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Inclusive and semi-inclusive reactions
NUCLEAR PHYSICS A ELSEVIER
Nuclear Physics A622 (1997) 357c-361c
Inclusive and Semi-Inclusive Reactions
A. Sch£fer Institut fiir Theoretische Physik, Universitiit Frankfurt, D-60054 Frankfurt, Germany
During the last years much of the activity in QCD has shifted from the determination of parton distribution functions and cross sections in leading order to the investigation of more detailed questions. This development went along with an increased emphasis on semi-inclusive reactions. The vastness of the field and the many still poorly understood aspects are reflected in the great variety of the contributions to this parallel session, all of which are of significant importance for currently discussed issues. One of the major tasks for modern nuclear physics is to understand in greater depth the nature of what is usually defined rather vaguely as 'constituent quark'. If one aims at bridging the gap between perturbative QCD and more traditional nuclear physics, formulated in terms of nucleons, specific resonances and mesons, one is unavoidably lead to concepts which i n v o l v e ~ p i c a l momentum scale of 1 GeV respectively a typical distance scale of 0.2-0.3 fm. One of the central questions is how one has to interpret these correlations and how to build phenomenological models incorporating them.
The talks by V. Vento and E. Perazzi elucidate certain aspects of such constituent quark models. The physics of the constituent quark is certainly at the heart what can be investigated at ELFE. To clarify it one does not Ned results at very small Bjorken-x but rather very precise results at modest Q2. The latter is needed to separate QCD-radiative corrections which typically involve log Q2 terms from higher-twist ones, involving 1/Q 2 ones.
Vento et al. have analyzed under which conditions a model with constituent quarks and gluons can evolve under DGLAP-evolution into the well known structure functions at large Q~. They find in agreement with similar investigations by other authors that a good match requires a very low starting point for the Q2 evolution (about 0.2 GeV 2) plus a substantial constituent gluon contribution. They point, however, to the well known problem, that DGLAP evolution at such small virtualities cannot be justified. In fact the phenomenologically acceptable fits at larger Q2 result to a large extent 0375-9474/97/$17.00 1997 - Elsevier Science B.V. PII: S0375-9474(97)00349-7
358c
A. Schiifer/Nuclear Physics A622 (1997) 357c-361c
from the fact that the DGLAP upward evolution converges to rather similar results for quite different starting distributions. Vento and Traini add to this general argument the observation that below the scale of the chiral phase transition at 1 GeV the evolution equations should really change, involving effective degrees of freedom like the pion field. It is actually known from model studies involving instanton configurations that the latter, which are only connected to the chiral symmetry phase transition, but do not produce confinement, are sufficient to generate the phenomenological properties of low mass hadrons (see the work by Shuryak et al.). This illustrates the importance of a description focusing on the chiral properties of QCD to obtain a satisfactory phenomenological description. Vento et al. are working on an improvement of their theory in this direction. Any such theory would necessarily involve dimensional parameters and thus 1/Q 2 terms. They would have to be mapped smoothly to the higher-twist corrections of the usual operator product expansion analysis of QCD. If successful such a description would be a major step towards a better understanding of this most important link between QCD and low-energy nuclear physics.
Perazzi et al. are actually working with a somewhat similar quark-gluon-pion model for the low energy properties of hadrons. Such models have been quite successful in the past in fitting mass spectra. Perazzi et al. performed a very severe test of these models by calculating the photon-coupling amplitudes for a number of resonances. Such amplitudes can be expected to be highly sensitive to details of the internal hadron structure and a successful fit would be therefore a very strong argument in favour of the underlying model. Unluckily the results are not encouraging. It turns out that the most sophisticated description involving configuration mixing as well as pion exchange currents does not give a better fit than simpler ones. This observation points to the difficulty that a realistic effective theory should allow for a systematic development, i.e. by including higher order terms the existence of which follows from theoretical arguments, it should be possible to achieve a better and better description of an ever wider range of data. The authors conclude that their results illustrate the limitations of a nonrelativistic model based on constituent quarks. I think that one can also draw a more optimistic conclusion. An acceptable effective low-Q 2 theory of hadron structure is of great importance. If it can be reached this success would certainly also be based on such detailed investigations as those performed by Perazzi et al.
S. Gerasimov gives a general analysis of SU(3) flavour symmetry predictions for hadronic properties, which can serve as a necessary boundary condition for model constructions on the level of constituent quarks as well as for the interpretation of perturbative spindependent QCD processes. The interpretation of the present data for the polarized proton and neutron structure functions in terms of the total spin carried by quarks is based on flavour SU(3) symmetry and involves a parameter F/D which describes the relative strength of the two manners in which three SU(3)-octets can couple. Gerasimov analyzes this quantity by confronting the magnetic moments an daxial-vector couplings
A. Schiifer/Nuclear PhysicsA622 (1997) 357c-361c
359c
of baryons.His result agrees only marginMly with that of Ratcliffe and suggest a much stronger negative strange quark polarization. This result has far reaching consequences, also for a future experimental program at ELFE. It turned out that NLO fits to the presently available data provide rather precise prediction for the polarized distribution functions Au(x) and Ad(x). However, the polarized gluon distribution AG(x) and the polarized strange quark distribution function As(x) is far less precisely predicted. Therefore most future effort in nucleon spin physics is directed towards a direct measurement of AG(x) and As(x) and it is very important that theory should come up with a generally accepted prediction with a realistic error bar before these experiments are done.
Another talk directly related to nuclear spin physics was given by R. Jakob. He and his collaborators analyzed the general structure of spin dependent reactions in which also the transverse momentum of an outgoing hadron is detected. Such reactions involve higher-twist structure and fragmentation functions which are the QCD objects for which one can hope to identify a low Q2 counterpart. The investigation of such quantities should play an ever greater role in the next decades and the systematic identification of all independent quantities is a necessary prerequisite for such studies. As one result of their complete classification Jakob et al. were able to derive several relations between fragmentation functions. The different fragmentation functions appeared originally in a complete Lorentz-decomposition of the relevant matrix elements and probably nobody would have been able to guess the derived relations from this original definition. The complete classification achieved by Jakob et al. is a necessary step, but only the first one in a far reaching program. The next steps will probably be the estimation of the identified independent quantities in some phenomenological models and a careful investigation of their Q2-dependence. Once these aims will be achieved it will be possible to deduce most interesting informations from a large class of new semi-inclusive experiments. Thus the present work promises to become of great phenomenological importance in the not too far future. This field of research could become especially important for ELFE because the new structure and fragmentation functions depending on the transverse momentum are most probably numerically small, such that very high intensity would be needed to measure them. Therefore ELFE could actually be the only place to perform such studies, which in the end would be of major help to pin down the internal nucleon wave function.
Peign6 et al. have studied a very different question, namely the energy-loss of high energy quarks or gluons in nuclear matter. This is not really a specific QCD problem, but rather a general one of many-particle physics which can be discussed equally for QED only. However, a reliable description of the partonic energy loss is possibly of vital importance for the interpretation of high energy heavy ion collisions. Presently the situation with respect to signals for the QCD phase transition, in partic-
360c
A. Schiller~Nuclear Physics A622 (1997) 357c-361c
ular the theoretical situation, is rather unsettled. None of the many proposed signals is uncontroversal. In this situation it is probable, that the discovery of the quark-gluonplasma will only be possible through a chain of quantitative arguments, none of which alone would provide sufficient evidence. Consequently a really quantitative theory of the hot QCD-phase is needed and this is still very badly missing. One crucial aspect of such a theory is the correct description of the screening effects due to the many soft gluons and quark-antiquark pairs created during the early phase of the collision. One aspect of this question is how the emission rate for bremsstrahlung is modified by the interference between amplitudes involving different scattering centers in the nuclear medium. This problem has already a long history and is usually discussed under the heading 'Landau-Pomeranchuk-Migdal' effect. The fundamental theoretical task is rather easy. One has to describe how, depending on the individual momentum transfers qi~z and distances between consecutive scattering reactions ziu, the interference between the different plane wave phases changes. The task is therefore to make realistic assumptions for the distribution of these quantities and to calculate the resulting sums of interfering amplitudes. Peign~ et al. stress in their contribution that the usually used random walk picture is not applicable because the Fourier-transformed scattering potentials do not decrease fast enough for large momentum transfers. From their improved description they arrive at the conclusion that the typical energy loss of a parton increases with the square of the distance travel through the nuclear medium (within the range of energies and temperatures in which their approximations are applicable). Such a quadratic length dependence is not as exotic as it might sound. It describes the fact that the usual suppression of Bremsstrahlung due to the LandauPomeranchuk-Migdal is less effective for larger distances. Quantitatively Peign~ et al. come up with the following predictions. For a nucleus of diameter 10 fm the typical energy loss of a parton is about 2 GeV for cold nuclear matter and 30 GeV for hot nuclear matter. For cold nuclear matter this energy loss could actually be derived from a detailed experimental investigation of hadron fragmentation, as any energy loss shifts the final hadron energies to smaller values. However, it could well be that the ELFE energy is too low for such investigations. I would like to mention that this work actually generated a large number of theoretical investigations and is presently one of those most actively discussed by the heavy-ion community.
Finally M. Vgntinnen et al. have studied the EMC-effect for so-called Ioffe-time distributions. This is formally completely equivalent to the usual discussions which make use of normal Bjorken-x distribution functions, and involve basically a Fourier-transformation in x. However, it is argued that the physical nature of the EMC-effect is more transparent in the Ioffe-time representation. The typical property of Ioffe-time distributions is that their behaviour for small Ioffe times y+ and/or small Bjorken-x (more precisely for xv + small) is just a straight line as a function of y+ the derivative of which is given e.g. by the first moment of F2(z). The latter is well known, being determined by the momentum fractions carried by the different quark-flavours. All the subtle effects of hadron structure show only up at large
A. Schiifer/Nuclear Physics A622 (1997) 357c-361c
361c
y+. This very general result is confirmed by V/~nttinen et al. for the EMC effect, which is thus illustrated to be due to a modification of the nucleon structure at relatively large distances.
Nuclear Physics A622 (1997) 357c-361c
Inclusive and Semi-Inclusive Reactions
A. Sch£fer Institut fiir Theoretische Physik, Universitiit Frankfurt, D-60054 Frankfurt, Germany
During the last years much of the activity in QCD has shifted from the determination of parton distribution functions and cross sections in leading order to the investigation of more detailed questions. This development went along with an increased emphasis on semi-inclusive reactions. The vastness of the field and the many still poorly understood aspects are reflected in the great variety of the contributions to this parallel session, all of which are of significant importance for currently discussed issues. One of the major tasks for modern nuclear physics is to understand in greater depth the nature of what is usually defined rather vaguely as 'constituent quark'. If one aims at bridging the gap between perturbative QCD and more traditional nuclear physics, formulated in terms of nucleons, specific resonances and mesons, one is unavoidably lead to concepts which i n v o l v e ~ p i c a l momentum scale of 1 GeV respectively a typical distance scale of 0.2-0.3 fm. One of the central questions is how one has to interpret these correlations and how to build phenomenological models incorporating them.
The talks by V. Vento and E. Perazzi elucidate certain aspects of such constituent quark models. The physics of the constituent quark is certainly at the heart what can be investigated at ELFE. To clarify it one does not Ned results at very small Bjorken-x but rather very precise results at modest Q2. The latter is needed to separate QCD-radiative corrections which typically involve log Q2 terms from higher-twist ones, involving 1/Q 2 ones.
Vento et al. have analyzed under which conditions a model with constituent quarks and gluons can evolve under DGLAP-evolution into the well known structure functions at large Q~. They find in agreement with similar investigations by other authors that a good match requires a very low starting point for the Q2 evolution (about 0.2 GeV 2) plus a substantial constituent gluon contribution. They point, however, to the well known problem, that DGLAP evolution at such small virtualities cannot be justified. In fact the phenomenologically acceptable fits at larger Q2 result to a large extent 0375-9474/97/$17.00 1997 - Elsevier Science B.V. PII: S0375-9474(97)00349-7
358c
A. Schiifer/Nuclear Physics A622 (1997) 357c-361c
from the fact that the DGLAP upward evolution converges to rather similar results for quite different starting distributions. Vento and Traini add to this general argument the observation that below the scale of the chiral phase transition at 1 GeV the evolution equations should really change, involving effective degrees of freedom like the pion field. It is actually known from model studies involving instanton configurations that the latter, which are only connected to the chiral symmetry phase transition, but do not produce confinement, are sufficient to generate the phenomenological properties of low mass hadrons (see the work by Shuryak et al.). This illustrates the importance of a description focusing on the chiral properties of QCD to obtain a satisfactory phenomenological description. Vento et al. are working on an improvement of their theory in this direction. Any such theory would necessarily involve dimensional parameters and thus 1/Q 2 terms. They would have to be mapped smoothly to the higher-twist corrections of the usual operator product expansion analysis of QCD. If successful such a description would be a major step towards a better understanding of this most important link between QCD and low-energy nuclear physics.
Perazzi et al. are actually working with a somewhat similar quark-gluon-pion model for the low energy properties of hadrons. Such models have been quite successful in the past in fitting mass spectra. Perazzi et al. performed a very severe test of these models by calculating the photon-coupling amplitudes for a number of resonances. Such amplitudes can be expected to be highly sensitive to details of the internal hadron structure and a successful fit would be therefore a very strong argument in favour of the underlying model. Unluckily the results are not encouraging. It turns out that the most sophisticated description involving configuration mixing as well as pion exchange currents does not give a better fit than simpler ones. This observation points to the difficulty that a realistic effective theory should allow for a systematic development, i.e. by including higher order terms the existence of which follows from theoretical arguments, it should be possible to achieve a better and better description of an ever wider range of data. The authors conclude that their results illustrate the limitations of a nonrelativistic model based on constituent quarks. I think that one can also draw a more optimistic conclusion. An acceptable effective low-Q 2 theory of hadron structure is of great importance. If it can be reached this success would certainly also be based on such detailed investigations as those performed by Perazzi et al.
S. Gerasimov gives a general analysis of SU(3) flavour symmetry predictions for hadronic properties, which can serve as a necessary boundary condition for model constructions on the level of constituent quarks as well as for the interpretation of perturbative spindependent QCD processes. The interpretation of the present data for the polarized proton and neutron structure functions in terms of the total spin carried by quarks is based on flavour SU(3) symmetry and involves a parameter F/D which describes the relative strength of the two manners in which three SU(3)-octets can couple. Gerasimov analyzes this quantity by confronting the magnetic moments an daxial-vector couplings
A. Schiifer/Nuclear PhysicsA622 (1997) 357c-361c
359c
of baryons.His result agrees only marginMly with that of Ratcliffe and suggest a much stronger negative strange quark polarization. This result has far reaching consequences, also for a future experimental program at ELFE. It turned out that NLO fits to the presently available data provide rather precise prediction for the polarized distribution functions Au(x) and Ad(x). However, the polarized gluon distribution AG(x) and the polarized strange quark distribution function As(x) is far less precisely predicted. Therefore most future effort in nucleon spin physics is directed towards a direct measurement of AG(x) and As(x) and it is very important that theory should come up with a generally accepted prediction with a realistic error bar before these experiments are done.
Another talk directly related to nuclear spin physics was given by R. Jakob. He and his collaborators analyzed the general structure of spin dependent reactions in which also the transverse momentum of an outgoing hadron is detected. Such reactions involve higher-twist structure and fragmentation functions which are the QCD objects for which one can hope to identify a low Q2 counterpart. The investigation of such quantities should play an ever greater role in the next decades and the systematic identification of all independent quantities is a necessary prerequisite for such studies. As one result of their complete classification Jakob et al. were able to derive several relations between fragmentation functions. The different fragmentation functions appeared originally in a complete Lorentz-decomposition of the relevant matrix elements and probably nobody would have been able to guess the derived relations from this original definition. The complete classification achieved by Jakob et al. is a necessary step, but only the first one in a far reaching program. The next steps will probably be the estimation of the identified independent quantities in some phenomenological models and a careful investigation of their Q2-dependence. Once these aims will be achieved it will be possible to deduce most interesting informations from a large class of new semi-inclusive experiments. Thus the present work promises to become of great phenomenological importance in the not too far future. This field of research could become especially important for ELFE because the new structure and fragmentation functions depending on the transverse momentum are most probably numerically small, such that very high intensity would be needed to measure them. Therefore ELFE could actually be the only place to perform such studies, which in the end would be of major help to pin down the internal nucleon wave function.
Peign6 et al. have studied a very different question, namely the energy-loss of high energy quarks or gluons in nuclear matter. This is not really a specific QCD problem, but rather a general one of many-particle physics which can be discussed equally for QED only. However, a reliable description of the partonic energy loss is possibly of vital importance for the interpretation of high energy heavy ion collisions. Presently the situation with respect to signals for the QCD phase transition, in partic-
360c
A. Schiller~Nuclear Physics A622 (1997) 357c-361c
ular the theoretical situation, is rather unsettled. None of the many proposed signals is uncontroversal. In this situation it is probable, that the discovery of the quark-gluonplasma will only be possible through a chain of quantitative arguments, none of which alone would provide sufficient evidence. Consequently a really quantitative theory of the hot QCD-phase is needed and this is still very badly missing. One crucial aspect of such a theory is the correct description of the screening effects due to the many soft gluons and quark-antiquark pairs created during the early phase of the collision. One aspect of this question is how the emission rate for bremsstrahlung is modified by the interference between amplitudes involving different scattering centers in the nuclear medium. This problem has already a long history and is usually discussed under the heading 'Landau-Pomeranchuk-Migdal' effect. The fundamental theoretical task is rather easy. One has to describe how, depending on the individual momentum transfers qi~z and distances between consecutive scattering reactions ziu, the interference between the different plane wave phases changes. The task is therefore to make realistic assumptions for the distribution of these quantities and to calculate the resulting sums of interfering amplitudes. Peign~ et al. stress in their contribution that the usually used random walk picture is not applicable because the Fourier-transformed scattering potentials do not decrease fast enough for large momentum transfers. From their improved description they arrive at the conclusion that the typical energy loss of a parton increases with the square of the distance travel through the nuclear medium (within the range of energies and temperatures in which their approximations are applicable). Such a quadratic length dependence is not as exotic as it might sound. It describes the fact that the usual suppression of Bremsstrahlung due to the LandauPomeranchuk-Migdal is less effective for larger distances. Quantitatively Peign~ et al. come up with the following predictions. For a nucleus of diameter 10 fm the typical energy loss of a parton is about 2 GeV for cold nuclear matter and 30 GeV for hot nuclear matter. For cold nuclear matter this energy loss could actually be derived from a detailed experimental investigation of hadron fragmentation, as any energy loss shifts the final hadron energies to smaller values. However, it could well be that the ELFE energy is too low for such investigations. I would like to mention that this work actually generated a large number of theoretical investigations and is presently one of those most actively discussed by the heavy-ion community.
Finally M. Vgntinnen et al. have studied the EMC-effect for so-called Ioffe-time distributions. This is formally completely equivalent to the usual discussions which make use of normal Bjorken-x distribution functions, and involve basically a Fourier-transformation in x. However, it is argued that the physical nature of the EMC-effect is more transparent in the Ioffe-time representation. The typical property of Ioffe-time distributions is that their behaviour for small Ioffe times y+ and/or small Bjorken-x (more precisely for xv + small) is just a straight line as a function of y+ the derivative of which is given e.g. by the first moment of F2(z). The latter is well known, being determined by the momentum fractions carried by the different quark-flavours. All the subtle effects of hadron structure show only up at large
A. Schiifer/Nuclear Physics A622 (1997) 357c-361c
361c
y+. This very general result is confirmed by V/~nttinen et al. for the EMC effect, which is thus illustrated to be due to a modification of the nucleon structure at relatively large distances.