KEK-79-14 July 1979 TRISTAN
PHOTOPRODUCTION AT TRISTAN ENERGY
K. Ishida, T. ICobayashi and T. Yoshino
NATIONAL LABORATORY FOR HIGH ENERGY PHYSICS OHO-MACHI, TSUKUBA-GUN 1BARAKI, JAPAN KEK Reports are available from
Technical Information Office National Laboratory for High Energy Physics Oho-machi, Tsukuba-gun Ibaraki-ken, 300-32 JAPAN
Phone: 0298-64-1171 Telex: 3652-534 (Domestic) (0)3652-534 (International) Cable: KEK0H0 Photoproduction at TRISTAN Energy
K. Ishida, T. Kobayashi and T. Yoshino
Department of Physics Tokyo Metropolitan University Fukazawa, Setagaya, Tokyo 158 Japan
Abstract
Focussing our attention upon the structure of photon we discuss its complementary aspects represented by the vector meson dominance (VMD) and the perturbative quantum chromo- dynamics (QCD). Photoproduction of vector mesons and that of large transverse momentum jets are studied as testing ground for two aspects, in the energy range of TRISTAN
(Ee- x Ep2:20 GeV x 300 GeV). It is found that Vector Mesons of mass up to ~ 10 GeV will be produced more than once per day for tagged photons. Large- p^ jet production is found rather copious and it can be a good probe to study the photon structure function predicted from QCD. SI. Introduction
New energy range to be explored by coining very big accelerators would force us to concentrate our attention on very fundamental and unified aspects of high energy interactions. The Weinberg-Salam model ^ has succeeded in unifying electro magnetic and weak interactions while quantum chromodynamics CQCD) ' has become a prime candidate for the theory of strong +) interactions. In this respect TRISTAN project, an electron- proton colliding beam facility produced in KEK, will bring us valuable informations both on weak and strong interactions. While much attention has been paid on deep-inelastic lepton scattering, very high energy photoproduction will also provide us another important source of interactions. In this report we shall concentrate ourselves on studying the structure of photons at the TRISTAN energies; the laboratory momenta of colliding electron and proton are 20 and 300 GeV, respectively, and the luminocity of taggedT- P collision is 'vl029/cm2-sec. We are very much concerned about how photon manifests itself through interactions with other particles, particularly, with hadrons. It is widely accepted that the vector meson dominance model (VMD)3) provides a useful and successful description of low momentum transfer reactions. This implies that the photon has very similar internal structure to that of hadrons.*' Does this persist in higher energies? In the events with large transverse momentum hadrons, on the other hand, the process should be governed by the short distance mechanism and one might naively expect a point-like coupling of the photon with partons to dominate the cross sections. The perturbative QCD tells us, however, that the photon should also have internal quark structure which is calculable with the help of the renomalization group (RG)-equations. ' Photoproduction of large-Px jets will thus he useful to probe the photon structure predicted from QCD. In the present report we attempt our preliminary first step toward a unified understanding of the photon structure which should be revealed in future. If QCD is the correct theory of strong interactions, perturbative and nonperturbative (VMD) aspects will finally be unified as a complementary entity like resonance and Regge behaviors in the duality. It is our expectation that this ambitious program may gradually be realized through studies of high energy photoproduction process. In J 2 we show predictions of the VMD on the total photon- proton cross section and on vector meson production. These investigation will give a simple criterion for the validity of the VMD. Section 3 deals with the high-p^ jet production in photon-proton collisions in the framework of the perturbative QCD. At TRISTAN, the colliding beam facility of 300 GeV proton and photons from the 20 GeV electrons, enable us to carry out various kinds of interesting experiments. Some topics other than those described in $ 2 and § 3 are briefly mentioned in|4. Photoproduction data are obtained from ep collisions in the limit of small momentum transfer, say, Q 2 < m£2. For actual calculations
- 3 - we neglect this small Q values and assume it to be equal to zero. The effective luminosity of tagged-photon proton collisions will thus be two-orders of magnitude smaller than that of electron-proton collisions.
$2. Hadronic Behavior of Photons
The vector meson dominance model (VMD) has been successful in describing various aspects of photoproduction processes at small momentum transfers in the presently available photon energy region. In order to get the first clue to phenomena in yet unattainable high energy region a simple extrapolation of the existing model may be useful. In this section we extrapolate the predictions of the VMD to the TRISTAN energy range. This kind of calculations were already done by others in planning the future projects. ' We will, however, make some improvement on several respects.
2.1. Total Photon Cross Section on Protons
It has been well known that the total photon cross section on proton ( fli^ ) shows the remarkable similarity to the pion- nucleon total cross section apart from the overall normalization. This strongly suggests that the vector meson dominance (VMD] mechanism would be responsible for a major part of the total cross section. It is of great interest to see whether or not the similarity holds in the TRISTAN energy range (s < 24,000 GeV ) which is far beyond the one presently available. The total photon cross section on proton can be written in the VMD as
t(s) = i) °# f T^;crvt,(s) c,
Here & (= 1/137) is the fine structure constant of QED, s being the total center of mass energy squared, OTWs) and VL. are the vector meson-proton total cross section and the photon-vector meson coupling constant, respectively. We assume that the sum over vector mesons Z extends over f, to , 0 , and J/ty-. V Additive quark model is used for the Vector Meson total cross sections of proton. Figure 1 shows the result. At the maximum TRISTAN energy we have Oifli^^" ,1D' *^w e comPare our result with the
total cross section at presently available energy (Ey Js. 180 GeV) ' the rising behavior seems to be rather slow. Our moderate energy dependence is attributed to the slowly rising asymptotic cross sections parametrized •" as a + b In s. If a new quark flavor is produced above certain threshold energy, it is expected that trt the total cross section (Sip will show an abnormal rise at the threshold. Whether such a behavior can be 3een or not remains an open question.
2.2. Vector Meson Photoproduction
Since the vector mesons have the same quantum number JPC = l"~ as the photon they are diffractively produced at high energies as shown in Fig. 2. Then we expect new heavy vector
- S mesons to be diffractively produced copiously at TRISTAN. The VMD idea is also useful here. The total cross section for r + p —»V + P can he written as 9^
where By denotes the slope parameter of the differential cross section appearing in
at vdt k^z^J^
andQvp(s), the total cross section of Vp collisions. Here t represents the usual momentum transfer squared and t . is its kinematically allowable minimum. For light Vector mesons if,CO ,
parameter we examine two altarnatives: (a) Bv = const.
2 2 2 4) = Bu=i 7.5 GeV' , BBff ==££ 5.5.55 GeGeV"V , BBJ/(J/(.. ::xx 2.2.00 GeV"GeV
(b) Bv(s) = bT + 2 (X'finCs/sc). Here bv = Bv - 2'a'€nC50/so] ,
1 K ~ 0.2 is the pbmeron slope ' and s0 is the scale parameter f set equal to 1 GeV . Shown in figure 3 are the VMD estimates of the total photoproduction cross sections of light vector mesons plotted against s. In estimating heavy vector meson production cross sections beyond the J/iJ-, we have to be careful because of too many unknown factors. Nevertheless, some reasonable assumptions allow us to evaluate the production yields. First we have to properly take into account the threshold behavior. As the simplest form we adopt the parametrization for the J/$|r photoproduction used by Thorndike •*,
4)
where sth and s0 are, respectively, the threshold of the heavy vector meson and the appropriate mass scale. We find that the choice
s o " sth =; 7.5 m*
can reproduce both J/^r and $ photoproduction threshold behavior. Empirically, we have '' '
12, >
which works reasonably well. After passing over the steep rise in the threshold region, the cross section is leveled off and follows the behavior of that of light vector mesons. As
for the slope parameter we also examine two cases (a) Bv = Bjt^
2 2 = ZGeV" and (b) By(s) = Bj^ +2tf £n(s/s0), ft' being 0.2 GeV" . In fig. 4, we show energy dependence of the production cross sections of T and VCtf). The cross section of }T photo production' at s 2£20,000 GeV can be read
- 7 - The use of untagged photons probably increases the yield by about two-orders of magnitude. The counting rate of V[tt) heavier than 20 GeV, however, is too low to be observed even at the highest TRISTAN energy.
2.5. Pseudoscalar Meson Production via Primakoff Effect
Another interesting photoproduction process is the Primakoff production of a new even-charge conjugation states with J * 1 composed of new quark flavors, especially, pseudscalar partners of heavy vector mesons. Shown in Fig- 5 is the schematic illustration of the production process Y+ P -*x * p followed by the decay X-+YY. The differential cross section can be written as '
4 where t ^2i -m* mp/s and Fp [t) is the proton f(f|cjm factor which we assume to be the familiar dipole type (1 ~ 0TT7T-'
the artial For /""«_»2 y P width of the pseudoscalar X to two photons, we employ the evaluation in the quarkonium model
ps 3 (2 n rx^2rc > • VreeM. -
eq being the quark charge in unit of the proton charge. Figures 6 and 7 show differential cross section and total cross section, respectively, for 7LD,'J » 7c » *lb' t'le pseudoscalar partner of Tf and speculative "t, the pseudoscalar partner of V(tt). We use direct experimental data or the result'
7 7 are on70° and ? . For 7C and ?!,, the value of fx-+ZTf evaluated
- 8 - in terras of eq. (2.7) utilizing the experimental data. The
/ e empirical relation fe'eC»0 ' q = constant gives us J"" (y(tt))
2£5keV et being 2/3 which is employed by us in the "J}t production. If we take into account the limitation of angle for proton detection i,e, }J10 mrad to beam direction, our results of total cross section integrated to the kanematically allowable t are mjr. overestimate. However, the yields of new pseudoscalar (e.g. ^b» ?t) aTe still too low to be detected at TRISTAN energy region. A way out of this situation may be to do the inclusive measurement, t + P —*X + anything, without detecting ' the scattered proton together with increasing the luminosity by using untagged photons. j3. Jet Production in Photon-Proton Collisions
It is widely accepted that the jet production plays a primarily important role in high energy particle reactions. Perturbative quantum chromodynamics (QCD) •* approach has provided us rather powerful tools ' for elucidating mechanisms of large-pj_ jet production, which enables us to get a deeper insight into particle production processes. Application of the QCD-approach on photoproduction processes, however, has just started ' and, to our knowledge, it is still in primitive stage compared to various analyses in other large momentum transfer reactions. Based on the perturbative QCD we discuss heTe very high energy photoproduction of laTge transverse momentum jets
- 9 - JT+ p—»Jet + X . This process is of great interest since it gives us certain information about how the photon interacts
with the proton in high-px process, i.e., at short distances. Does TRISTAN give us any experimental feasibility to make clear about this point? This is our primary concern underlying the following discussion. When the projectile photon acts as an elementary field on a constituent (quark q, antiquark q and gluon G) in the
proton, it transfers entire energy to outgoing large-px jets and no spectator jet should be found in the foward direction in the photon-proton center-of-mass system. Accounting the spectator jet from the target proton, we find three -jet structure in this case. On the other hand when the photon acts as a quark-antiquark system, in the leading logarithmic approximation, the interaction with the proton is realized through the constituent and we have a four-jet structure including "the spectator jet associated with the projectile photon. In the large-pi jet trigger experiments, angular distributions of the away jet will distinguish between these two mechanisms from each other. In the parton model, invariant cross section for inclusive one jet Cc) production is given by
*^4?{!TP-»-CX) = 2 fa*, fa* Pa*fe.6?)Ph/i,fe,Cf) d \P a,b J J A An- *^nr(a-b-»cd) (3.13
- 10 - 2 2 where Pa/r(xlf Q } and Pb/pCx2, Q } denote, respectively, parton distribution functions inside the photon and proton with respective momentum fractions x. and x, (see Fig. 8). A A The letters a/and |> ( u) and p )'denote, respectively, the energy and momentum of the parton c in the J?"t>(ab) center-of- mass system. We take the scale parameter Q to be the transverse
momentum squared (pj. ) of the jet c which coincides with the momentum transfers of the subprocesses -t and -u in the limit of t/s—»0 and u/s—>0, respectively. For proton structure function, we adopt the parametrization of Buras and Gaemers ' for valence quarks and the one improved by Owens and Reya '
for gluons and sea quarks. As for Pa/--Cx, Q ) we take the following two terms:
P-Vj-Cx, Q2) = S(x - 1) (3.2a)
p (x QZ, =_3_C The density (3.2a) corresponds to the elementary photon neglecting the small corrections of order Ot . The latter one (3.2b) shows the valence quark distribution in the photon , which includes effects of all order in the QCD coupling constant squared 0(5 in the lowest order of electromagnetic fine structure constant 0(. We use the four flavor form of the running coupling 2 2 2 constant, 0(S(Q ) = 12K/2s£n(Q /A ) with A = 0.5 GeV. In eq. (3.2b) e„ denotes the quark electromagnetic charge (in unit of the proton charge) and 7fE = 0.577-.. is Euler's constant. - 11 - The subporcesses with the elementary photon in the initial state are jTq—»qG, Jfq—>Gq, JfG—»qq and JTG—*qq, where cross sections are calculated in the lowest order QCD perturbation (see ref. IS for the explicit form). The subprocess cross sections entering in the four-jet processes can be found, e.g., in ref. 21. In actual calculation we take s = 2,400 GeV , one tenth Cf the maximum center of energy squared available in TRISTAN. Figure 9 shows the invariant cross section y? (ff"* p—•Jet + X) dr for the three-jet event at Q = 90° plotted against xx = ?fc.A/s. The prominent gluon contribution is due to the large gluon A production cross section —Sf-CJTq—*Gq) in the backward direction dt in the constituent cm. frame. Large contributions also come from !Tu—»uG at large Xj. (xj. 2. 0-4), and from 2TG—>uu, uu at small Xx (xj. •£ 0.3). If we assume the luminosity of Photon-proton collisions to be 102 9 cm- 2 sec -1, the rate of 2 large -pj_ events at Xj. ~ 0.3 is about 1/day GeV . Shown in Fig. 10 is the production cross section of large - t»x jets in the four-jet events. Comparing Fig. 10 with Fig. 9 we can see that for Xj_ ^ 0.4 the four - jet events dominate over the three - jet events. Angular distributions of jets at fixed Xj. = 0.3 and 0.5 are shown in Fig. 11(a) and 11(h), respectively. One can clearly see the dominence of the four - jet events at smaller xj. . We expect the marked difference in angular distributions of the away jets between the three - and four - jet processes - 12 - since in the three-jet events the away jet location is kinematically fixed by the triggering jet. The rapidity dis tributions of the away-jet are plotted in Fig. 12 to 14. For the three-jet events one naively expect delta function - type distribution. Regarding the finite resolution of the detector and the transverse momentum spread of jets, we assumed for simplicity the Gaussian form with its dispersion 0.10 or 0.05 in the rapidity space. At xx=0.3 and 0cm= 135° (Fig- 12) large contribution from the four-jet processes prevents us from clearly distinguishing two types of events. We see a clear difference between them at xx = 0.5 as shown in Fig. 13. As far as the production rate is concerned, however, xA = 0.5 is not a favorable option. Figure 14 shows the same distribution as before at xA = 0.3 but at Qct, = 45°. In this case, the away-jet rapidity distribution in the three-jet events is remarkably different from that in the four-jet events. j4. Supplementary Remarks 2 In contrast to physics with large Q , physics with small 2 Q is still in vague. Photoproduction by almost real photons 2 just brings us an interpolation problem between Q = 0 and large 2 2 Q (deep inelastic processes). Are these regions of Q smoothly 2 connected? Reactions induced by continuously variable Q will reveal us interesting aspects of photoproduction. In this respect we mention some topics other than those discussed in previous sections. - 13 - (1) Multiparticle final state: The average multiplicity is a useful observable which characterizes global features of multiparticle final states. In virtual photoproduction the 2 average multiplicity is a function of Q and collision energy. Low energy experimental data ', however, show that Q dependence of average multiplicity is very weak for Q jC 8 GeV and is almost equal to that of Q = 0. This does not seem to be accidental. Some years ago Bjorken and Kogut suggested a correspondence arguments foT high energy collisions. They emphasized that the dynamics in high Q should be continuously linked with the small Q dynamics. The average multiplicity seems to be a good example of this correspondence argument. 2 At high collision energy and high Q it is often expected that both a hadron plateau and current plateau emerge as separated in the rapidity distribution. According to corre spondence arguments, the heights of hadron plateau and current plateau should be equal. This will experimentally be further tested at TRISTAN. (2] Basic ideas of the Regge pole model is still useful although it is not fashinable now. One of the problems which remains still unsolved there is the existence of the fixed pole at 241 J = 0 in the scattering amplitude for elastic Compton scattering. This seems to invalidiate the similarity of photo-reactions to purely hadronic ones where no fixed pole appears at all. The parton model gives 3/2 for the ratio of the value of the proton 25 J1 fixed pole to the neutron one . - 14 - Experimentally, however, the value for the neutron is consistent with zero. The accurate data on high energy photon cross section on nucleon would be crucial to evaluate reliable values of the fixed pole. (3) Inelastic Compton scattering is also a fruitful source of information on the deep structure of the nucleon . ' Some attempts '' on this line has recently been made. (4) The Regge pole analyses of various inclusive reactions will still be valuable. •* The Q dependence_of the inclusive cross sections is interesting-in connection with the inclusive- exclusive interrelations. Acknowledgements We would like to.express our gratitude to Professor J. Arafune and Dr. Y. Shimizu for encouragements and to Professor T. Nishikawa for the hospitality of KEK. We thank Dr. K. Hagiwara for his help and valuable discussion on the subjects developed in 552 and 3. We are also grateful to Dr. S. Saito and Dr. H. Minakata for careful reading of the manuscript. - IS - Reference +) T. Nishikawa, Proceedings of the International Symposium on High Energy Phys. Tokyo (1974), P. 157. "A Preliminary Design of Tri-Ring Intersecting Storage Accelerators in Nippon, TRISTAN", KEK-Preprint-3 (1974). Proceedings of the First Workshop on Physics Aspects in the TRISTAN-Projecj (in Japanese) KEK-7S-6 (1975). Proceedings of the Third TRISTAN Workshop, KEK-77-8 (1977). 1) S. Weinberg, Phys. Rev. Letters 1![ (1967) 1264; A. Salam, in "Elementary Particle Physics" edited by N. Svartholm (A'lmquist and Forlag, Stockholm, 1968), 367. For recent phenomenology, see e.g., S. Weinberg, in Proc. XIX Int. Conf. on High Energy Phys., Tokyo, 1978, P.907 • Z) For reviews, see e.g., H. D. Politzer, Phys. Reports 14c (1974) 129; W. Marciano and;H. Pagels, Phys. Reports 36c (1978) 137. 3) Lecture: D. Shildknecht, Springer Tract, Volume 63, P. 57. 4) An extensive review on hadronic properties of photon is found Jin T. H. Bauer, R. D. Spital, D. R. Yennie and F. M. Pipkin, Rev. Mod. Phys. M> (1978), 261. Many references will be found there in. 5) E. Witten, Nucl. Phys. B120 (1977), 189. Applications to photon-photon collisions can be found, e. g., in S. J. Brodsky., T. De. Grand, J. Gunion and J. Weis, Phys. Rev. D19 (1979), 1418. 6) CHEEP, CERN, Yellow report, 78-02 (1978); C. H. Llewellyn Smith and B. H. Wiik, Preprint, DESY 77/38 (1977). - 16 - 7) E. Gabathuler, Proc. XIX Int. Conf. on High Energy Phys., Tokyo, P. 841. See also A. Lu. et al Phys. Rev. Lett. 40_ (1978), 1ZZZ. 8) A. N. Diddens, in Proc. XVII Int. Conf. on High Energy Phys. London, 1974), P. 1-41. 9) V, BaTgar, Lecture given at the HcGill Institute of Particle Physics International Summer School, June 1975. 10) H. J. Behrend. et. al. Preprint DESY 78/36 (1978) and Errata. 11) E. H. Thorndike Phys. Rev. Dl£ (1976) 30S9. See also Ref. 10) 12) F. E. Close, D. H. Scott and D. Sivers, Nucl. Phys. B117 (1976) 13) V. L. Auslande'r et. al. Phys. Lett. 25B (1967) 433: Balakin et. ai. Phys. Lett. 34B (1971) 4; Bizot et. al. Phys. Lett. 32B (1970) 5;. D. Benaksas et. al., Phys. Lett. 39B (1972) 289; V. Sidrov," rapporteur talk at the 1976 Tbilisi conference; Review of Particle Properties, Phys. Lett. 7SB(1978). " 14) J. D. Jackson, C. Quigg and J. L. Rosner in Proc. XIX Int. Conf. on High Energy Phys., Tokyo, 1978. P. 391. 15) H. Primakoff, Phys. Rev. 81 (1951), 899 N. Jurisic and L. St.odolsky, Phys. Rev.. D3 (1971), 724. 16) Thomas Appelquist, R. Michael Barnet and Kenneth Lane, Annual Review of Nuclear Science Vol. 28 (1978). 17) See e.g., H. D..Politzer, Proc. XIX International Conference on High Energy Phys., Tokyo 1978, P. 229.' 18) H. Fritzsch and P.. Minkowski, Phys. Letters 69B (1977), 316; L. M. Jones and H. 1». Wyld, Phys. Rev. D17 (1978), 759. 19) A. J. Buras and K. J. F. Gaemers, Nucl. Phys. B132 (1978), 249. - 17 - 20) J. F. Owens and E. Reya, Phys. Rev. D17 (1978), 3003. 21) B. L. Combridge, J. Kripfganz and J. Ranft, Phys. Letters 7OB (1977), 243; R. CutleT and D. Sivers, Phys. Rev. DT7 (1978), 196; see also, J. F. Owens, E. Reya. and M. Gluck, Phys. Rev. Dlj[ (1978), 1501. 22) G. Wolf, Procl International Conference on Lepton and Photon Interactions, SLAC 1975, P. 831. 23) J. D. Bjorken and J. Kogut, Phys. Rev. D8 (1973), 1341; J. D. Bjorken, Lectures given at the International Summer Institute in Theoretical Physics, DESY 1975. 24) M. Damashek and F. J. Gilman, Phys. Rev. DL (1970), 1319. 25) J. D. Brodsky, F. E. Close and J- F. Cunion, Phys. Rev. D5_ (1972), 1384; C. A. Domiguez, J. F. Gunion and R. Suaya, Phys. Rev. D6 (1972), 1404. 26) J. D. Bjorken and E. Paschos, Phys. Rev. 185 (1969), 1975. 27) H. Terazawa, Preprint INS-Rep.-330, 1979. "We thank ' Prof. Terazawa for sending us the preprint and for illuminating talk at this Workshop. 28) Tu Tung-sheng and Wu Chi-min, Preprint Ref- TH-2646-CERN (1979). 29) N. S. Craigie, G. Kramer and J. Koraer, Nucl. Phys. B68 (1974) 509. - 18 - Figure Captions Fig. 1. Total Photon cross section (fC? versus center «f mass energy squared s. Vector meson photon coupling constants used in the calculation are as follows. •* f2j>/4n. = 2.16 + 0.28, f(,?/4TC.= IS.8 +4.8 f2^/470= 17.2 + 2.0, f?f-/4Tl>= 11.5 shaded region represents the ambiguity in the above coupling constants. Fig. 2. Diffractive photoproduction of vector mesons. Fig. 3. Total cross sections of light vector mesons. Solid and dashed lines denote case (a) and case (b) respectively. Fig. 4. The photoproduction cross section of the J" and the 2 V(tt). The coupling constants f r/4lt>and f^CttJ/At are determined by the experimental data on "£ —*e e decay width, Q-Cfl —1-3 KeV14^ , together with the empirical relation J-1 (v)/e = indep. of V. Fig. 5. The Primakoff diagram responsible for the photoproduction of pseudoscalar mesons. Fig. 6. Differential cross sections of pseudoscalar meson production by the Primakoff effect s = 10,000 2 GeV versus t. Fig. 7. Total cross sections of pseudoscalar meson production by the Primakoff effect versus s. - 19 - Fig. 8. Schematic diagram of If + p—>Jet + X. Fig. 9. Production cross section of jets at 8 = 90° J cm against Xj. = 2 |J/ Js in the case of three-jet structure. Throughout the calculations done in the present section, s is set equal to 2,400 GeVZ. Fig.10. Production cross section of jets at 0 = 90° against xx = 2 |lA/s" in the case of four-jet structure. Fig.\1. (a) Angular distribution of jets at Xj.= 0.3 and (b] Angular distribution at xA - 0.5. Solid and dashed lines represent the three- and the four -jet processes. Fig.12. Rapidity distribution of the away jet for the trigger jet at Qcm = 135° and xx = 0.3. Solid and dashed lines represent the three- and the four-jet processes. The Gaussian distribution with dispersion 0.1 is taken for the away jet in the case of three-jet structure. Fig.13. Rapidity distribution of the away jets for the trigger jet at 0 = 135° and Xj.= 0.5. Dash-dotted line and solid lines correspond to the away jet with dispersion 0.10 and 0.05, respectively, in the case of three-jet structure. Dashed line corresponds to four-jet structure. Fig.14. Rapidity distribution of the away jets for the trigger jet at 0 = 45° and xx = 0.3. Solid line with dispersion 0.10 and dashed line correspond to the three- and the four-jet structure, respectively. - 20 - 21 jTV ,fv Fig. 2 - 22 - 10„+ 2 c "—•—• i 11 n| 1—i—i i 1111| 1—i—i i 1111 rp—»VP +1 10 Q. T Q. S(GeV2) Fig. 3 23 - (riyp-»vPHhb] 24 Fig.5 - 25 - ict5 S = 1xio4GeV2 10- ItKGeV2) Fig. 6 26 1 S(GeV^ 2) Fig. 7 - 27 •n bo 28 PxlGev) 2.1(5 7.3 12.2 - 29 Po.(Gev) 2 -«»5 7.3 1 12.2 17.1 22.0 10" • i i i • 1 " \ \ \ ID"2 \ \ \ \ io-3 \ \ \ ,_, \ ^ ,n->* \ > 10 \ O0) \ \ \ ^^ - ID",5 \ •—• \ \ •olo- \ 3I"0 -6 \ 10 \ \ \ \ \ lO"7 \ \ \ \ -8 \ 10 \ \ \ 9 A lO" • \ n » 1 • I I _. Lj_ 0.3 0.5 O.T 0.9 Fig-10 - 30 - 1.0 - 31 0.8 - 32 - ^^(Mb/Gev2) - 33 - d mdjf(jUyG«y2 ) CO \ - 34 - - SE dlPfXP [zwM*JifrF