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QCD and parity violation in high-energy NN scattering
Physics Letters B 268 ( 1991 ) 287-290 North-Holland
P H YS I C S L E T T E R S B
QCD and parity violation in high-energy NN scattering M. S h m a t i k o v Institute of Theoretical and Experimental Physics, SU-117 25 9 Moscow, USSR Received 8 July 1991
The parity violating effect is estimated in high-energy N N scattering. The longitudinal analyzing power AL is found to be = ( 12 ) × 10- 6 being practically constant in a wide energy range, The AL value obtained is close to the experimental result measured at somewhat lower energy.
A long-standing and challenging problem for the theory of weak N N interactions is the large value of the longitudinal analyzing powerAL measured in highenergy ~N scattering. AL is defined as follows: AL - - 0"+ a+ -+ a0"_ _ '
(1)
where a+ ( ~ r ) refers to the cross section for incident protons with positive (negative) helicity. The AL value measured for proton scattering on water at the laboratory momentum pl,b= 6 G e V / c was found to be [1] AL(p H 2 0 ) = (26.5_ 6.0_+ 3.6) × 10 -7
(2)
the first error being statistical and the second systematic. The nucleons in the target screen each other so that the AL value for the "elementary" ~N scattering process which corresponds to (2) is approximately 1.5 times larger [2 ]: AL= (45-+- 12) X 10 -7 .
(3)
The AL value was calculated in a number of approaches (see ref. [3 ] ). Most of them yielded a value of AL that was an order of magnitude smaller than the experimental result (2). The models which provided AL at the I0 -6 level are strongly criticized [3]. It is worth noting: that these latter approaches have one feature in common: a large AL value stems from the weak interaction of quarks belonging to one and the same nucleon. We consider another mechanism which can hopefully generate a large (i.e. ~ 10 -6) value of AL: weak
interaction of quarks belonging to colliding nucleons. Parity violating effects in the N N system reflect the combined action of weak and strong interaction between nucleon constituents. This implies that both strong and weak couplings should be described in terms of one and the same set of degrees of freedom or (more pragmatically) within one and the same model. Aiming at the N N interaction at high energies, one should also keep in mind that such a model must reproduce all its rich phenomenology: a constant or slowly increasing total cross section, a multiperipherical character of interaction, a large inelasticity or differently stated scattering amplitude, being practically purely imaginary. These features of the high-energy NN interaction are materialized in a plethora of models. To make quantitative conclusions one should choose one where the strong interaction amplitude is calculable explicitly in term of quarks and gluons. The model which meets these requirements and suits best our purposes is the one formulated in ref. [ 4 ]. Relegating the reader to ref. [4 ] for details we highlight the main points of the model which are of importance when calculating the amplitude of P-odd N N scattering. The main assumption of the model is that the characteristic momentum transfers q among quarks and gluons are large ( ~ 1 GeV). As a result the QCD coupling constant c~ (q2) is small, thus enabling applying methods of perturbative QCD (one can also find in ref. [4] arguments pro and contra such an approach). The smallness of o~ is compensated for by a large In ( s / q 2) factor (x/s being the CMS energy of the colliding particles). The
0370-2693/91/$ 03.50 © 1991 Elsevier Science Publishers B.V. All rights reserved.
287
Volume 268, number 2
PHYSICS LETTERS B
amplitude of NN scattering is obtained then by summing all [ a~ In (s/q2 ) ] n terms in the leading logarithmic approximation in energy LLA(E). Such a picture of high-energy NN interaction based on perturbative QCD predicts the Froissart regime for the energy dependence of the total cross section, the rapid increase of total multiplicity reproducing as well the main features of hadron interactions in a wide energy range; x/~= 50-900 GeV. The amplitude F of the quark-quark interaction in LLA(E) can be represented schematically by the diagram in fig. 1. The blob in this figure contains the gluonic ladder (corresponding to the bare pomeron) and the so-called semi-enhanced ("fan") diagrams. It is relevant to note that LLA(E) in the lowest order in a~ corresponds to the two-gluon model of the pomeron. Stripping factors unessential for further consideration, one can write the unitarity condition in the form Im F=p.cr,
(4)
where F is the forward scattering amplitude and p is the quark momentum. The crucial point is that the evolution of the gluonic cascade responsible for the interaction between quarks is triggered by the emission of only one gluon (filled circle in fig. 1 ). Other gluonic ladders recombine back without interacting with the t~rget, thus resulting in the renormalization of the quark wave function only. We cast the (forward scattering) amplitude F in a form which takes this property explicitly into account (quark bispinors are omitted for notational brevity): F=Tr f
o~.1~2a?uD~,(q)D(p-q) d4q
(5)
×fu',' D~',(q)" ½2~?, (27g)4, where Du~, (q) is the Green function of the gluon, D
!
10 October 1991
is that of the quark and f ~ is the amplitude of the quark-gluon scattering. The matrices/~a are the GellMann color matrices entering in the vertex of the quark-gluon coupling. Note that (5) is nothing but the definition of the quark-gluon scattering amp!itudef We proceed now to include the weak interaction in the amplitude of the high-energy qq scattering treated above. This amplitude does not involve Oq pairs since account of each of them entails loss of the large In (s/ q2) factor [ 4 ]. However, parity violation occurs due to the weak self-interaction of a quark emitting a gluon. We mean the vertex depicted in fig. 2. It is quite similar to the celebrated "penguin" diagram entering in the amplitude of nonleptonic decays of hyperons. So, relegating the reader to ref. [ 5 ] for the technique of the calculations, we concentrate our attention on the peculiarities of the diagram under consideration. First, both charged (W +-) and neutral ( Z °) bosons are operative. Second, the logarithmically diverging integral over the loop momenta is cut off by the propagator of the intermediate-vector boson (and not due to the cancellation by the same loop containing a heavy quark as occurs in the AS= 1 case), Besides, to make the results more lucid we neglect the right-hand components of the neutral weak quark current. These neglected terms are proportional to sinZ0w so their omission results in a -~ 20% error. The weak-interaction vertex of the gluon emission by the quark reads
-x//2 Gq2lc(g~v q~qv'~ q2 ] gs(tPL~v'½2a~L) (6) where G is the Fermi coupling constant, q~ is the fourmomentum of the gluon and gs is the strong quarkgluon coupling constant (g~ = ors). The K factor, assuming that the cut-off parameters at high (M) and low (#) momenta are the same for the loops with charged and neutral intermediate-vector bosons, reads //"
\\ N,*
Fig: 1. The amplitude of quark-quark scattering. Solid lines denote quarks and dotted lines gluons.
288
Fig. 2. The vertex Of P-odd gluon emission by the quark. The notations are as in fig. 1. The dash-dotted line denotes the inter, mediate vector boson.
Volume 268, number 2
x=
M2 In tt 2 .
PHYSICSLETTERSB
AL =2x/r~ ~cG( q2) 2 q cr . (7)
Parity violation manifests itself in the fact that only the left-hand component of the quark wave function [ 7JL= ½( 1 + 75) ~] is operative in the qqg vertex (6). (Recall that the left-handed particle possesses negative helicity). Note also that the vertex (6) is one and the same for both u- and d-quarks. In short-hand notation the parity-violating quarkgluon vertex reads (terms proportional to the quark mass are neglected) - x / 2 ~ c ( G "q2)(gs'Y~'~~)~a) p L ,
(8)
where PL is the projection operator filtering out lefthanded quarks, i.e., PL= 1 for such a quark and vanishes otherwise. Gluons are known not to couple with intermediate vector bosons. So the only possibility to violate parity in the qq scattering is to switch on the mechanism shown in fig. 2. It reduces to substituting the parityviolating qqg vertex (depicted by the empty circle in fig. 2) for one of the strong-interaction qqg vertices (filled circle in fig. 1 ). Thus the modified amplitude Fw can be readily obtained from (5) by changing as in the integral to - x/~ lc ( G. q2 ) "as'PL according to (8). The imaginary part of Fw then corresponds to the interference of strong- and weak-interaction amplitudes:for qq scattering. Now, in order to obtain the result in closed form, we take the q2 factor out of the integral at some characteristic Value ( q 2 ) . Then the Fw amplitude coincides up to a numerical factor with the strong interaction amplitude F yielding Im F,~ --- - x / ~ tcG(q2)PL Im F .
10 October 1991
(9)
Two remarks concerning (9) are relevant. First, the mechanism of weak interaction which we have considered yields a highly inelastic (and hence purely imaginary) amplitude of the P-odd qq scattering. Second, its energy dependence is the same as that of the strong-interaction cross section. The value of Im Fw averaged over the spin wave function of the projectile gives the difference of the cross sections (g+-~r_ ) in the numerator orAL (1). At the same time the denominator of AL is nothing but the total cross section ato, of the NN scattering. We get an expression for AL in the form
(10)
(Ttot
When deducing this expression from (9), i.e., averaging the PL operator over the polarized nucleon wave function we assumed, in the spirit of the patton model, an incoherent contribution of the valence quarks to the polarization of the nucleon. Then )],qis the mean helicity of a quark in the polarized nucleon with positive helicity. The ratio ~r/~r~otdeserves special attention. Earlier [see (4) ], cr denoted the total cross section of the NN interaction which corresponds to the imaginary part of the forward scattering amplitude F. The point is that the blob in fig. 1 contains not all conceivable diagrams which describe quark-gluon scattering. The leading logarithmic approximation LLA(E) enables to take into account ladder (one-pomeron exchange) and semi-enhanced ("fan") diagrams. At the same time enhanced reggeon diagrams and multipomeron exchanges are not included in the calculations [4]. For this reason the total cross section ~rcalculated in LLA(E) can differ from the measured value of the NN cross section ~rtot. So the ratio ~= a/a~ot shows the accuracy of perturbative QCD supplemented by LLA(E). Generic estimates given in ref. [4] which base on the analysis of Drell-Yan pair production give ~-~ 0.5. The accuracy of the approach is expected to increase with growing energy (~-~ 1 ) but very slowly. Independent estimates [ 6 ] show that in the w/s = 20-500 GeV energy range the one-pomeron exchange contributes to ~rtotat - 70% level (~_~0.7). Before proceeding to the calculation of AL we would like to emphasize that (10) was obtained without making any assumptions additional to those which underlie the strong-interaction model [ 4 ]. Parity violation occurs since (only) the left-handed quark can trigger the development of an additional gluonic ladder which evolves due to the same QCD mechanism which governs the strong interaction of quarks and gluons. The point of crucial importance is the characteristic value of the transversal momenta (or virtuality) ( q2 ) which travels along the gluonic ladder. According to ref. [ 4 ] a consistent description of high-energy data is achieved for large enough (q2) values. Namely, provided # being the virtuality of a quark in the nucleon (#-~ 300-400 MeV), ~ - ~ 4/z (we 289
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PHYSICS LETTERS B
refer the reader to ref, [4] for corresponding arguments). Recall that # is the low-momentum cut-off parameter in the integral entering in the P-odd qqg vertex [ see ( 7 ) ]. Then for #-~ 400 MeV we obtain AL~10-5~q
.
(11)
The resulting value OfAL depends on the polarization of quarks within the polarized nucleon. So we must make an assumption concerning the 2q value. Note that up to now no assumptions were introduced but those which underlie the strong-interaction model [ 4 ]. As a conservative guess we assume that the proton's spin is carried by quarks and, besides, it is distributed equally among them. Such an assumption implies that ~q = ½, yielding AL--3X 10-6~.
(12)
Nonstandard mechanisms suggested for the explanation of EMC data [7 ] assume that the proton's spin is generated either by the orbital motion of quarks [ 8 ] or it is carried by gluons [ 9 ]. Any of these issues implies that the quarks in the nucleon are unpolarized so that the resulting AL value is much smaller than (12). Thus in the favorable case when the quarks in the nucleon are polarized and the characteristic momenta of the gluons are rather large, one can expect that AL at high energies amounts to ( 1-2 ) X 10 -6. We can conclude that perturbative QCD supplemented by LLA (E) which describes successfully highenergy NN interactions yields as well a large value of the parity-violation effect. Parity violation in N N scattering occurs because the left-handed quark (in contrast to the sterile right-handed one) can emit a
290
10 October 1991
gluon which evolves into the pomeron ladder. Calculations, both in strong- and weak-interaction sectors, are based on a large value of the characteristic momentum in the gluonic ladder ( ~ 1 GeV). The probability of such a process is driven by the value of the G
P H YS I C S L E T T E R S B
QCD and parity violation in high-energy NN scattering M. S h m a t i k o v Institute of Theoretical and Experimental Physics, SU-117 25 9 Moscow, USSR Received 8 July 1991
The parity violating effect is estimated in high-energy N N scattering. The longitudinal analyzing power AL is found to be = ( 12 ) × 10- 6 being practically constant in a wide energy range, The AL value obtained is close to the experimental result measured at somewhat lower energy.
A long-standing and challenging problem for the theory of weak N N interactions is the large value of the longitudinal analyzing powerAL measured in highenergy ~N scattering. AL is defined as follows: AL - - 0"+ a+ -+ a0"_ _ '
(1)
where a+ ( ~ r ) refers to the cross section for incident protons with positive (negative) helicity. The AL value measured for proton scattering on water at the laboratory momentum pl,b= 6 G e V / c was found to be [1] AL(p H 2 0 ) = (26.5_ 6.0_+ 3.6) × 10 -7
(2)
the first error being statistical and the second systematic. The nucleons in the target screen each other so that the AL value for the "elementary" ~N scattering process which corresponds to (2) is approximately 1.5 times larger [2 ]: AL= (45-+- 12) X 10 -7 .
(3)
The AL value was calculated in a number of approaches (see ref. [3 ] ). Most of them yielded a value of AL that was an order of magnitude smaller than the experimental result (2). The models which provided AL at the I0 -6 level are strongly criticized [3]. It is worth noting: that these latter approaches have one feature in common: a large AL value stems from the weak interaction of quarks belonging to one and the same nucleon. We consider another mechanism which can hopefully generate a large (i.e. ~ 10 -6) value of AL: weak
interaction of quarks belonging to colliding nucleons. Parity violating effects in the N N system reflect the combined action of weak and strong interaction between nucleon constituents. This implies that both strong and weak couplings should be described in terms of one and the same set of degrees of freedom or (more pragmatically) within one and the same model. Aiming at the N N interaction at high energies, one should also keep in mind that such a model must reproduce all its rich phenomenology: a constant or slowly increasing total cross section, a multiperipherical character of interaction, a large inelasticity or differently stated scattering amplitude, being practically purely imaginary. These features of the high-energy NN interaction are materialized in a plethora of models. To make quantitative conclusions one should choose one where the strong interaction amplitude is calculable explicitly in term of quarks and gluons. The model which meets these requirements and suits best our purposes is the one formulated in ref. [ 4 ]. Relegating the reader to ref. [4 ] for details we highlight the main points of the model which are of importance when calculating the amplitude of P-odd N N scattering. The main assumption of the model is that the characteristic momentum transfers q among quarks and gluons are large ( ~ 1 GeV). As a result the QCD coupling constant c~ (q2) is small, thus enabling applying methods of perturbative QCD (one can also find in ref. [4] arguments pro and contra such an approach). The smallness of o~ is compensated for by a large In ( s / q 2) factor (x/s being the CMS energy of the colliding particles). The
0370-2693/91/$ 03.50 © 1991 Elsevier Science Publishers B.V. All rights reserved.
287
Volume 268, number 2
PHYSICS LETTERS B
amplitude of NN scattering is obtained then by summing all [ a~ In (s/q2 ) ] n terms in the leading logarithmic approximation in energy LLA(E). Such a picture of high-energy NN interaction based on perturbative QCD predicts the Froissart regime for the energy dependence of the total cross section, the rapid increase of total multiplicity reproducing as well the main features of hadron interactions in a wide energy range; x/~= 50-900 GeV. The amplitude F of the quark-quark interaction in LLA(E) can be represented schematically by the diagram in fig. 1. The blob in this figure contains the gluonic ladder (corresponding to the bare pomeron) and the so-called semi-enhanced ("fan") diagrams. It is relevant to note that LLA(E) in the lowest order in a~ corresponds to the two-gluon model of the pomeron. Stripping factors unessential for further consideration, one can write the unitarity condition in the form Im F=p.cr,
(4)
where F is the forward scattering amplitude and p is the quark momentum. The crucial point is that the evolution of the gluonic cascade responsible for the interaction between quarks is triggered by the emission of only one gluon (filled circle in fig. 1 ). Other gluonic ladders recombine back without interacting with the t~rget, thus resulting in the renormalization of the quark wave function only. We cast the (forward scattering) amplitude F in a form which takes this property explicitly into account (quark bispinors are omitted for notational brevity): F=Tr f
o~.1~2a?uD~,(q)D(p-q) d4q
(5)
×fu',' D~',(q)" ½2~?, (27g)4, where Du~, (q) is the Green function of the gluon, D
!
10 October 1991
is that of the quark and f ~ is the amplitude of the quark-gluon scattering. The matrices/~a are the GellMann color matrices entering in the vertex of the quark-gluon coupling. Note that (5) is nothing but the definition of the quark-gluon scattering amp!itudef We proceed now to include the weak interaction in the amplitude of the high-energy qq scattering treated above. This amplitude does not involve Oq pairs since account of each of them entails loss of the large In (s/ q2) factor [ 4 ]. However, parity violation occurs due to the weak self-interaction of a quark emitting a gluon. We mean the vertex depicted in fig. 2. It is quite similar to the celebrated "penguin" diagram entering in the amplitude of nonleptonic decays of hyperons. So, relegating the reader to ref. [ 5 ] for the technique of the calculations, we concentrate our attention on the peculiarities of the diagram under consideration. First, both charged (W +-) and neutral ( Z °) bosons are operative. Second, the logarithmically diverging integral over the loop momenta is cut off by the propagator of the intermediate-vector boson (and not due to the cancellation by the same loop containing a heavy quark as occurs in the AS= 1 case), Besides, to make the results more lucid we neglect the right-hand components of the neutral weak quark current. These neglected terms are proportional to sinZ0w so their omission results in a -~ 20% error. The weak-interaction vertex of the gluon emission by the quark reads
-x//2 Gq2lc(g~v q~qv'~ q2 ] gs(tPL~v'½2a~L) (6) where G is the Fermi coupling constant, q~ is the fourmomentum of the gluon and gs is the strong quarkgluon coupling constant (g~ = ors). The K factor, assuming that the cut-off parameters at high (M) and low (#) momenta are the same for the loops with charged and neutral intermediate-vector bosons, reads //"
\\ N,*
Fig: 1. The amplitude of quark-quark scattering. Solid lines denote quarks and dotted lines gluons.
288
Fig. 2. The vertex Of P-odd gluon emission by the quark. The notations are as in fig. 1. The dash-dotted line denotes the inter, mediate vector boson.
Volume 268, number 2
x=
M2 In tt 2 .
PHYSICSLETTERSB
AL =2x/r~ ~cG( q2) 2 q cr . (7)
Parity violation manifests itself in the fact that only the left-hand component of the quark wave function [ 7JL= ½( 1 + 75) ~] is operative in the qqg vertex (6). (Recall that the left-handed particle possesses negative helicity). Note also that the vertex (6) is one and the same for both u- and d-quarks. In short-hand notation the parity-violating quarkgluon vertex reads (terms proportional to the quark mass are neglected) - x / 2 ~ c ( G "q2)(gs'Y~'~~)~a) p L ,
(8)
where PL is the projection operator filtering out lefthanded quarks, i.e., PL= 1 for such a quark and vanishes otherwise. Gluons are known not to couple with intermediate vector bosons. So the only possibility to violate parity in the qq scattering is to switch on the mechanism shown in fig. 2. It reduces to substituting the parityviolating qqg vertex (depicted by the empty circle in fig. 2) for one of the strong-interaction qqg vertices (filled circle in fig. 1 ). Thus the modified amplitude Fw can be readily obtained from (5) by changing as in the integral to - x/~ lc ( G. q2 ) "as'PL according to (8). The imaginary part of Fw then corresponds to the interference of strong- and weak-interaction amplitudes:for qq scattering. Now, in order to obtain the result in closed form, we take the q2 factor out of the integral at some characteristic Value ( q 2 ) . Then the Fw amplitude coincides up to a numerical factor with the strong interaction amplitude F yielding Im F,~ --- - x / ~ tcG(q2)PL Im F .
10 October 1991
(9)
Two remarks concerning (9) are relevant. First, the mechanism of weak interaction which we have considered yields a highly inelastic (and hence purely imaginary) amplitude of the P-odd qq scattering. Second, its energy dependence is the same as that of the strong-interaction cross section. The value of Im Fw averaged over the spin wave function of the projectile gives the difference of the cross sections (g+-~r_ ) in the numerator orAL (1). At the same time the denominator of AL is nothing but the total cross section ato, of the NN scattering. We get an expression for AL in the form
(10)
(Ttot
When deducing this expression from (9), i.e., averaging the PL operator over the polarized nucleon wave function we assumed, in the spirit of the patton model, an incoherent contribution of the valence quarks to the polarization of the nucleon. Then )],qis the mean helicity of a quark in the polarized nucleon with positive helicity. The ratio ~r/~r~otdeserves special attention. Earlier [see (4) ], cr denoted the total cross section of the NN interaction which corresponds to the imaginary part of the forward scattering amplitude F. The point is that the blob in fig. 1 contains not all conceivable diagrams which describe quark-gluon scattering. The leading logarithmic approximation LLA(E) enables to take into account ladder (one-pomeron exchange) and semi-enhanced ("fan") diagrams. At the same time enhanced reggeon diagrams and multipomeron exchanges are not included in the calculations [4]. For this reason the total cross section ~rcalculated in LLA(E) can differ from the measured value of the NN cross section ~rtot. So the ratio ~= a/a~ot shows the accuracy of perturbative QCD supplemented by LLA(E). Generic estimates given in ref. [4] which base on the analysis of Drell-Yan pair production give ~-~ 0.5. The accuracy of the approach is expected to increase with growing energy (~-~ 1 ) but very slowly. Independent estimates [ 6 ] show that in the w/s = 20-500 GeV energy range the one-pomeron exchange contributes to ~rtotat - 70% level (~_~0.7). Before proceeding to the calculation of AL we would like to emphasize that (10) was obtained without making any assumptions additional to those which underlie the strong-interaction model [ 4 ]. Parity violation occurs since (only) the left-handed quark can trigger the development of an additional gluonic ladder which evolves due to the same QCD mechanism which governs the strong interaction of quarks and gluons. The point of crucial importance is the characteristic value of the transversal momenta (or virtuality) ( q2 ) which travels along the gluonic ladder. According to ref. [ 4 ] a consistent description of high-energy data is achieved for large enough (q2) values. Namely, provided # being the virtuality of a quark in the nucleon (#-~ 300-400 MeV), ~ - ~ 4/z (we 289
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refer the reader to ref, [4] for corresponding arguments). Recall that # is the low-momentum cut-off parameter in the integral entering in the P-odd qqg vertex [ see ( 7 ) ]. Then for #-~ 400 MeV we obtain AL~10-5~q
.
(11)
The resulting value OfAL depends on the polarization of quarks within the polarized nucleon. So we must make an assumption concerning the 2q value. Note that up to now no assumptions were introduced but those which underlie the strong-interaction model [ 4 ]. As a conservative guess we assume that the proton's spin is carried by quarks and, besides, it is distributed equally among them. Such an assumption implies that ~q = ½, yielding AL--3X 10-6~.
(12)
Nonstandard mechanisms suggested for the explanation of EMC data [7 ] assume that the proton's spin is generated either by the orbital motion of quarks [ 8 ] or it is carried by gluons [ 9 ]. Any of these issues implies that the quarks in the nucleon are unpolarized so that the resulting AL value is much smaller than (12). Thus in the favorable case when the quarks in the nucleon are polarized and the characteristic momenta of the gluons are rather large, one can expect that AL at high energies amounts to ( 1-2 ) X 10 -6. We can conclude that perturbative QCD supplemented by LLA (E) which describes successfully highenergy NN interactions yields as well a large value of the parity-violation effect. Parity violation in N N scattering occurs because the left-handed quark (in contrast to the sterile right-handed one) can emit a
290
10 October 1991
gluon which evolves into the pomeron ladder. Calculations, both in strong- and weak-interaction sectors, are based on a large value of the characteristic momentum in the gluonic ladder ( ~ 1 GeV). The probability of such a process is driven by the value of the G
~ 50 GeV. So one cannot compare directly the AL value (12) to the experimental result (2) obtained for x/~-~ 20 GeV and it should be considered rather as a prediction for future high-energy experiments. The author is grateful to K. Boreskov and P. Volkovitsky for helpful discussions.
References [ 1] N. Lockyer et aL, Phys. Rev. Lett. 45 (1980) 1821. [ 2] L.L. Frankfurt and M.I. Strikman, Phys. Lett. B 107 ( 1981 )
99. [3]M. Simonius, Proc. Syrup. on Spin and symmetries (TRIUMF, Vancouver, 1989), eds. W.D. Ramsey and W.T.H. van Oers, report TRI-89-5 (1989) p. 20. [4 ] E.M. Levin and M.G. Ryskin, Phys. Rep. 189 (1990) 267. [5] L.B. Okun', Leptons and quarks (North-Holland, Amsterdam, 1982). [6] K.A. Ter-Martirosyan,Phys. Lett. B 44 (1973) 377. [7] J. Ashman et al., Phys. Lett. B 206 (1988) 364. [8] S. Brodskyet al., Phys. Lett. B 206 ( 1988 ) 309. [9] B. Lampe, Phys. Lett. B 227 (1989) 469.