nuclei will be relatively more significant, compared to that for extrinsic states. In addition to the heavy quarks Q, such rescattering may affect the light partons involved in the intrinsic state (e.g., the quarks q in Fig. 2(b). These light quarks tend to be separated by a larger transverse distance than the heavy quarks, further enhancing the rescattering.
Consider now the formation of intrinsic heavy quark states in nuclear wave functions. At high energies, partons from different nucleons can overlap, provided only that their transverse separation is small. Thus the partons which create intrinsic heavy quarks in Fig. 2 can come from two nucleons which are separated by a longitudinal distance in the nucleus. Now it is reasonable to assume that partons belonging to different nucleons are uncorrelated, i.e., that the two-parton amplitude rij in Eq. (4) is proportional to the _ product.r;rj of single parton amplitudes. Hence the amount of intrinsic charm in nuclei may possibly be more reliably calculated than for hadrons. The probability for intrinsic
charm will increase with the nuclear path length as A l/3 .Moreover, the total longitudi-
nal momentum of the intrinsic quark pair, being supplied by two different nucleons, can be larger than in a single hadron, and can in fact exceed the total momentum carried by one nucleon. All that we have said above concerning heavy quark Fock states applies equally to states with light partons carrying large transverse momentum. Extrinsic and intrinsic mechanisms for generating large pi in hadronic wave functions are shown in Fig. 3. Using Eq. (5) as a guideline for the probability of intrinsic hardness, we see in fact that the parton mass and pi appear in an equivalent way. Remarkably QCD predicts that these high mass fluctuations occur in the nucleon and nuclear wavefunctions with
the minimal power law fall off: P( M2 > Mi) N l/M:. We again expect that the
intrinsic mechanism will be dominant at large XF, and in particular in the cumulative (ZF > 1) region of nuclear wave functions. In^ each^ case one^ can^ materialize^ the^ large mass fluctuations in electroproduction even at minimal photon mass Q2. The crucial experimental requirement is the ability to identify the target fragments in the target fragmentation region.
Figure 3. (a) An extrinsic contribution to large transverse momentum partons in a hadron and (b) an intrinsic contribution.
The possibility of parton fusion has been considered previously in the context of the evolution of parton distributions with momentum transfer (Q2).2g030 At very large Q and small x, the number of gluons can become large enough to force them to overlap and
coalesce. Our emphasis here is different. We are interested in rare phenomena at large 2, where processes involving two or more gluons and valence quarks can give dominant effects, even though the likelihood for such fluctuations is small. The colliding partons in Figs. l-3 are to be thought of (in a first approximation) as nearly on-shell, and having small pr. Only the part of the processes in Fig. 3 leading to large pi partons is to be considered as a new contribution to the wave function. In particular, the fusion of two partons into one (e.g., qG -+^ q),^ which^ cannot^ give^ large^ pi,^ is^ a part^ of^ the non-perturbative wave functions I’, and hence does not contribute to intrinsic hardness.
CHARM PRODUCTION IN HADRON AND NUCLEAR COLLISIONS
The concept of intrinsic charm was originally inspired by hadron-hadron scatter-
ing experiments
31 showing unexpectedly abundant charm production at large SF =
%-‘charm/&rn. When^ extrapolated^ to^ small^ XF,^ the^ data^ suggested^ total^ charm^ cross sections in the millibarn range, far beyond the predictions (20 - 50 /A) of the standard QCD gluon fusion process (cJ Fig. 4(a)). L a er dt a a witht^ good^ acceptance^ at^ low^ XF showed that the total charm cross section actually is compatible with the gluon fusion process.32 Nevertheless,^ more^ evidence^ was also obtained^ showing^ that^ charm^ produc- tion at large XF, albeit a small fraction of the total cross section, still is larger than expected.33 The large ZF data also shows correlations (leading particle effects) with the quantum numbers of the beam hadron that are incompatible with gluon fusion.
Figure 4. (a) The gluon-gluon fusion process in &CD. At high energies, the extrinsic Qa pair preforms in the incoming wave function and is put on mass-shell by a soft gluon from the target. (b) An example of intrinsic heavy quark production. The heavy quark can get additional momentum from a light valence quark, and the produced hadrons at large IF may get quantum numbers that are correlated to those of the valence quark (leading particle effect). The scattering can be from one of the light partons involved in the intrinsic state.
The intrinsic charm production mechanism (Fig. 4(b)) is expected to be smaller than the extrinsic one, due to the l/m$ suppression from the requirement of spatial overlap of initial light partons. However, at sufficiently large XF the intrinsic mechanism will dominate, because the momentum of several incoming partons can be transferred to the heavy quarks. Our present, improved understanding of intrinsic charm, as outlined above, will allow a more quantitative theoretical discussion of these phenomena than was possible heretofore. Such an analysis will also become increasingly meaningful as the data on hadroproduced charm at large XF improves.
the intrinsic charm wave function, using multiparton distributions, coupled with better data on open charm at large SF is clearly needed. Electroproduction studies can play a definitive role by measuring the charm structure function in semi-inclusive reactions, and by measuring the distribution of charmed hadrons and charmonium in the large XF proton fragmentation region.
THE INTRINSIC HARDNESS OF NUCLEAR WAVE FUNCTIONS
We noted above that intrinsic hardness should be enhanced in nuclear wave func- tions, due to the increased probability for spatial overlap of light partons from different nucleons. All of the data on charm production discussed above was obtained with beams of ordinary hadrons, and the experimental acceptance generally limited the observations to the forward (XF > 0) hemisphere. This data thus reflects the importance of charm in the wave functions of the beam particles. An important exception to this is the EMC measurement of the charm structure function of the Fe nucleus.21 An enhance- ment over the extrinsic photon-gluon contribution was observed at large XF, but the limited statistics prevented a firm conclusion. Several features of scattering on nuclear targets show that the nucleus cannot always be treated as a collection of ordinary nucleons. Measurements of deep inelastic lepton scattering have revealed 42’43’44deviations of the nuclear structure functions from those of free nucleons, both at very small and at intermediate values of x (the “EMC Effect”). There are also indications45 that the quark distributions in nuclei extend beyond x = 1. Unusual states of the nucleus could be involved as well in the production of large pi particles in hadron-nucleus collisions, where the yield is known to increase faster than
the nuclear number A (The “Cronin Effect”).46’ 47
The most direct evidence for an enhancement of the nuclear structure function at large x comes from the so-called “Cumulative Effect”p Cumulative particles are de- fined as hadrons produced in the fragmentation region of a nucleus which have XF > 1, i.e., they carry more momentum than the individual nucleons (apart from Fermi motion effects). In practice, experiments are mostly done by scattering a variety of particles (lep- tons, hadrons and nuclei) on stationary nuclei, and observing hadrons that are moving backward in the laboratory. A simple kinematical exercise shows that at sufficiently high
beam energies, the energy Eh and longitudinal momentum pi of a hadron h produced
on a free stationary nucleon must satisfy
XG Eh-I’;^51 mN
(8)
where mN is the nucleon mass and pi < 0 in the backward direction. The variable x defined by (8) is th e usual (light-cone) fractional momentum, which is equivalent to the
Feynman momentum fraction XF of h in the CM system. This equivalence is strictly
true for infinite beam momentum; a number of alternative definitions of x have been used in order to take finite energy effects into account. The^ difference^ between^ the^ various definitions will not be important for our qualitative discussion below.
Cumulative particle production has been seen in many experiments using a variety of beam particles and energies, up to values of x = 4 or so. To a first approximation, Feynman scaling (i.e., independence of beam energy) sets in already at quite low ener- .
fP% Abeam N^2 GeV^ (Fig.^ 5(a)).^ The^ shape^ of th e cumulative^ hadron^ distribution^ is
insensitive to the type of beam particle used. These features suggest that the cumulative particle distribution reflects properties of the nuclear wave function.
1041 I^ I^ I^ I \ (^) \ ---^90 MeV^ ptAl^ +p(140°) \ -^ 600MeVptC-~(160") ! 0 1. (4 \ lA^ 4.092.1 (^) I GeV ptC-~(180~) \ (^) \ v 7.71 1 iAh0 n^400 GeV^ p+C+^ p(160")-
(^500 ) P (MeV/c)
I o-w
102 103 104 105 ,+2/3,.+4/ P 1 6764/d
Figure 5. (a) Laboratory momentum distributions of cumulative protons produced by protons scattering on carbon and aluminum nuclei. In an analogy to the Rutherford experi- ment, the backscattering of 1 GeV protons from a beam of 2 GeV protons suggests encounters with small structures within the nucleus. (b) Dependence on the atomic number of the target (At) and projectile (Ap) f or cumulative protons in the target fragmentation region. The data were fitted to a gaussian momentum distribution with a total rate parametrized by crl, which scales when plotted as a function of A,2’3A4’t 3. Data and further references in Ref. 50.
I I^ I^ I^ I^ I
2- (a)
0 Pions 77 0 Protons G i 5 - G d
t I- c l-
0
+++
I) l 4 0 I^ I^ I 1 2 3 x-B
Figure 6. (a) The mean square transverse momentum of cumulative pions (0) and protons (0) produced by 10 GeV protons on Ta and Pb. The scale of the z-axis is offset by B = 1 for the protons (B = 0 for the pions). Data from Ref. 52. (b) The ratio of cumulative I(- to ?r- production on several nuclei as a function oft. Data from Ref. 54.
for all quarks in a given range of pr or quark mass, according to Eqs. (5) and (6). At the x-values considered here, the typical m-values are larger than, or at least comparable to, the strange quark mass (cj. Fig. 6(a)). H ence the ?r and I( mesons produced by intrinsic u, d and s quarks are expected to have similar x-distributions, as observed. The I<+ mesons can get their momenta from intrinsic u valence quarks. Since the creation of an ss pair is not suppressed at the relatively large m-scale involved, we can understand the equality of the I(+ and ws meson rates. The production of a I(- meson at large x, on the other hand, requires an energetic B or s sea quark. In this case momentum must be transferred from the valence quarks and gluons according to Fig. 2. Hence it is not surprising that the rate of K-mesons is suppressed by about a factor 20 in the cumulative region, as seen in Fig. 6(b).
Our interpretation of the cumulative phenomena in terms of an enhancement in the 47,48,56, nuclear structure function for x > 1 is compatible with some earlier suggestions. Models of multiquark bags, have been used to provide a unified explanation of the EMC, Cronin, and Cumulative Effects. An analysis of the EMC Effect in fact suggested the
existence of a small admixture in nuclear wave functions of “collective” sea quarks, which are as energetic as the valence quarks. 58 The multiquark bag models do not, however, predict the probability for bag formation, nor the z-distributions of the quarks in the bag. The properties of the intrinsically-hard component of nuclear wave functions, on the other hand, can be calculated from perturbative QCD in terms of the known quark and gluon distribution functions of nucleons. An immediate consequence is that the multiquark correlations must have a small transverse range, implying an increase of the average pr at large z, as observed in the data (Fig. 6(a)). Other puzzles involving fast nuclear fragments, which also may be related to intrinsic hardness, include the production of particles from nuclei below threshold for collisions on free nucleons. For example, subthreshold production of antiprotons has been observed both in p + Cu and Si + Si collisions.5g While^ the^ p rate^ was thought^ to^ be understood for the p + Czl data, based on the high cumulative momenta being interpreted as due to Fermi motion, it turned out that the corresponding calculation underestimated the rate for Si + Si collisions by three orders of magnitude. In our view, the cumulative momenta should be discussed at the parton level. The rate for p production may then proceed much more favorably through, e.g., the gg + pjj reaction, whose threshold is just 27~2~in the center-of-mass. Clearly the most unambiguous way to unravel the mysteries of cumulative effects and other high momentum nuclear enhancements is to study the nuclear target frag- mentation region in electroproduction eA + e’HX both at large negative XF and in the subthreshold region since the basic interaction of the photon probe with the quark currents of the nucleus is well-understood.
ACKNOWLEDGEMENTS
Some of the material presented above is based on collaborations with G. de Teramond and I. Schmidt. PH wishes to thank the SLAC theory group for its warm hospitality during his sabbatical. Part of this talk was also presented at the Topical Conference on Particle Production near Threshold, Nashville, Indiana, 1990.
REFERENCES
- For a review of QCD physics at HERA see S. J. Brodsky, SLAC-PUB 5312 and 5313 (1990.)
- S. J. Brodsky, J. R. Cudell, and P. V. Landshoff, in preparation.
- S. J. Brodsky, P. Hoyer, and A. H. Mueller, in preparation.
- See S. J. Brodsky and G. P. Lepage, in Quantum Chromodynamics, edited by A. H. Mueller, (World Scientific, 1990 and references therein.)
- S. J. Brodsky, SLAC-PUB-5382 (1990), SLAC-PUB 5371 (1990), and SLAC-PUB- 5013, published in the Prodeedings of the Topical Conf. on Electronuclear Physics with Internal Targets, Stanford, CA, Jan 9-12, 1989.
