Kaon Reactions (exp)

Rapporteur's talk: Chairman: Filthuth H. (Heidelberg) Rapporteur: Morrison D. R. 0. (CERN) Secretary: Yamdagni N. (Stockholm)

Parallel sessions: SA. Total cross-sections, elastic scattering. Discussion leader: Lundby A. (CERN) Secretary: Blomqvist G. (Stockholm) SB. Inelastic two-body reactions. Discussion leader: Sens J. C. (FOM/CERN) Secretary: Jonsson L. (Lund) SC. Many-body reactions. Discussion leader: Goldschmidt-Clermont Y. (CERN) Secretary: Holmgren S. 0. (Stockholm) '

Review of Strong Interactions of Kaons

D. R. 0. MORRISON CERN

Introduction cross section is greater than the K+p cross section at all ener­ gies, including infinity. Naively it may be noted that in K-p This review of the strong interactions of K-mesons will be interactions the summed cross section for the channels divided into the following subjects K-+p-+ hyperon+pions (1) 1. Total cross sections 2. Elastic scattering is "'5 mb whereas such reactions do not exist in K+p interac­ 3. Inelastic two-body reactions tions presumably due to the absence of a positive strangeness 4. Many-body reactions 5. Production of "Rare" particles, p, 8, Q- 6. Summary and future. 26 o. Galbraith el al bl • IHEP-CERN (Preliminary) The outstanding results are: 25

1. The first data on total cross sections from Serpukhov 24 have given an unexpected result. 'j)' 23 2. A large amount of new data on elastic scattering has ..§., 22 become available, in particular polarisation experiments. The 0 '6 21 second peak is discussed. + t 3. In a two-body reaction a strong disagreement with Regge 20 + pole predictions has been ob. erved. 4. The subject of many-body reactions has suddenly become 19 "fashionable" because of the development of calculable theo­ 180 10 20 30 40 50 60 70 ries and of new ways of presenting the data. P [GeV/c] As agreed with other rapporteurs, phase shift analysis of low energy K-Nand K+Nwill be presented by Dr. Levi Setti, while Fig. 1. Plot of total K-p cross section against the incident lab. certain aspects of many-body reactions of pions will be treated momentum. in this review paper.

6 Galbrailh •l al bl o Foley et al

• lHEP·CERN (Pr~iminary) 1. Total Cross Sections - R•ggepoletitloprevious data 50· Bug er et al dl a. K- with hydrogen

Tho · ·RN-lH P ollaboration [I] has presented preliminary data on the first tot'tll ross section measurements of K- , 1r­ and p made at lhc 70 eV Seri ukhov accelerator. The results Asympto~c -+ 0 limll for K-p interactions are shown in F ig. 1. The outstanding b 3 result is that the cro s section is approximately constant over the momentum range from 20 to 60 GeV/c. The importance of these results may be appreciated from Fig. 2 where the data 20 for K-p, n-p and pp reactions are shown with a Regge pole fit to the data at lower energies made by Barger, Ollson and Reeder [2]. This fit has been extrapolated to higher ehergies making use of the assumption that particle and antiparticle 0 10 20 30 ,0 50 60 'IO cross sections are equal at infinite energy. Thus for K-p and P [ GeV/c] K+p interactions the two total cross sections should both approach a value of 17.2 mb at infinite energy. It can be seen ig. 2. Total cross section for pp, rep and K- p reactions plotted against t11c incldent lab. momentum. The pp total cross section curve from Fig. 2 that the new experimental data, especially the K-p is shown fot• comparison. The other curves arc Regge Pole fits to low results, deviate significantly from the Regge pole predictions. energy data, which are extrapolated to higb energy but which do not One is tempted to wonder whether it is possible that the K-p agree witl1 the new experimental data [1]. 238 D. R. 0. Morrison

AND K p TOTAL CROSS SECTIONS

60

50

.0 40 E

30 z 0 u~ w 20 (/')

(/') (/') 0 a::: u

3 5 6 7 B 9 10 1 2 3 'l 5 6 7 B 9 10 CMS ENERGY SQUARED GEV• •2 Fig. 3. Compilation of K+p and K-p total cross sections plotted against lab. momentum. Data from ref. 4 and 1.

baryon. It is interesting to note that at 10 GeV/c the K-p total The relative absence of structure in the K+p total cross section cross section exceeds that of K+p by about 5 mb, and that the suggests that there is little or no direct formation. The maxi­ cross section for reaction (l) is also about 5 mb [3]. On the mum near 1.2 GeV /c may be due to threshold effects. other hand the assumption of equality of particle and antipar­ It has been shown [5] that for two-body reactions at high ticle total cross sections at infinite energy is based on crossing energies the cross section a varies with the incident laboratory symmetry which is not a principle that one abandons lightly. momentum, PLab according to the relation However, when the unthinkable, becomes thinkable, progress a=K Pr,ab-n (3) is sometimes made. The new Serpukhov data is presented in Fig. 3 where a where Kand n are constants. Fitting the K +p total cross section compilation [4] of K-p and K+p total cross section data above data above 5 GeV /c with such a formula, one finds n= + 0.01, 1 GeV/c are shown. It may be seen that the K +p curve rises that is effectively constant cross section. Fitting the 22 data sharply to about 1.2 GeV/c, falls slowly to near 3 GeV/c and points* for K-p above 10 GeV/c, one finds n= 0.04± 0.01, then is about constant. It shows little evidence of structure that is a small decrease. Some of this decrease may come whereas the K-p total cross section at low energies has consid­ from the 10 to 20 GeV/c, region but not all. Thus further erable structure, but such structure dies out (or becomes too experimental work would be welcome. It is interesting to small to be detectable) at about 4 GeV/c. The K-p cross section note from Fig. 3 and from similar distributions, that systematic then decreases slowly with increasing energy. This structure in errors between one experiment and another exist and that the K-p total cross section is due to the direct formation of these systematic errors may sometimes exceed the quoted errors. resonant states, that is It has been suggested by Cabibbo et al. [6] that total cross sections are zero at infinite energy (this naturally satisfies the x-+ p--+ Y*--+ x-+ p. (2) Porneranchuk theorem). They propose that the ar should 0 07 "' Note that the numerical values above 20 GeV/c were read off decrease as PLab - • • It may be seen that the exponents observ­ from Fig. 1. ed are significantly less than this value of 0.07. Kaon Reactions 239

1- I 1 -~.--- , r-rn n --·r--1 ,--, 1-, ·, t A general comment, for which further illustration is given 10,000 1-,--rrn K2 , >4 GeV/c MEAN ~7 GeV/c SLAC/ HEPL later, may be made about the failure of the Regge pole model .D , n , 10 GeV /c to fit the data from Serpukhov. This comment is experimental E in the sense that it is based on the history of the Regge pole z Q model since 1962. uw 1/l Applied to known experimental results -successful 1/l 1,000 1/l Interpolation between known experimental 0 0:: results -successful u Extrapolation or new processes -often unsuccessful. _J f:! 0 I- The Serpukhov results are an example of extrapolation. However, past history shows that because of the large number 100 t J I 1 1 1 1 [ I Ll~-~ 1 -L...L.Lu,J 10 100 of parameters available in the Regge pole model, data which ATOMIC NUMBER initially gave disagreement have, with further efforts, been successfully fitted. Fig. 5. Total cross section plotted against Atomic number for "'7 GeV/c K3°-meson [7] and 10 GcV/c neutrons [8].

b. Total and absm·ption cross sections on nuclei

The CERN-IHEP Collaboration reported on absorption cross On ly Ku 0-mesons of energy greater than 4 GeV were taken by section measurements with x-, n- and antiprotons of 40 GeV/c using (ime of flight criteria. The average energy was about on eight different nuclei. The extrapolation range used was 7 GeV. Tlie results are shown in Fig. 5 together with those for 0.09:0:: it l:O:: 0.23 GeV 2 where tis the square of the four momen­ 10 GeV/c neutrons [8). It may be seen that in first approxima­ tum transfer. Since the t-region near t= 0 was not investigated, tion the data can be fitted with two parallel lines corresponding these results are for absorption and not for total cross sections. to equation (4). From a fitting of the data l'rom A= 12 to The results are shown 'on a log-log plot in Fig. 4 as a function A= 206, we find o good fit (x2 = 1.1 for 2 degrees of freodom) of the Atomic Number A. It may be seen that the data are well for K ~ 11 with the c poncnt c= 0.86± 0.02, while for the 10 GcV /c fitted by the expression neutrons c= 0. 79± 0.01, but the fit is p or (x2 = 67 for D. F. = 3). a= const. A" (4) Iloth values of the exponent are larger than 2/3, ugg ting t11at the nucleus is still transparent. If the nucleus is considered as a completely black disc, then the exponent c should be 2/3. For x-, n- and p the values of care 0.76, 0.75 and 0.64, respectively. 2. Elastic Scattering In a recent experiment at SLAC, Lakin et al. [7] measured

total cross sections of K2°-mesons on C, Al, Cu and Pb targets. Elastic scattering is a subject on which a great deal of work has been done in the past, but the experiments reported to this conference again give new results of great interest and it is very probable that in the future further experiments will still yield important results. In general elastic scattering is best studied in counter experiments, but in K+p and K-p scattering 2000 · some of the best results are from bubble chamber experiments. This section will be divided into

1000 a. Total elastic cross section b. Forward da/dt distribution c. Interpretation of second peak 500 - d. Polarization experiments P =40GeV/c e. Real part of forward scattering amplitude f. Slopes of differential cross section distributions g. Backward scattering 200 - h. Final comment.

a. Total elastic cross section 100 - In Fig. 6, the total elastic cross sections of K +p and K -p scattering arc shown [4]. The [(+p cross section shows no signif­ icant . tructurc as expected from the absence of positive slran" 50 - geness hyperons, Z*, whereas the K-p cross section has struc­ Li Be C Al Cu Sn Pb U ture due to Y* production up to about 3 GeV/c. The most remarkable thing about Fig. 6 is that above 3 GeV/c the two ATOMIC NUMBER cross sections are about equal-this is surprising as the details Fig. 4. Total absorption cross section as a function of Atomic of the da/dt distributions are very different as will be shown number A, ref. 1. below. 240 D. R. 0. Morrison

+ K p AND K p ELASTIC SCATTER I NG

20 t K -p .0 K+p E 1PtJ . 10 t z 8 0 6 '~iw, f- u + .• f ~ w 4 - t t t t (/) +f t~ +t (/') r (/) 2 0 0:: u 1 6 8 10 2 3 'l 5 6 6 101 2 3 '! 5 6 8 10 UBCIAArnAY NCINENfUM CEV/C

I I I I 3 '! 5 6 7 8 CJ 10 2 3 '! 5 6 7 8 9 102 CNS ENERGY SLllJRAElJ GEV••2 Fig. 6. Compilation of K+p and K-p total elastic cross sections plotted against lab. momentum. Data from ref. 4.

b. Forward differential cross section da/dt distributions for n+p and n-p scattering-this plot does not contain the latest data, but illustrates the main features of the What do we expect the K+p and K-p forward differential reactions. distributions to be like? For comparison we show in Fig. 7 the (1) From t= 0 to t= -0.6 GeV2, the data can be fitted by the expression

1000 •-r--

~ N u (a) ~ (bl ...... 3.0 0.1 >Cl> ...... , 4,0 pp-pp jip-jip ~ 0 ...... >' ..c .. ~ .s 0.01 10 .0 8.0 8.0 ' ! .....s "O ...... - b lt2..0 _ ~ "O 0.001 - 12.0 ..,'b 'll'+p -'ll'+p t 'll'·p -'ll'·p 0 000 · b o.4 o.s 1.2 1.6 2.0 o o.4 o.a 1.2 1.6 2.0 O.'o 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0 0.2 1.0 1.2 1.4 -t (GeV/c)2 -1 (GeV/c) 2

Fig. 7. Indication of the variation with incident lab. momentum of Fig. 8. Indication of the variation with incident lab. momentum of the differential cross section distribution, da/dt versus it i, for n+p the differential cross section da/dt with it i for pp and pp elastic and n-p elastic scattering. Taken from ref. 92. scattering. Taken from ref. 92. Kaon Reactions 241

J. ALLABY et al. pp -+ pp 1a2s REFERENCE MOMENTUM (GeV/c) o PALEVSKY et al. ( 1967) 1. 70 1a-2• A CLYDE ( 1966) 3.0, 5.0, 7.0, 7.06 V ANKENBRANDT ( 1966) 3.0, 4.0 V FOLEY et al. ~1963) 19 .6 1o-27 FOLEY et al. 1965) 19.84 ..r-1 x HARTING et al. ( 1965) 8.5, 12.4 2 -u 10- • + OREAR et al. (1966) 8.0, 12.0 > • ALLABY et al. (I) ~ 1968) 7. l ' 8. l ' 9. 2 ' 10. 1 ' 11. 1 ' 12 . l -Q) ALLABY et al. 1967) 14.25, 16.9, 19.3, 21.3 ~ 1o-z• • ALLABY et al. (II) ( 1968) 19. 2 "E 1o-30 ~... ~ 11 b 10- -~ 10-:12

1O"'> 1o-u

1o·ss 0 2 4 6 8 10 12 14 16 18 It I [CG eV/c) 1 J

Fig. 9. Differential cross section, da/dt versus It I for pp elastic scattering. Taken from ref. 9.

da/dt= canst. eAt (5) We now wish to draw graphs similar to Figs. 7 and 8 for K-p and K+p scattering. This has only become possible recent­ where the slope A varies little with incident momentum. ly with the new results presented to this conference which are of crucial importance in establishing the presence or absence of 2 (2) There is a second maximum near t= -1.5 GeV , which dip plus second maximum structures. decreases quickly with incident energy. The dip between the In Fig. 10 are shown the forward differential cross sections 2 two maxima is at about ,.,o.6 GeV • for K-p scattering for four groups of incident momenta. Below In Fig. 8, pp and jjp scattering results are similarly shown 2 GeV/c a diffraction peak is observed, but the influence of in an illustrative manner. The ftp scattering resembles n±p direct formation of Y*, i.e. the process scattering in having a second maximum which decreases quick­ (2) ly with energy. On the other hand in pp scattering (also in pn scattering) no secondary maximum is seen at low energies. affects the second maximum so much that consistent trends are Recently Allaby et al. [9] observed as shown in Fig. 9 that at difficult to distinguish. In Fig. 10 curves have been drawn by high energies, "'20 GeV, a structure appeared near t= -1 hand through the data points. Each curve is a straight line, i.e. 2 GeV • While this structure could possibly have a similar theo­ Eq. (5), from t= 0 to near the dip. The position of the dip is not retical explanation to the dip plus second maximum structure too easy to determine since the results of different experiments observed in n+, n- and Ji scattering, it has a completely diff­ tend to indicate different positions varying from 0.78 [10] erent behaviour-it is not observed at low energies but the to 1.16 GeV2 [11], but by combining results at various effect increases as the energy increases, whereas the second energies more consistent estimates can be obtained. In Fig. 11 maximum is observed at low energies but decreases quickly are shown these four hand-drawn lines on one graph. It may with increasing energy. From a purely observational point of be seen that the position of the dip fluctuates. While the dip view, we regard these two effects as different. It is interesting is generally observed near 0.85, the curve c for the range S.O to to speculate whether the structure observed in pp scattering will 9.0 GeV/c is inconsistent. Here the dip at 0.95 GeV2 was estab­ also be observed when high intensity beams of 20 GeV/c lished mainly from the high statistics experiment of Owen et n±, K± and of Ji become available. al. [12]. 16 - Konferensrapport 242 D. R. 0. Morrison

K- p ELASTIC SCATTERING

. • 2.18 GeV/c DAUM • 3. 0 Ge Vic FOCACCI x 2.28 v 3.46 GORDO!'; fJ. 2.33 _,,_ )( 3. 55 BANAIGS c 4 .1 MOTT

10 a ) b )

t

1 ;-

0 .1

I I \ ~Ir ~ I I I N I I I I I I l ~ I I (.!) I I I \ .0 0.01 E 100 x 5.5 GeV/c MOTT • 9. 7 GeV/c OWEN 0 5.8 OWEN 0 10.1 A.B.C.LV. "'C - v 7.2 FOLEY x 11.9 FOLEY b FOLEY v 13 .6 OWEN "'C 6 15 9 FOLEY

- I I I I I I I I \ I

0. 001 '---L-----'-----'--' --'-~-~~~~' 0 2 0 \ 2

2 GeV It I '

Fig. 10. Differential cross section du/dt versus It I for K-p elastic scattering. The lines are hand­ drawn to guide the eye. The data are from Daum [10], Focacci [82], Gordon [83], Banaigs [11], Mott [84], Owen [12], Foley [85], ABCLV [86]. Kaan Reactions 243

The main conclusions from Fig. 11 is that K-p elastic scatter­ ELASTIC SCATTERING ing has a dip near 0.85 followed by a second maximum and this second maximum decreases quickly with increasing energy, Thus K-p forward scattering resembles n+p, n-p and J)p a 2.18-2.33 GeV/c forward scattering. It is interesting and perhaps important to b 3.0 - 4.1 note that in all four interactions the rate of decrease of the second maximum is about the same, being proportional to c 5.5 - 9.0 (PLab) - " with /1 about 3 to 4. d 9.7 - 15.9 A similar analysis of K+p scattering is shown in Fig. 12 for four groups of momenta. Again hand-drawn curves have been 10 drawn through the data. Unlike K -p scattering, it was not possible to draw straight lines through the data. These four curves are shown together in Fig. 13. Here it may be seen that there is no structure. The new results of the bubble chamber experiments of Danysz et al. [13] are very important in giving a N good limit on the size of a possible second maximum. I > The main conclusions are Q.I 1. There is no evidence for any dip or second maximum. .0 2. The expression da/dt= canst. eAt gives a poor fit to the da­ ta at small It I-values. E 3. While the value of da/dt at t= 0 is approximately constant with increasing energy, the values of da/dt for large It I-values 2 .... (1 to 2 GeV ) decrease rapidly so that the curved shape of ,, /Yb the da/dt distribution at low energy tends to a straight line 0.1 shape at higher energi~s. b - -0 Thus K+ p elastic scattering resembles pp elastic scattering (apart from structure similar to that observed by Allaby et al. [9] which could not be detected with existing data).

c. Interpretation of second peak 0.01 The experimental situation is that n+p, n-p, pp, jjn and K-p have a dip followed by a second peak that dies away quickly. The position of the dip varies with the incident particle, being It I ""'0.6 GeV2 for n+p and n-p scattering, It I"" 0.5 GeV2 for [Jp and j)n, It I"" 0.85 GeV2 for K-p scattering. On the other hand pp, pn and K+p scattering show no dip or second maxi­ mum and the cross section at large It I, """1to2 GeV2 decreases quickly with increasing energy. 0.001.____._~~-_._~~_._~~_._~~~~ There are a variety of ways of looking at the data, e.g. 0 2

1) Effects of direct formation-Duality I t I In n+p, n-p and K-p reactions and to a certain extent also Fig. 11. Differential cross section da/dt versus It I for K-p elastic in j)p reactions there is evidence for the direct formation of scattering. The lines are the same as those of Fig. 10. excited states, e.g. n ±p--+ N*, K-p--+ Y*. lnpp reactions there is no evidence for formation of excited states, while in K+p and pn the evidence for z •:• and d* states is weak. Thus there is a relation between the direct formation of excited states and However, it does seem surprising that the absorption should the occurrence of dip plus second maximum. This relating of be so negligible in some cases unless one really believes that t-channel and s-channel processes is called the principle of absorption is due solely to direct formation of resonant states duality [14]. as in 1).

2) Optical model. 3) Regge dips. The target is considered as a disc with variable amounts In Regge pole theory when a trajectory has a "nonsense" of absorption so that the da/dt distribution is essentially similar value at a certain t-value, the amplitude for exchange of that to a diffraction pattern as observed in optics. In support of trajectory goes to zero at that t-value, and hence a dip is this is the fact that secondary dips are observed [12] in pp produced. Thus in n+p and n-p scattering the dip at t= -0.6 and n-p scattering at about three times the t-value of the GeV2 is considered as being due mainly to rho-exchange, while first dip. the dip at t,., -0.5 GeV2 in pp scattering is interpreted in 244 D.R. 0. Morrison

K+p ELASTIC SCATTERING

• 2.11 GeV/c DANYSZ • 3.0 GeV/c DEBAISIEUX t. 2 .31 )( 3.5 BAE RE )( 2 .53 t. 3.55 _,,_ BANAi GS

' j 0.1 N I ~ C!> ..ci E 0.01 100 -'1J • 5.0 GeV/c BAERE • 9.8 Ge Vic FOLEY -b 0 5.2 _.,_ BAKER t. 12.8 '1J t. 6 .8 _,._ FOLEY )( 14. 8 >< 7 . 0 _,,_ BAKER v 7. 3 _.,_ CHIH-YUNG CHIEN 10

c ) d )

1 :-

0.1

0.01:----'----'--'--l--..J._J__J_..L...1__LI__L__J 0 2 0 2 2 It I , GeV

Fig. 12. Differential cross section da/dt versus It I for K+p elastic scattering. The lines are hand-drawn to guide the eye. The data are from Danysz [13), Debaisieux [87), De Baere [88), Banaigs [11), Baker [89), Foley [85], Chien [90). Kaon Reactions 245

terms of w-exchange. However, it is not clear to which exchang­ ed trajectory the dip at ""-0.85 GeV2 in K-p scattering is ELASTIC SCATTERING

due':'-not the p and w, not the A 2 which seem to give no dip a 0.865 GeV/c (from n-p--+ 1711, Guisan et al. [15]); and probably not the P' b 1. 087 whose parameters are the most flexible-is the idea of "non­ c 1. 372 sense" values nonsense? d 1. 96 e 2.1-2.7 4) Quark model. f 3.0 _3.55 g 5.0_7.3 The quark model tends to be regarded with considerable h 9.8_14.8 doubt. However it has frequently made predictions (extra­ polated predictions as well as interpolated predictions) which have turned out to be right. The fact that these predictions are then explainable by one or more other theories does not neces­ sarily invalidate the merits of the model. Akheizer and Rekalo [17] observing that n±p and pp elastic N I scattering do have dips while pp scattering does not, proposed > Cl.I an explanation based on the quark model. If q is the general (.!) symbol for the three quarks, p', n' and A,', then they assumed that qq scattering gives a second maximum while qq scattering ..0 does not. This is an assumption with no theoretical justifica­ E tion, though it is natural to expect that there is more absorption in qq reactions because of the possibility of annihilation. The ..... authors' assumption may be tested in Table 1. It may be seen "C that for the first five reactions n+p, n-p, pp, pp, and pn the as­ b sumption works well. Akheizer and Rekalo stated that they - "C 0.1 expected K+p scattering to have a second diffraction peak be­ cause of the quark reaction A,' qns ->- A,' qns where qns is a non­ strange quark, i.e. p' or n'. However, as we have shown above, thanks to the new data on K+p scattering, there is no diffraction peak. Hence this quark explanation is wrong, unless we save it by introducing here the additional assumption that the (strange quark-non-strange quark) interaction is weak. As shown in the table, these two assumptions would then fit all elastic O.Ql .,___.___,__....____.__.__....____.__._ _ _.__ reactions. However consideration of Fig. 12 shows that the , 0 2 (),q) interaction would have to be very weak indeed. 2 In the paper of Akheizer and Rekalo also inelastic processes ltf, GeV are considered and a number of interesting predictions Fig. 13. Differential cross section da/dt, versus It I for K+p elastic scattering. The Jines are the same as those of Fig. 12 plus some Jines drawn through lower energy data [18] [19]. Table 1. Comparison of the existence of a second peak in elastic scattering of the particles in the first column with protons, with the nature of the quarks in the quark-quark scattering. The quarks are p', n', ..l'. qns is a non-strange quark, i.e. p' or n'. are made that could be tested, e.g., considering only the second peak Incident particle Scattering on proton (p'p'n') da/dt(pp--+ pp)= 9 da/dt(n-p--+ n-p)= (6) Quark Both non- One strange Second = 9 drr/dt(n+p ->- n+p)= 9 da/dt(K-p--+ K-p) Name com po- strange quark peak? nents Approximately this relation seems to hold, though the constant q,., il' qns qns qns CJns qns A:' 9 may be too large. However, the fact that da/dt is greater for pp scattering may be due to the fact that the second peak n+ p'n' 3 3 yes occurs at appreciably smaller It I-values. n p'n' 3 3 yes J_j fi'fi'n' 9 yes p p'p'n' 9 no 5) Conclusions. ll p'n'n' 9 no As a first approximation we may summarize the theoretical K+ p'l•. ' 3 3 no situation as obeying the Principle of Multiduality:- K- ]_j'A' 3 3 yes "All results are explained by all theories".

* In the discussion Lovelace pointed out that in a paper [16] sub­ There are two versions of this principle:- mitted by himself, the known experimental data on np and Kp elastic scattering have been fitted using the Veneziano model. For " All results are explained by all theories on the average'', K-p elastic scattering the calculation gives a small dip near -0.85 which is called global or weak Multiduality, and 2 GeV • This fit is reasonable for "'5 GeV/c where the second maxi­ mum is small, but is poor at low momentum where the second "Almost all results are explained by almost all theories'', maximum is large. which is local or strong Multiduality. 246 D. R. 0. Morrison

I

DIP IN dcr AT SMALL t --- - d.n. DIP I~~ AT SMALL u

FIG 150 FIG 15 c

-3.0 3.0 - t - t - u (GeV/c)2 (G~V/c)2

2.0

2 -t v = 0 7 8 GeV/c 0

-10 1.0

0 I Of <) I \I) t I 0 ·- ' 15 2.0 2.5 15 20 25 ZERO IN POL . AT SMALL ZERO IN POL. AT SMALL u

FIG 15 b FIG 15 d

30 -3,0 -t -1 -u 2 ' 2 (GeV/cl (GeV/c)

2,0 2,0

1 0 1.0

I I I ! I I I - j I t

1 5 2.0 2.5 15 2 0 2.5 KAON LAB. MOMENTUM ( GeV/c l KAON LAB. MOMENTUM (GeV/c)

Fig. 15. Position of the dips observed in differential cross section distributions and of change of sign of the polarisation in K-p elastic scattering at different lab. momentum. The data are from ref. 10. Kaon Reactions 247

K+p ELASTIC SCATTERING DATA+ PHASE SHIFT FITS -- SOLUTION I , II ----SOLUTION m

do' d.12 1.215 GeV/c 1.372 GeVlc 1.453 GeVk mb/sr

1.0

-1 .0 _____._ ___...._ ___....._ ___.. ___ _._ ____,!_-----'"--...... ,..,,...,..,,,_--.__--__.,----L-----I +1.0 0 cos6cm -1.0+1.0 0 cos6cm -1.0+1.0 0 cosecm -1.0

Fig. 16. The upper graphs are differential cross sections da/dt versus cos Ofor K+p elastic scattering at different lab. momentum. The lower graphs are the corresponding measurements of the polarisation. Data are from ref. 18.

was also noted by Daum et al. that there is some evidence for a All the available data are summarised in Fig. J7. For the dip in the differential cross section in the backward direction high energy (> 3 GeV/c) data on K+p polarisation a straight and also there is a tendency for the polarisation to go from line was fitted through the experimental points, the other negative to positive values at about the same 11-value. The curves are hand-drawn. For K+p it may be seen that the positions of this backward dip and zero in polarisation are polarisation is always positive over the t-range studied. At also plotted in Fig. 15. It can be seen that the effect occurs in low energies the polarisation is large, up to 70 % and decreases 2 both cases at a fixed u-value, -0.32 GeV • This surprising slowly with increasing energy, but this decrease is slow, the result will be further discussed below. A word of caution is polarisation still being more than 20 % even at 14 GeV/c. necessary, however; the data in the backward direction are of The absence of change of sign of the K+p polarisation is low statistical significance, as can be seen from Fig. 14, and hence the apparent consistency of the values of the dip and zero are based to a fair extent on the fits to the data at other Table 2. Table of high energy experiments on polarisation in elastic angles. scattering. There is a wealth of new data on K+p polarisation. At low Incident Momentum !ti-Range Reference energy Andersson et al. [18, 19] have shown, Fig. 16, that the particle Range, GeV/c GeV 2 polarisation is positive for all t-values, though there is a tendency for the polarisation to approach zero at large It 1- K- 1.4 to 2.4 "'o to "'max. CERN-Holland [10] values. K- 6 0.15 to 0.6 CERN-Orsay-Pisa [21] The results at higher energies of Booth et al. [20] at 3. 75 and K+ 0.85 to 1.5 "'Oto "'max. CERN-Holland [18] 4.40 GeV/c and of the CERN-Orsay-Pisa Collaboration K+ 1.22 and 2.48 "'0 to 1.3 CERN-Holland [19] [21, 22] at 6.0 and 14.0 GeV/c show that the K+p polarisation K+ 3.75 and 4.40 0.2 to "'0.9 Chicago-Argonne [20] is always positive and is approximately constant over the K+ 6 0.15 to 0.75 CERN-Orsay-Pisa [21] 2 K+ 14 0.15 to 0.8 CERN-Orsay-Pisa [22) It I-range from 0.15 to 0.9 GeV • 248 D. R. 0. Morrison

POLARISATION IN K± p ELASTIC SCATTERING

- f 2.03-2.13 GeV / c DAUM

fs GeV/c BORGHI NI

+ 0. 5

z 0 I­ <( (./) 0 ------0:: <( __J 0 a..

-0.5

-1.0 .___._ _ _.___,'--_.__..__._ _,___J.___.__...___.. _ _,__.___, ~_..___. _ _,__~~_._-~~-~-~~-~-~~-- 0 os 1n o 0.5 1.0 2 t I Gev

Fig. 17. Summary of data on measurements of polarisation in K+p and K-p elastic scattering. The lines are hand-drawn except for K+p data at 3.75, 4.40, 6 and 14 GeV/c where they are straight lines fitted to the data. The data are from 1.22 and 2.48 GeV/c [19], 3.75 and4.40GeV/c [20], 6 GeV/c Borghini [21], 14 GeV/c [22], Daum [10].

further evidence against any appreciable Z* formation. At e. Real part of forward scattering amplitude low energies the K-p polarisation is positive, with its maxi­ It has been predicted that at infinite energy the forward 2 mum value near ltl=0.6 GeV , somewhat similar to K+p, scattering amplitude will be purely imaginary. To investigate but near 0.8 GeV2 the polarisation quickly reverses sign and whether there is any real part, in Fig. 19 the values of (da/dt) becomes large and negative. The only high e,nergy data are those at t= 0, obtained by extrapolation from the elastic scattering of Borghini et al. [21] at 6 GeV/c, but the data are preliminary data are compared with the Optical Theorem values obtained and as can be seen in Fig. 17 the errors are large. However, from the total cross sections assuming that the scattering am­ there is an indication that the polarisation may be negative at plitude is purely imaginary. It may be seen that for K'p scatter­ small It I-values-that this result could be important is shown ing the experimental values are consistently higher than the in Fig. 18. In this figure the results of Esterling et al. [23] for Optical Theorem values, indicating that there is an appreciable n±p polarisation at 6 GeV/c are compared with those of Bor­ real part even at the highest energies so far available. On the ghini et al. for K±p polarisation at the same energy. It may be other hand there is no evidence for a real part in K-p scattering seen that for small It I-values the positive pion polarisation is (or the real part is small) at high energies, though at low positive and the negative pion polarisation is negative. At energies, where direct Y* formation occurs, there is an app­ high energies, when Y* formation ceases to be important it reciable real part. may be expected that positive K polarisation will be positive and negative kaon polarisation negative. It is clear that the K-p data are not yet quite adequate to say whether the low f. Slopes of differential cross section distributions It I polarisation will change from large positive values at low energies (where Y* formation is important) to negative values An interesting quantity to study is the variation of the slope at high energy. of the elastic differential cross section da/dt with incident Kaon Reactions 249

SCATTERING AT 6 GeV/c Kt p ELASTIC SCATTERING - OPTICAL THEOREM VALUE FROM err CZ] 25 0.2 ! ! '> 20 J:: II l f .a E I z ' 15 0 -0.2 0 I­ II <( Ul ..... I < et:: I 0 <( • K+ f ....J o.~ ; 60 x K- 0 b f Q. -"Cl 0.2 ! ! 30 - f 0 1

-0.2 INCIDENT LAB. MOMENTUM , GeV/c I I 0 0.5 1.0 Fig. 19. Value of da/dt at t = 0 as a function of incident lab. momen­ 2 tum for K'p and K-p elastic scattering. The lines are calculated jtj,GeV from the total cross section using the Optical Theorem and assuming Fig. 18. Polarisation as a function of It I for n±p and K ±p elastic no real part to the scattering amplitude. scattering. The data are from (21].

28 momentum. By slope is meant the parameter B when the 26 expression 2.4 da/dt= const. eBt (5) is fitted to the differential cross section distribution for small ~ '. d ~ ~~~~ aa ~a.~~ value of It I (the actual range oft-values fitted increases slightly 20 •, '•... Ii '.f·;i;+;, +;~~ i l =: with incident momentum). The variation of B with incident "'·~ ~ 1 8 - ~ ~ ~~~~ ig ~H ~ momentum is shown in Fig. 20 in a compilation made by :;; ~ Lasinski et al. [24]. It may be seen that for K-p interactions at :::: 16 I -1~V!H!H! low energies the slope fluctuates violently because of the direct =-CD B(k)t ·14 du~ A(k)e formation of hyperon resonances, but above 4 GeV /c, the slope ...: 0 dt ·-· 2 Q) Bis constant at a value of about 7 Gev- • On the other hand a.12 + K-p -K-p "E the slope of K+p elastic scattering at small angles starts near 0 I y K•p -K•p ~ 10 - I ~ zero (i.e. an almost isotropic angular distribution) and slowly .£? I but steadily increases as the energy increases (plotting the 'O 8 - I + Q) 1· + ++ +++ + incident momentum on a logarithmic scale). Thus again there a. • ++ • I+ I 0 t is no evidence for significant direct formation of hyperon Vi 6 - I ! +1 states of strangeness. An interesting question is whether at j ! f 4 j ii\ ! ! higher energy the slope for K+p scattering will continue to I increase and become greater than that for K-p scattering. I ~ .. I 'I\~ 0 0.2 0.3 0.5 0 ,7 1.0 2.0 3.0 5.0 7.0 10 15 20 g. Backward elastic scattering K Laboratory momentum ( GeV /c) a. J(+p scattering Fig. 20. Variation as a function of incident lab. momentum of the In Fig. 21 are given the experimental data on K+p backward slope B obtained by fitting the relation da/dt =Const. eBt to small scattering including the higher energy data of Baker et al. [25) angle K+p and K-p elastic scattering. Taken from ref. 24. 250 D. R. 0. Morrison

• BNL - ROCHESTER - 100 1000 : • CERN-SACLAY • ILLINOIS • CERN

10 K+p-K+p 1100 elastic backward scattering data f •

10 t - 100

I • •' !~ 1 1 ~ 2.33 G~fc 100 .o - 10~1~ - ::i. I~~

"Ubl:;, "U "Ubl:;, "U

100

~~-~~- 1 - l_ J,_ _,__,, 10 -1.0 -0.5 0 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 2 - u (GeVfc) -u(Gevtc)2 -u(GeVfc) 2

Fig. 21. Backward differential cross section du/du versus u for different momenta. Taken from ref. 27.

presented to this conference. The most important feature of the of the hypothesis of exchange degeneracy first proposed by results is that there are no dips. On a simple Regge Pole theory Arnold [26]; that is the two trajectories, /la and Ay are such one would expect a decrease towards u= + 0.2 GeV2 due to a that the dips are exactly cancelled. The curves on Fig. 21 are nonsense value of the /Ju trajectory and also a dip near -0.7 calculations by Pretzl and Jgi [27] using the Veneziano model 2 GeV caused by a nonsense value of the /JY trajectory (see (with exchange degeneracy) and give satisfactory fits to the Fig. 22). It is now considered that this is evidence in favour data.

b. K-p backward scattering ]_ The work of Daum et al. [10], shown in Fig. 15, indicated that 2 at 11= -0.3 GeV2 there is both a dip in the K-p backward ~~~' ...... 5.. ~'b"' differential cross section and also a reversal in the sign of the polarisation. The only other data available are those of the ~2 \'Ir ,., BN L-Rochester collaboration [28] which are shown in Fig. 23...... 3 -.:S - '\ It may be seen that these data do not extend as far as u= -0.3

An interesting result is obtained by studying the fall- off h. Final comment of the backward K+p and K·p cross sections as a function of It was shown in Fig. 6 that the total K+p and K-p elastic cross incident momentum. This is shown in Fig. 24 taken from the sections are approximately equal above 3 GeV/c. This is paper of Banaigs et al. [I I] where the values of da/dt at u= 0 remarkable since they differ in almost all properties, values of are plotted. It is found that they decrease as Pv1u· ·1 for K+p drJ/dt at t= 0, existence of a second peak, slope near t= 0, and PLaJJ- 10 for K ·p backward scattering. Thus the values of real part of forward scattering amplitude and backward drJ/d11 at u= 0 have similar energy dependence as the integrated scattering. relationship of equation (3). The value 4 for the exponent n in equ. (3) for K '"]J scattering is similar to that found [5] for other two-body reactions requiring baryon exchange. However, the exponent n= 10 observed for K · p backward scattering is exceptionally high and can be considered the best example of 500 "nothing" exchange, i.e. of a two-body reaction in whicl1 no one single particle can be exchanged. Very few other examples 200 . of "nothing" exchange are known-they are mainly near (~~lv.o threshold and have exponents "" 6. 100 ~ Michael [3 l] has calculated the energy variation of da/du (GeV/c) 2 liQ at u= 0 for K·p scattering assuming that two particles are exchanged. The results of his calculation are shown in Fig. 25. It may be seen that the fall-off is much more gentle than is 211 observed at lower energies. The exact value of the exponent to be expected from double Regge particle exchange is dif­ 10 ficult to calculate but should be about 4 to 6. Experimentally it will be difficult to test Michael's prediction until greatly imp­ roved statistics are available.

s(GeV)2

_J,__ 11 -- ,6~-~ ~~ L )Q 12 2 4 5

B NL- ROCHESTER

K"p-+ K"p BA CKWARD Fig. 24. Values of da/du at u = 0 versus the lab. momentum for K'p and K·p elastic scattering. The data are from BNL-Rochester [28], CERN-Saclay [11] and CERN [25].

1.20 Ge){_ BACKWARD K-p SCATTERING, AT u=O

Ge';,{ 103 10 '

'i\ ----- p · 9 FIT d o 1.60 Gex N du I LAB > IO 2 Q1 ~b '! (!) \ - DOUBLE REGGE (G~)2 1, 72 G~ I ' EXCH . (MICHAEL) ..c l I \ =2.._ 10 \ \ t t \ \ 198 Ge_Yo 0 II ,....:J 't 10' :J "O 1 f f 218 GeYc b 10- . - + t ...... "" i 10-2 + 2" G'/{ 2 5 10 20

10 '---+-+-~---'--"---~ \/Ll' INCIDENT LAB. MOMENTUM, GeV/c ·2 ·I • \ u (G e;fc;

Fig. 25. Backward differential cross section da/du at u = 0 versus lab. Fig. 23. Backward differential cross section do/du versus u for K·p momentum, p, for K-p elastic scattering. The expedmental data are elastic scattering. The data are from ref. 28. The curves are a best fit fitted (dotted line) with a P"n dependence. A prediction by Michael using a superposition of known s-channel resonances. [31] using a double exchange model is shown as a solid line. 252 D. R. 0. Morrison

3. Ine]astic Two-Body Reactions I I I I

The subjects to be discussed are

this experimen1 a. Cross sections 0 • K- --+ R n b. K-p charge exchange p o other experiments 6 I .0 c. Comparison of neighbouring reactions E d. K* Production (1) how much quasi two-body? c (2) reaction mechanism 0 u e. K-n--+ An-, a test of Regge theory 4 "'~ f. K-+ n--+ n-+ (I =0 hyperons), a problem ~ ~ ~ u

2. - a. Cross sections It has been found [5] that the cross section, a, for two-body reactions at high energies in general depends on the value of 0 LJ' ~~~~~.1-' ~~~~~·L_~~~~~' ~~~~~'L-J the incoming momentum in the lab. system as 10 15 2.0 2.5 30 K laboratory momenlum ( GeV/c) (3) Fig. 26. Cross section for the reaction K-p--+ K 0n versus lab. where the value of the exponent n seems determined by the momentum. The black dots are from ref. 32. nature of the "particle" assumed to be exchanged in the reac­ tion. The new results presented to this conference are found to agree with previous ones and the present situation is sum­ boration [33] has measured the K-p --+ K 0n differential cross marised in Table 3. In the last column the value of {2- 2a(O)} section at small It I-values at 4.2 GeV/c and obtained, results is plotted because the Regge theory would give this for the in agreement with those of Ast bury et al. [34] at higher energies. exponent n as a first approximation (here a(O) is the intercept of the Regge trajectory considered, i.e. the value of a(t) at t= 0). Since the experimental results occur at values oft other than zero, it is expected that {2 - 2a(O)} should be less than c. Comparison of neighbouring reactions the observed value of n, as can be seen in Table 3. Instead of studying each two-body reaction separately, several authors have studied groups of reactions. This is illustrated in Fig. 27 where Matthews [35] has considered the three reactions Table 3. Summary of the dependence of cross section, a, with inci­ dent Jab. momentum, Pr,aJJ, with the nature of the particle exchanged with incident negative mesons, in two·· body reactions. The data are fitted with the formula u =con­ stant (PLab)-". Jn the last column the quantity {2 -2f,(0)} is given n;-p -> n;On p-exchange where a(O) is the intercept with the t = 0 axis of the lrnjccl'ory of the n-p -> 17°12 A2-exchange cxd ·1t.tn gcd. It 0 particle assumed to be is expected that {2 - 2a(O)} K-p-> K n (p+ A2)-exchange should be less than the e,xpo ncnt n. and also the three reactions with incident positive mesons

Particle 11 2-2 a(O) Exchanged

Pom ~ ron} last1c 0.2 0 S=O Meson 1.5-2.0 1-2 S= 1 Meson 2.0-2.5 1.5 Baryon } K+p--+ pK+ 3.5-4.0 2.7 Nothing } K-p->pK- 10

b. K -p charge exchange

The total K-p charge exchange cross section has been measured by Bricman et al. [32]. The results are shown in Fig. 26. The statistical errors on the experimental points are particularly small (since the experiment was designed to look for resonances), Inelastic rP.nctinn~ Elastic reactions while the systematic errors are about the same (2 %) due to Fig. 27. Feynmann diagrams for the reactions analysed by Mathews normalisation difficulties. The Amsterdam-Nijmegen Colla- [35]. The assumed particle exchanges are marked. Kaon Reactions 253

·--.- 1.0 it>t 2.0 + .. on '10" t(O n 2.0 1.0 t .,,o~++ .,.,06,++ Ko f!l++ tit' 1.0 1-tf " fit 0 0 . 1 1 ·- t- - t-- - ... ·t t· · 0.1 uubl<- ·- =4r- -1"'t- ·-1- + + t++t '--... 0 . 1 b,.- + "OU 0 .01 :" tl 0.01

0 .01

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0 0 . 2 0.4 0 .6 0.8 1.0 1.2 1.4 2 - t (GeV 2) -t (GeV 2 ) -t (GeV )

Fig. 28. Differential cross section du/dt distributions normalised to their value at t = O versus - t. The first graph is for the reactions ~- -• o + 0N•I<+ + Tl d · f, o ' " P · n n an d n P -> n . 1e secon ts or n-p -> 17 n and n+p-+ rJ° N*+ +. The third is for K -p-+ K 0n and K+p-+ K 0N*+ +. Taken from ref. 35.

n+p -+ n°N*++ p-exchange In Fig. 29, the cross sections for reaction (7) and for each of

n+p -+ r1°N*++ A 2-exchange the four channels, are shown as a function of the incident 0 K+p-+ K N*++ (p+ A2)-exchange. momentum P Lab· It may be seen that apart from the threshold That reactions with similar types of particle exchange have effects for K *(1420) production, all the cross sections decrease 2 similar differential cross section distributions is shown in Fig. approximately as (PLab)- • This effect can be appreciated better 28. For p-exchange there is a flattening at t= 0 and a dip near in Fig. 30 where each channel is expressed as a percentage of 2 the total cross section for reaction (7). The recent values of t= -0.55 GeV • For A2-exchange there is a flat region from 2 Brunet et al. [38] between 2.1 and 2.7 GeV/c are shown with t=O tot "" -0.25 GeV • Using SU3 , it is possible to combine errors. The variations between these results and previous ones the results for p- and for A2-exchange to predict the differential give an estimate of possible systematic errors due to different cross section for the reactions in which bothp-and A2-exchange are possible. The prediction is that there is some flattening near groups analysing the background in different ways. It may be t= 0 and that there is no appreciable dip near t= -0.55 GeV 2 seen that the fraction of observed quasi two-body reactions is and this is as observed experimentally. Similar calculations approximately constant at a level of about 60- 70 % over the have been performed by Krammer and Maor [36]. Also Hof­ range of incident momentum from 2 to 12.7 GeV/c. mokl and Szeptycka [37] have compared cross sections, using At first sigllt this is a somewhat surprising result and it equation (3), for a large number of reactions. The comparison should be confirmed with other reactions. A few important is based on the quark model. In general agreement of experi­ points should be noted. ment and theory is obtained but some disagreement is also 1. The percentage of quasi two-body reaction quoted should noted for certain types of reactions. be taken as a lower limit since other two-body reactions may exist but may not be recognised if the resonances involved are not clearly visible. d. K* Production 2. A few reactions of low multiplicity have a large amount ( ""' 50 %) of quasi two-body reaction, e.g. the SABRE Collab­ (1) Percentage of quasi two-body reactions oration [39] finds that at 3 GeV/c, the two-body channel The reaction (8) K+p-+ pK0n+ (7) occurs in 53 % of the cases of the reaction is known to be dominated by the production of a few resonan­ ces, namely K*(890), K*(1420) and N*++(1236). Each of these (9) resonances is clearly observable (i.e. the signal to noise ratio is large). It is interesting then to use this reaction to study the Also tJrn Saclay-College de France-Imperial College-West­ questions "How much quasi two-body production occurs" and field College, London Collaboration [40] finds that between "How does the percentage of quasi two-body reactions vary 2.11 and 2.72 GeV/c about 50% of the reaction with energy". (10) We consider reaction (7) as being composed of four channels (assumed to be non-interfering), namely proceeds via the quasi two-body process

K+p-+ K*+(890)p (11) -+ K*+(1420)p -+ N*++(1236) K 0 3. The percentage of the sum of all the recognised quasi -+ pK0n+ (non-resonant) tvvo-body reactions of the total cross section, decreases with 254 D. R. 0. Morrison

+ 0 1T+ z K p-K p S? 100 t- AND QUASI TWO-BODY CROSS SECTIONS &l TOTAL - pK"n+, of the "compone11ts" 0 of this reaction-the "components" being the various two-body I- reactions whose final states pK*(l420), pK*(890) and K"N*"" are u indicated, plus the "background". Based on ref. 4. w (/)

(/) (/) for J(':'(l 420), results for K·1·p reactions have been submitted to 0 a:: the conference by the CERN-Brussels Collaboration [41] and u 0.1 K-p results at 10 GeV/c are previously published [42]. The results can be simply summarised if we group the f reactions into two classes, one with no exchange of charge, Q= 0, and the other witl1 charge exchange, Q= 1. The summary

is given in Table 4. Study of the density matrix element p00, indicates that Q= 0 reactions proceed by ca-exchange, while Q= 1 reactions have n-exchange. Jt is not clear why this is so (though part of the explanation comes from isospin considera­ tions). The observation of a dip near t= 0 in the differential cross section, du/dt for Q= 0 reactions is characteristic of vector meson exchange reaction, while the non-observation of 00 · 1 1'----2~_, _ _.__-Ls _.__.__...__._._10------120_ __, such a dip in Q= 1 reactions is consistent with other pion­ exchange reactions. Despite the fact that the two types of reactions have different mechanisms, they both seem to have INCIDENT LAB. MOMENTUM GeV/c the same energy dependence and in addition the constant in the relation a= (constant). (PLteLi) - 2 has about the same value in Fig. 29. Plot of cross section versus lab. momentum for the reaction both cases [43]. A further point of interest is that in the reac­ K+p -+ K 0pn+ and for the quasi two-body components of this tions proceeding mainly by ca··exchange, no dip in the du/dt reaction, and for the "background" which is the difference between 2 the total reaction cross section and the sum of the components. distribution is observed near it I= 0.5 GeV though a dip might Based on ref. 4. be expected from Regge theory because of the existence of a "nonsense" value of the ca-trajectory.

increasing energy, being about 25% for 5 GeV/c K+, 11 % for Table 4. Summary of the results on K*(890) production in J(+p 8 GeV/c n' and 8% for 11 GeV/c n-. But as noted in 1. above, and K-p reactions. The rcsulls are grouped in two columns accord­ these numbers are lower limits. Thus while for a given channel ing to whether the baryon has changed its charge Q by zero or one (here K'p ->- pK'·n°) the percentage of two-body reactions is unit. approximately constant, for all channels taken together (i.e. K*(890) and K*(1420) production. the total cross section) the percentage of two-body reactions decreases with increasing energy. Q=O Q= 1

K-p - >- K* -p K-p-'l- K*011 (2) Reaction mechanism of K"' production K ·1·p ->- K*"p K+p->- K *0LJ++ The reaction mechanisms of K* production are of particular interest since the results are somewhat surprising and since co-Exchange n-Exchange they provide a particularly sensitive test of theories. The results DIP in du/dt at t = 0 NO DIP 2 have been established by a number of experiments for K*(890); a=const. PLab- a= const. PLab-a Kaon Reactions 255

However by using many Regge trajectories Markytan [44] has fitted most of the data of K*(890) production. More recent­ 3 GeV / c BARLOUTARD ET AL 4.5 GeV / c VEN ET AL ly Dass and Froggatt [45] tried to fit the same reactions, but 1000 •-r--->r-r-..-..--.--;--- .----r----r-- noted that it was difficult to account for the energy depend­ a) c) ence. REGG E PO LE The SABRE Collaboration [39] studied the reaction

(8) at 3 GeV/c and found it proceeds mainly by pion exchange in agreement with Table 4 but noted some differences from the reaction

K+p ->- K *0(890) N*++(l236) (11)

in particular that the value of p 00 is rather low, which perhaps suggests some vector meson exchange. However part of the d) ,______, differences can be accounted for if absorption is taken into account. The SABRE Collaboration also studied correlations in the decay angles for reaction (8) and compared them with the quark model predictions of Bialas and Zalewski [46]. The results are similar to those found in reaction (10) at 5 GeV/c [47] and in the reaction n+p - >- p0N•:.++ at 8 GeV/c (48]. I t I The CERN-Bruxelles-Miinchen Collaboration [49] in study­ ing K+d reactions at 3 GeV/c found results similar to those Fig. 31. For the reaction K-n--+ An-, (a) and (c) differential cross given in Table 4, in particular for the reaction section da/dt versus it i, (b) and (d) Polarisation versus it i. The solid lines are Regge Pole predictions (extrapolated) by Reeder and Sarina [50 i. The dotted line is a fit to the dat;l assuming tkr/ r/1 = (12) = constu nt eAt, The 3 GeV/c data are from ref. 52, the4.5 GeV/cdata from rel'. 51. They observed a marked asymmetry of the K*(890) decay distribution in this reaction. f, K-+n--+ n-+(1=0 hyperon), a problem At the 1968 Vienna Conference, Bellettini [54] reported a result e. K -11 ->- An - , a test of Regge theory obtained by the SABRE Collaboration [55] which was not easy Reeder and Sanna [50] have used Regge Pole theory to fit to understand. For the four reactions a large amount of data on np and Kp reactions requiring charge K-+n--+ n-+(l=O hyperon) (13) exchange and hypercharge exchange. Good agreement was obtained with the experimental data. Their predictions for the where the (/= 0 hyperon) was successively A 0 , yo(1405), reaction yo(1520) and Y0(1820), production angular distributions were obtained at 3.0 GeV/c. These are shown in Fig. 33 where (12) Cos 0 is the c.m. angle between the outgoing n- and the in­ coming x-. It is expected in these four reactions that there have been compared with experiment by Yen et al. [51] at should be a large foward peak corresponding to mesonic 4.5 GeV/c. Their results, together with those of the SABRE exchange and a small backward peak corresponding to baryon­ Collaboration [52] at 3.0 GeV/c are shown in Fig. 31. Tn the ic exchange. For the lower mass byperons, A and Y(l405), Regge Pole model the trajectory functions for K':'(890)-and there is a large forward peak in the n- angular distribution K*(l420)-exchange should vanish at t-values of -0.4 and and no backward peak, as expected. However, for the higher -0.35 GeV2 respectively, while the cross-over factor should mass hyperons, there is a large backward peak and a small or 2 vanish at -0.53 GeV , thus a dip may be expected in theda/dt non-existent forward peak-this is difficult to understand. 2 distribution near t= -0.4 GeV • Also the polarisation is To investigate this further, new data at other energies have 2 expected to change sign near -0.4 GeV • It may be noted been collected. At l.45 and 1.65 GeV /c, where effects due to that the change in the sign of the polarisation observed in the direct formation of Y* resonances might be expected to be im­ reaction n+p - >- Ic+r+ was explained by invoking the cross-over portant, the Birmingham-Edinburgh-Glasgow-London (J.C.) factor. It may be seen from Fig. 31 that there is serious dis­ Collaboration [56] have obtained basically similar results for the agreement with the theory. Further results at 3.9 GeV/c from three lower mass hyperons. At the higher momentum of 5.0 Kwan Lai et al. [53] shown in Fig. 32 confirm that there is no GeV/c, the Argonne and Carnegie-Mellon groups' result [57] appreciable dip in the differential cross section near -0.4 GeV2 are shown in Fig. 33. It may be seen that for the three higher and that near t= -1.0 GeV2, the polarisation is positive and mass hyperons, the forward peak is.dominant- that is, at higher not negative. Thus as commented earlier, Regge Pole theory energies the difference with the expected results is small. Res­ was able to account for known results but when "extrapolated" ults from the BNL-CCNY Collaboration [53] at 3.9 GeV/c, to a new reaction, disagreement was found. shown in Fig. 34, confirm this. However it may be noted that 256 D. R. 0. Morrison

BNL CCNY The Ecole Polytechnique-Saclay Collaboration [58] studied S= -2 baryon production in K-p interactions at 3.95 GeV/c. The E-hyperons produced were frequently found to occur as K n-1\ ,,.- decay products of E* resonances. In Fig. 35 are shown the 3.9 GeV!c angular distributions of the two-body reactions producing a E or 3*(1530) and a K-meson. There are strong peaks near N u= O corresponding to hyperon exchange, but no peak near ~ {!) t= O when the E is negatively charged, as this process would require the exchange of two units of charge. N 0 The Aachen-Berlin-CERN-London-Vienna Collaboration 0 [59] presented results on strange particle production in 10 GeV /c K-p reactions and compared several distributions with the If) multiperipheral model of Chan, Loskiewicz and Allison [60] I- --z 10 obtaining fair agreement. In Fig. 36 the average transverse LLJ momentum is plotted as a function of the mass of the particle > lJ..J produced, these particles varying from n and K mesons to s- and Q- hyperons. The values for 10 GeV/c. K-p reactions (dots) are compared with those [61] for 10 GeV/c n-p reactions (triangles) and the two sets of values are found to agree closely. The general tendency for the average transverse momentum to increase with mass, first reported by Bigi et al. [61], can be seen.

z +1 3.0 GeV/c SABRE 5.0 GeV/c 0 ft+ I- a) <( CARNEGIE - MELLON If) 200 /\ a:: 0 K- p <( 0 t+------100 _J W1J ~-n• 0 ----- + -- --- a.. 0 < b) e) (1405) v: (1405) 50 v: z -1 20 c ++ ~ OJ .... 25 rn Ill :::0 Im -~ 0 2 4 6 0 0 2 ~ 0 t' GeV ~ ' c) f) "rn v: (1520) ~ (1520) < Fig. 32. Number of events versus It I and polarisation versus Jt I for 100 rn the reaction K-n-+ An- at 3.9 GeV/c [53]. c: 1,0 z -I ~ VI 'tJ 50 20

for Y0(1820) the backward peak is still appreciable. A point 0 0

which might be significant is that in the SABRE data the d) g ) Y(1405) is observed in its (An) decay mode only, the Y(1520) v; (1820) v; (1820) 100 decays half into (An) and half into (K-p), while the Y(1820) 20 decay was observed only in the (K-p) mode. Thus in conclusion notwithstanding the numerous new re­ 50 sults, the reaction mechanism for reactions (13) is still not well understood.

4. Production of "Rare" Particles Fig. 33. For the reactions K-+n-+ n-+(I = 0 hyperon) where the hyperon is (a) A, (b) and (e) Y* 0(1405), (c) and (f) Y* 0(1520) (d) and As the number of events measured on bubble chamber photo­ (g) Y* 0(1820), plots of da/dQ or of number of events versus the cosine graphs increases steadily, "rare" particles, i.e. p, E, Q-, were of the angle between the outgoing n- and the incoming K- in the c.m. For the 5.0 GeV/c results [57), in graphs (e), (f) and (g) the yo at first only observed and their production cross section esti­ decays into (K-p) are unshaded and the decays into (E-n+) are shown mated, but now one begins to try and study their production shaded. For the 3 GeV/c results [52), the yo decay modes are given mechanism. in the text. Kaon Reactions 257

also at 4.2 to 6 GeV/c [63, 64, 65]. Although the number PRELIMINARY DATA - BNL + CCNY of events is very small, it may be seen that there is a tendency g:; BACKGROUND SUBTRACTED for the Q - to be produced forwards in the c.111. as has been observed for the production of other hyperons of negative charge such as the s- or J;-. Thus when the charge on the !iOO h (11151 - 500 Al15201 500 Al1815l (896 EVENTS) (76 EVENTS) I 281 EVENTS I

t.0 OUT .!,! ~ :::;:

100 100 ::o·soo ­ ::i 1-- z UJ ~o "!50 • ~ I-- ~ ~ U) U) ::;: 1-­ 1-­ z z UJ 6. w w Vl > > w w ffi 400 > zVl <( 10 0:: • .... 6. w 5 ~ 0:: UJ200 '----~1 ___~1 ______~1 -~1 ~ ,l ._~1 -=---- ·''-=---' ~ Tf' K p /\ r: ::::- fl.- MASS

Fig. 36. Average transverse momentum of particles versus their mass I '-----'-----' I for 10 GeV/c K-p interactions [59], (dots) and for 10 GeV/c n-p -I 0 -I 0 cos o;_ cos o;_ interactions [61] (triangles).

Fig. 34. Number of events versus the cosine of the angle in the c.m. between the n:- and K- for the reaction x-n-+ n-yo where yo 0 0 is A, Y (1520) and Y (1815). .n,- PRODUCTION

--9Jr... AT 4.2 GeV/c d(cos e*J N(events) 4.6 GeV/c z-K'.i·• •• AND 5.0 GeV/c •Background • l13!2)JJb 25 I' b • N(events) d(c~e"' J '2.- K+ 20 20 bsi J)flb 25 JJ b ~ ::l 15 16 .,_ 20 N(events) z AT 5.5 GeV/c 0 LLJ AND 6 .O GeV/c 15 Z°K (J !2)µ b} 10 10 - 10 IO Z~ " K'C5! 6 )µb Added ~ 8"°K0·(7!2)}J b 0 • .. - 10 ~ • • • a) b) c) •• . s 5 LLJ 01------"'-~-~-'-~~~~ ~-----1 5 ...... en a: • I + I 0 • l LLJ cose*s,s* > -+------++ u (GeV2) en - 1,,59 ' . 25 -4.12 •.15 z <( Fig. 35. Number of events versus the cosine of the angle between .,_a: the outgoing 8 and the incoming K in the reactions, first graph • K-p--+ s-K+, second graph K-p-+ s-K*+(S90), third graph K-p giving s° K 0, 8*(1530) K+ or 8*0(1530) K 0 at 3.95 GeV/c [58]. • • 0 The ABCLV Collaboration [62] have also reported on Q­ -2 -1 0 +1 +2 production at 10 GeV/c, seven events having been observed. c.m. LONGITUDINAL MOMENTUM ,GeV/c The production characteristics of Q- hyperons are of particular interest since the baryon changes its charge by two units and Fig. 37. Scatter plot of transverse against c.m. longitudinal momen­ its strangeness by three units. One therefore wonders where it tum for Q- particles produced in K-p interactfons. Data at 10 GeV/c from ref. 62, at 6.0 GeV/c from ref. 63, at 5.5 GeV/c from ref. 64 and will be observed on a plot for each particle of the transverse the lower momentum data is from a compilation by Allison [65], the momentum against the c.111. longitudinal momentum. This is 4.2 GeV/c events being from Maryland, and the 4.6 and 5.0 GeV/c shown in Fig. 37 for Q- hyperons produced at 10 GeV/c and events being from Brookhaven. 17 - Konferensrapport 258 D. R. 0. Morrison

CROSS SECTIONS a) b) ~ ::::E: K K in 200 - I I - 100 10 N

""z~ UJ > ~ 100 50 0 0:: UJ ID p ~ .0 z "'-'-~~,_,_~~.i:;;:. ·....-~..L.l.,_,__.._._~;~ • • ~ 0 E 1.0 0 0.5 1.0 1.5 z MASS OF A , GeV ;::0 Fig. 38. Number of events versus mass of A calculated for the u w assumed four-prong reactions n-p-> n+pAA at 8 GeV/c and K-p ~ (.{) ~ K-pAA at 10 GeV/c from ref. [66]. See text for kinematic fitting (.{) procedure used. (.{) 0.1 0 u0:::

100 n'-p TOPOLOGIC CROSS SECTIONS

.t. ,,.-p- p ,,.-1T· ' 0.01 a ,,.-p- p 11'+1i-1T- e?"'- o fT- p- p fT+'li-T1°TT 0 ,- --~ -Qi _,,/"2 prongs{ ~I. v ,.,-p- p11•n•n-11·n· 6 ',~ 1neo1. I 't... x rr- p- p n•n•rr-rr-n- n• 10 ...... - 'I!. i~ qc,.,,~~ ..c •• / --- 6 ~ E 4 prongs .,/ 2 prongs -...... ~· / inelastic • ..:.::. .. __• r i :- '-....A, 0.001 .__~.._._._ , _· ~--~-~~~-~~~---" · z * 6prongs ./ 0.3 3 10 30 0 I- ·- " INCIDDJT LAB MOMENTUM, GeV/c u ~ .-- UJ Fig. 40. Cross section versus lab. momentum for the n-p reactions Cf) ~ indicated. The lines are hand-drawn. I I ' Cf) lit Cf) I I /0 0 a: ·~7 u 0.1 ; 10 P'/(t fled kinematically by the method of Ehrlich et al. [67] using ~ •" four prong events. The reactions , ) 12pr (14) /+ where M was a n+ or x- and A+ A- are any assumed particle­ antiparticle pair studied. After removing the events for which 0.01 ....___.__.___.__.___.__..___.__,___.__..___.__.__.. A+ A - are a n+n- pair, momentum and energy conservation 1 2 3 4 5 6 7 were used to identify events consistent with equation (14) and VS GeV the mass of A was determined. The resultant distribution of the Fig. 39. Cross section versus c.m. total energy for various n-p top­ A-mass is shown in Fig. 38. Peaks can be seen corresponding ologies-solid lines. The dotted line is after subtraction of elastic to the Kand proton masses. An interesting question is why the scattering from the observed two-prong cross sections. (pp) pair production is so small for K-p reactions compared to that in n+p reactions. baryon changes by two or more units, the baryon tends to be produced forwards. This is very different from the case of a 5. Many-body Reactions change by 0 or 1 unit when the baryons (p, n, A, E+) are pro­ duced mainly backwards in the c.m. To evaluate work on many-body reactions it is necessary to Antiproton production in meson-proton interactions has adopt a historical approach. While two-body reactions have been studied by the Aachen-Berlin-CERN and Aachen-Berlin­ been studied and interpreted with great vigour for many years, CERN-London-Vienna Collaborations [66] in 8 GeV/c n+p the subject of many-body reactions (many is defined as 2 3) and 10 GeV/c K-p interactions. The antiprotons were identi- has rather languished although there was a moderate amount Kaon Reactions 259

a. Variation of cross sections with energy CROSS SECTIONS A compilation [4] of cross sections has been used by Hansen POINTS ARE FROM K-p REACTIONS et al. [68] to compare the variation of cross sections with energy 10 - CURVES ARE FROM 11'-p REACTIONS for n-p and K-p reactions. In Fig. 39, cross sections for n-p interactions are plotted as a function of v; where sis the square of c.m. energy, for various topologies as observed in a bubble chamber, i.e. 2-prongs to 12-prongs. In Fig. 40, cross sections for n-p interactions are plotted as a function of the incident momentum for individual reaction channels, the final state in 3-BODY\ l each case being a proton, some charged pions and zero or one ..a ,_ I E neutral pion. In both Figs. 39 and 40 hand-drawn lines have ti been drawn for each channel. In Fig. 41, cross sections for z K-p interactions have been plotted similarly to Fig. 40 and 0...... 1- also the curves drawn in Fig. 41 are the same as those for u LU n-p interactions in Fig. 40, but all displaced bodily to Vl approximately fit the K-p data. Similarly in Fig. 42, the l/) 1/ Vl 0.1 ~(/ cross section values are plotted for n+p interactions and in 0 a:: Fig. 43 the cross section values for K+p interactions are plotted u and the curves drawn through the n+p are shown for com­ I parison. It may be seen that in first approximation the variation with /- 4-BOOV momentum of the various reaction channels for K±p inter­ actions are similar to those for n±p, respectively. The differ- 0.01 ~

,. K"p - pK-1T 0 v K-p - p K" rt1T•11-,y- c K"p- pK"rrY x K"p - p K-rr·rr·rr-rr"n° o K"p - pK·rr•rr·rr• CROSS SECTIONS

10 .

INCIDENT LAB. MOMENTUM , GeV/c

Fig. 41. Cross section versus lab. momentum for the K}J reactions indicated. The lines are the hand-drawn lines for n-p reactions in Fig. 40 but normalised to the K-p data.

.0 1 - E z of data available. The earlier analyses were somewhat simrila 0 to those done with Cosmic Rays, that is the transverse momen­ tum, Pr, was shown to be approximately constant ( ,,,,400 § (./) MeV/c) for all particles, and distributions of c.m. longitudinal (./) momentum, P1,\ were studied to show, for example, that as in (./) 0.1 - 0 Cosmic Ray work, "Leading Particles" occurred, i.e. the inci­ 0:: : 4-BODY dent particles in a collision tended to continue in the same u ~ direction with a large fraction of the total energy and with the same or nearly the same quantum numbers. Since bubble chambers could measure momentum and determine by kine­ matic fitting the precise reaction, data from accelerators tended l • rr•p-+p rr•n • n•p-+ p11•11•11- to be more precise and many finer points were obtained. How­ 0.01 v ~ n•p .... p 11•11""rCTT 0 ever the subject tended to suffer from the lack of any calculable / v n•p ... pn•n+11•11-rr- theory. In the last couple of years the situation has changed 0 x 11•p- p'T'l'+,,.+'!i'n·TT-T1° dramatically and a large number of both experimental and theoretical papers are devoted to this subject, which is perhaps only fair since the largest part ( ""'70% above 10 GeV /c) of the total cross section is many-body. 0. 001 L--L--.L-'-l-L.1--'-----'---'--~ ~~~-~-~ The subject will be considered under three headings 0.3 3 10 30 a. Variation of cross sections with energy INCIDENT LAB MOMENTUM I Gev/c b. Multiperipheral model Fig. 42. Cross section versus lab. momentum for the n+p reactions c. How to present data. indicated. The lines are hand-drawn. 260 D. R. 0. Morrison

K+ p C R 0 S S S E C T I 0 N S those based on the series of conventions and parameters deter­ -.--.---r--1····-,--- mined by Chan, Loskiewicz and Allison [60] by normalisation 1c"p POINTS ARE FROM K+p REACTIONS with 8 GeV/c and 6 GeV/c K-p data. Similar work has been done by other authors, in particular Bali, Chew and 10 ::- CURVES ARE FROM Tl'+p REACTIONS Pignotti [70]. Since the Multiperipheral Regge Pole model could be applied to almost all reactions, this resulted in a sudden surge of interest in the many-body reactions and considerable progress bas been made in understanding them. Thus historically speaking, a debt of gratitude is due to Chan and his co-workers . ..a 1 - Initially the Multi peripheral Regge Pole model appeared to E fit all reactions successfully. However difficulties in the fitting z have been observed, see for example the papers by the Birming­ 0 ;::: ham-Glasgow Collaboration [71] and by three collaborations u involving Aachen-Berlin-Bonn-CERN-Cracow-Heidelberg­ UJ I/) London-Vienna and Warsaw [72]. These difficulties come from I/) a number of sources I/) 0.1 0 a:: 1. The number of Regge exchanges is much too few e.g. u allocating one trajectory to both Pomeron exchange and posi­ tive G-parity meson exchange. 2. Too few coupling constants e.g. ref. 71 for difficulties when rJJ mesons are produced . ....r--4-soov 3. The model has no "good" manner for handling resonance 0.01 production. The parameters initially chosen by Chan et al. [60] tended to average over resonances. • K+p - p K+rr• 4. The model does not contain duality [14]. c K•p- pK+1Ttr- 5. The model does not satisfy unitarity if unlimited Pomeron o K•p - pK•rrir fr0 exchanges are allowed. These are all serious objections, some practical, some funda­

0.001 -~~~~~--~.-L-.. l -I ~ .~~---~~ mental. It is not surprising that most theoreticians have aban­ 0.3 3 10 30 doned it and are now engaged in studying the Veneziano Model. INCIDENT LAB. MOMENTUM, GeV/c This latter model bas important theoretical advantages [73] and recently Petersson and Tornqvist [74] have succeeded in fitting Fig. 43. Cross section versus lab. momentum for the K+p reactions distributions from the three-body reaction K-p ->- An•n-. In indicated. The lines are the hand-drawn lines for n+p reactions in general the fit is good and all important resonances (except the Fig. 42 but normalised to the K+p data. Y*(1690)) can be fitted. However this model also has disad­ vantages-theoretical ones, e.g. unitarity is not satisfied and practical disadvantages in that very few reactions can be ences that are observed, mainly in the three-body channel, can fitted. This is because the calculations are, at present, so com­ be ascribed to resonance production effects. While some of the plicated that only three-body final states can be fitted and also agreement could be interpreted in terms of "physics", as for because Pomeron exchange is not included in the model example the quark model, it may well be that much of the (except for elastic scattering in ref. 16). agreement is caused by the similarity of kinematic (i.e. phase The experimental physicist with results from many-body space) factors. reactions has now a problem. For example, suppose in some distribution, e.g. a mass distribution, a significant effect is observed. How does he draw a background to measure the b. Multiperiphcral model effect? The situations in which the Veneziano model can be In 1961, Amati, Fubini, Stanghellini and Tonin [69] proposed applied are so rare as not to make it a practical solution at a model of high energy reactions in which there was one present. If he uses the Chan, Loskiewicz and Allison model exchange line and each secondary particle was emitted separa­ (CLA), the theoretical difficulties of this model are liable to be tely from a vertex on this exchange line. This was the Multi­ pointed out-"what about Duality?''. peripheral Model and it had the great advantage that the Some possible practical solution to the experimentalists' average transverse momentum of each particle was small. problem is based on the following experimental fact-despite However it was extremely difficult to calculate and few predic­ its theoretical difficulties, the CLA model works surprisingly tions were made which could be tested. Later it was suggested well in most cases. There is thus no point in testing it further. that each of the exchanges should be reggeised. In principle The model can be used as a first guide as what to expect in one should draw all possible Feynmann diagrams and consider any given reaction, although because of the theoretical dif­ all possible Regge exchanges. However in the calculations per­ ficulties the result of the calculation should always be treated formed so far a few Regge exchanges have been considered to with common sense. be "dominant" and only these have been used in the calcula­ An example of this may be given. In the reaction tion. The most widely applied series of calculations have been (15) Kaon Reactions 261

at 4.6 and 5.0 GeV/c, three bumps have been observed [75] in the (AK-) mass distribution as can be seen in Fig. 44. lt has been claimed that each bump is a S':' resonance. However one suspects that the dominant Feynmann graph is one with the K­ at the incident K- vertex and the A at the proton vertex Fig. 44a and hence the (AK-) mass distribution should peak near the highest possible mass. Using the CLA model, a "back­ - - + ground" was calculated and indeed this peaks near the highest K p--Y K K AT 4.6 + 5.0 GeV/c mass bump at 2400 MeV, though it may be noted that the >a; width is greater. The use of such a "background" seriously ~ M. R. M. CALC . reduces the statistical significance of the peak at 2400 MeV. 0 ...:r This does not prove that there is no S* at 2400 MeV (actually --20 one expects several S* in this mass region) but suggests that ti) 1- the data in Fig. 44 may not be adequate to prove its existence, z since the most probable background peaks at this mass for this w given incident momentum. Tf the experiment were repeated at >w some higher momentum, then the existence of a peak at 2400 LL MeV would be good evidence since the peak of the CLA 0 10 "background would be shifted to a higher mass. Incidently, 0:: although reaction (15) is a three-body one, it cannot at present w be fitted with the Veneziano model because Pomeron exchange CD is possible. ~ :::> z c. How to present data 2.0 2.4 2.8 The first problem in data presentation is the realisation that ( Y Kf E FF. MASS , Ge V the problem of presentation exists. It is possible to compare models with experimental data using an insensitive variable Fig. 44. Number of events versus (YK)- mass for the reactions such that agreement is obtained whereas if another variable K-p-+ YK[(+ at 4.6 and 5.0 GeV/c [75]. The solid line is a multi­ peripheral Regge Pole model [60] calculated using the Feynmann had been used disagreement would have been found. The real diagrams (a) (b) and (c) with yo as a A for 4.6 GeV/c. problem is to find variables, or ways of displaying the data such that the "physics" of the experiment is clearly visible. This is often not easy and while some new methods of presentation are described here, one expects other methods to be discovered In the search for significant variables and for diagrams that in the future. illustrate the "physics", two new ways of plotting data have Jn their first reggeisation of the Multiperipheral Model, been suggested: Chan and his co-workers [76] considered only the region of 1. Longitudinal Phase Space plots, by Van Hove [77] phase space wheres, the effective mass squared of two particles, 2. Triangular t-plots by Muirhead [78]1 was large as this is, strictly speaking, the only region where Regge Pole theory can be applied. lf one considers a three-body It has been found that one of the most sensitive variables to reaction, this means the central region of the Dalitz plot. The the reaction mechanism is the c.m. longitudinal momen­ difficulty of comparing the model with experiment was that at tum, PL*· high energy there are almost no events in the central region of The longitudinal phase space (LPS) analysis may be explain­ the Dalitz plot, while the edges of the Dalitz plot are densely ed in terms of the plot shown in Fig. 45 for the three-body populated. Jn the second form of reggeised multiperipheral reaction, model proposed, CLA [60] described the entire Dalitz plot, (17) that is both high and low s-regions. The formulae used were such that they were almost of a pure Regge form for the high The three variables plotted are the c.m. longitudinal momentum s-region, while phase space factors are important on the of the three secondary particles, PL*(P), PL *(n-) and PL*(n°). boundary of the Dalitz plot where s is small. The fact that The three axis are inclined to one another at 120°. Thus for each the CLA formulation gives reasonably good fit to the data event there is a unique point on the LPS plot. This is the illustrates the importance of phase space factors. advantage of the LPS plot, for previously when one plotted An approach to data presentation is contained in the follow­ the PL* distribution of one emitted particle, the PL* values of ing rule: the other two were unknown e.g. in Fig. 45, for a given value of PL*(P), the crosses show three possible positions for the EXPERIMENTAL RESULT= (KINEMATICS)X event on the LPS plot. The experimental distribution of points X (MECHANISM) (16) from ref. 72 on the plot for reaction (17) is shown in Fig. 46. where kinematics= phase space It may be seen that the experimental points all lie near the mechanism= "physics". boundary of the LPS plot. This is because the transverse momenta of all three particles is small. This fact allows us to 1 It has recently been pointed out that a similar plot has been used convert this two-dimensional LPS plot into a simpler one­ previously by Beusch et al. [91] dimensional distribution. This is done by introducing as 262 D. R. 0. Morrison

AT 16 GeV/c Also the CERN-Brussels Collaboration [80] in studying at 5 GeV/c the reaction (18)

AT 16 GeV/c

C.l.A. MODEL 0.6 1308 EVENTS

100 ~ >a; (!)

'O .0 ~ 0 :::> -+ .... I- r"O z 00 05 10 (£J w ~· 0 'O it*, GeV/c 0 ~ II ci 0 0 ~

Vl 0.2 w Fig. 45. Longitudinal phase space plot. See text for explanation. -I- /\ Vl z a:: w GJ w > > 1-t 0.0 Vl w z

ANGLE w , DEGREES

Fig. 47. For the reaction n-p-> N*++n-n- at 16 GeV/c [72], num­ ber of events versus angle w defined in Fig. 45 and text. Also average transverse momentum of each particle shown versus angle w. The solid line is from the CLA model [60]. The dotted lines are this model with the addition of N*+ +exchange. The ratio of coupling constants used for N*+ + is shown.

-+ AT 16 GeV/c o.o 0.5 10 1111 EVENTS it*, GeV/c

Fig. 46. Longitudinal phase space plot for the reaction n-p-+ pn-n° at 16 GeV/c [72}. c) 't*<1Yi ) -/. sensitive variable the polar angle ro, which is counted anti­ clockwise from the axis with PL *(n-)= 0 as is shown in Fig. 45. An example [72] of the use of the co-variable is shown in Fig. 47 where the number of events and also the average transverse CUBOCTAHEDRON FOR momentum of each of the particles is plotted as a function of co. LONG. MOMENTUM PLOT It may be seen that the normal CLA model using the param­ 4 BODY Fl NAL STATE A eters of ref. 60 gives a rather poor fit to the data, but if in this model N*++ exchange is allowed, better agreement is obtained Fig. 48. Longitudinal phase space plot for the reaction n-p -> if the appropriate coupling constant is chosen. Using co-distri­ ->pn+n1-n2 - • butions, Bialas et al. [79] have indicated that, whenever possi­ (a) the four planes with PL*= 0 for each of the particles ble, the diffraction dissociation mechanism (single Pomeron (b) cuboctahedron showing the sides of the LPS plot exchange) dominates three-body reactions at high energy. (c) projection of the seven faces indicated in b. Kaan Reactions 263

AT16GeV/c LONG. MOM. PROJECTED ON CUBOCTAHEDRON FACES A

4

..~.. ::: ... l~p

l~p

Fig. 49. Plane projection of the seven faces of cuboctahedron (Fig. 48c) for the reaction rr,-p--+ prr,+rr,-rr,- at 16 GeV/c, ref. 72. Feynmann diagrams illustrate the type of reaction expected to dominate on each face.

have found that the co-distribution has two peaks. The second Finally in Fig. 48 a projection of these seven faces is shown. peak is unexpected as it corresponds to the emission of fast n­ Because the transverse momentum of all the particles is small, particles in the c.m. while the K+ mesons are slow. It is dif­ the experimental points from reaction (19) are found to lie ficult to explain this result in terms of a multiperipheral model near the surface of the cuboctahedron. Thus it is reasonable to because double charge exchange is implied. project from the centre on to the surface of the cuboctahedron, For three-body reactions the boundary of the LPS is, at high thus reducing a three-dimensional distribution to a two-di­ energy, a hexagon and these representations are often called mensional one which is easier to understand. This is done in hexagon plots. For four-body reactions, the LPS plot gives a Fig. 49, where because there are two identical particles in three-dimensional figure which is a cu boctahedron with 14 reaction (19), only half the plot is used. Feynmann diagrams faces. The 3 collaborations involving Aachen, Berlin, Bonn, corresponding to the various possible contributions are shown CERN, Cracow, Heidelberg, London, Vienna and Warsaw [72) for illustrative purposes. It may be seen that the majority of have studied the four-body reaction the events give points in the central triangle, 7, corresponding to a proton at one vertex and the three pions at the other. It (19) may be noted that most events correspond to reactions in at 16 Ge V/ c. In Fig. 48, the four intersecting planes correspond­ which Pomeron exchange can occur. ing to PL':'= 0 for each of the particles are shown. The figure The plot proposed by Muirhead for three-body reactions is shows also a cuboctahedron with seven of the faces numbered. illustrated in Fig. 50. For the reaction A+ B --+ 1+2+ 3, the 264 D. R. 0. Morrison

MUIRHEAD TRIANGULAR t - PLOT (20) A+B = 1+2+3 then the boundary, in the high energy limit, is a triangle as shown. It is interesting to note that the phase space distribu­ tion is almost uniform over the triangle. The Aachen-Berlin-CERN-London-Vienna Collaboration [81] have applied the triangular t-plot to the reactions K-p--+ K -pw (21) K-p--+ K-p (22) They find in general that at high energy the points are distrib­ uted near the boundary of the plot because of the multi­ peripheral nature of reactions. For the particular cases of these two reactions, the experimental points are found to be limited to certain regions of the boundary. It is possible to draw Feynmann diagrams for different regions of the boundary to illustrate the corresponding type of reaction and this is done in Fig. 51 where the results for 10 GeV /care plotted. Inspection of Fig. 51 suggests that for is emitted from the same Fig. 50. For the reaction A+B=1+2+3, the four momentum vertex as the incoming K- (tK-

tA2, tA3 are plotted projection has been made on the fv,,= 0 line and this is shown as shown. The boundaries of the plot have the values tA = 0, tA = 0 1 2 in Fig. 52. Also shown in Fig. 52 are CLA model predictions and tA8 =0. for the two Feynmann diagrams with t,,v small. The model is in agreement with the experimental results. This result can be explained as being due to the fact that the meson is strongly squared four-momentum transfer, t, for each emitted particle is coupled to the KK system but very weakly coupled to a mr calculated with respect to the same incident particle, these values system. being fAi. fA2, and tA3• These three t-values are then taken as It might be asked what is the shape of the t-plot for a four­ the variables to be plotted, with their three axes inclined at body reaction? It is a tetrahedron and this should prove some­ 120° to one another. Since we have what easier to analyse than a cuboctahedron.

TRIANGULAR t- PLOT

AT 10 GeV/c

t pK = 0 t PK = 0 a) b) } p =:E ~- } =:E ~-

w K- p p ¢ =:E ~ . =:E K ~ =:E ~-

. . .. , . 1~ • • -·

~ wK- ~ tpp :0 / ~ ~- =:E ; p ~r p Fig. 51. Triangular /-plots as defined in Fig. 50 and text, for the reactions K-p--+ K-pw and K-p--+K-p([J at 10 GeV/c [81]. Feynmann dia­ grams along the boundaries illustrate the expected reaction mechanism in that region. Kaon Reactions 265

PROJECTION ON tp = 0 LINE 6. Summary and Future K p-pK (> AT 10 GeV/c The main results may be summarized as follows:

EXPERIMENT 1. First results from the Serpukhov accelerator show that the total J(- p cross section is almost constant, which is in dis­ agreement with extrapolated predictions based on the Regge Pole model. 2. In elastic scattering, a second maximum occurs in n+p, 10 a) n-p, pp and K-p reactions, but does not occur in pp, pn or K+p scattering: A number of theories offer explanations of these results. 3. Jn K-p elastic scattering, dips are observed near t= -0.85 2 2 GeV and u= -0.3 GeV • The first cannot be explained in terms of "nonsense" values of a trajectory, but might be deriv­ able using the Veneziano model. The second may be due to the systematics of direct Y* resonances formation. 4. There are many experiments on polarisation in elastic N 0 ~ scattering. (!) 5. In the reaction K-n -> n-A, the polarisation observed is C.lA MODEL K in serious disagreement with an extrapolated Regge Pole l/) =r¢- prediction. -I- p z 6. 1t is a remarkable coincidence that the total elastic cross w 10 b) sections for J(+p and K-p are so similar, when the two reactions >w are so different in all other respects. 0 LL 7. In the reaction K+p -> pK+rr. , the percentage of quasi 0 two-body reactions is approximately energy independent. a: 8. The study of many-body reactions has greatly increased in w the last year and many new theoretical and experimental results OJ have been reported. New ways of plotting results have been ~ :::>z proposed and used. 0

I I 5 10 - - 107 K­ • ACCELERATOR • C..l:..A MODEL ==:E JZ/ • MEASUREMENTS p • 10 N ~ Cl. c ) (.!) ::> • 104 t 106 li! Cl 0 w .... [j et:: <( • c: ::::> ... ;!: ...... J ~ .... at 10 GeV/c [81] the ...J u

YEAR There then are two new ways of plotting data and they have Fig. 53. The black square points are the energy squared of the high­ helped in understanding many-body reactions. One expects est energy accelerator at the time of its first operation versus the that there are other variables or other ways of plotting data year of first operation. The dots are the annual measurement rate which are simpler or more sensitive to the "physics". of the Alvarez bubble chamber group as a function of the year. 266 D. R. 0. Morrison

For the future there is a problem. With the new accelerators, Morrison: much higher energy beams will be available. Reactions pro­ Perhaps I can repeat something which I said earlier, which is: ceeding by Pomeron exchange will be measurable as their cross the CLA model is not perfect. The Veneziano model is better, section is approximately constant, but for the majority of but not perfect and can rarely be applied. It is fashionable two-body reactions, whose cross section decreases with the now as the CLA model was fashionable a year or so ago. In square of the incident momentum, few events will be recorded. one year's time or two years' time some other model will be However, the measuring rate increases with time. The most fashionable. On the other hand if you look at all the results complete record available of the variation of measuring rate of the Ct.A model, in general they are surprisingly good. with year is that of the Alvarez bubble chamber group at There are, however, a few that are particularly bad, and these Berkeley. This is plotted in Fig. 53 together with the square of are the ones that tend to be shown at conferences. So until the energy of the largest accelerator. It may be seen that there there is something better, one can either use the CLA model is a perfect match and so one should still be able to measure or a band-drawn background. two-body reactions in the future.

Lipkin: I want to make a comment on the quark model. Perhaps in the Aclmowledgements spirit of this talk I should mention that there is a "Global quarkology" and "Local quarkology". Global quarkology It is a pleasure to acknowledge the help of Drs. A. Angelo­ takes the quark-antiquark amplitude and blames it for every­ poulos and H. J. Schreiber in the compiling of data. We are thing. Bad weather on Sundays, experimental errors, mistakes indebted to Drs. V. T. Cocconi, M. Jacob and C. Lovelace for in sign in a theoretical calculation and so on. This is not a helpful discussions. The generosity of those colleagues who joke. I know one good paper which used the quark-antiquark contributed unpublished data on request is much appreciated. amplitude to explain a mistake in sign in a previous calcula­ tion. However, the local quarkology says that you take the quark-antiquark amplitude and use it to explain only the Discussion imaginary part of the amplitude. And also you do not take any quark-antiquark amplitude, but just a quark and an Lovelace: antiquark of the same kind, pj}, nit, ).1 That automatically What you said about the K-p dip having no Regge explanation explains why you throw away the ). in this particular case. is wrong. It has a very clear and simple explanation. Because Also this particular model is essentially the basis of the duality diagrams. So tbat if you do it that way you actually get the of exchange degeneracy the sum of all the p-w-f-A 2 Regge contributions to K - p elastic scattering has the definite phase same predictions from duality. Now, this will give you slightly factor -exp [-ina,, (t)]. This becomes negative imaginary at different numbers than the ones you gave because for the av(t) = -t, and thus interferes destructively with the positive non-strange quarks you took ]J/1 and np whereas in this other imaginary Pomeron, causing a dip and a sign change of the approach you would not count them. So I am wondering 2 polarisation at t= -1 GeV • The quantitative fits to K-p are whetber any one has tried doing this and whether this gives extremely good. diITerent results. Also whether there is any indication that Second point, using Chan as background for resonances is the structure comes from the imaginary part rather than the certainly wrong because of duality. real part.

Morrison: Rushbrooke: I think Dr. Harari answered this question very well. You For this duality question I wonder if I could repeat a sugges­ should try something, fit the best available background, hand­ tion 1 made in Vienna last year in my review. lf you have a clrawn if need be, and state very clearly what your assumptions good Regge fit to a system, why not adopt the following are, so that the reader can easily interpret the results. procedure for coping with duality. You project out the appro­ priate partial wave of the suggested or suspected resonance and treat that projected out partial wave in the Regge amplitude Lovelace: and regard that as your background which you can then Give your data to theorists and let them do it for you. safely subtract from the observed structure. I have clone this in the case of pp -> pLJ + 'n- and one finds when one is worrying,

Harari: say, about the production of p 11 (1470) that the amount of the mass spectrum in the 1/2+ partial wave is very little and I said you should define clearly what you have done when you so one would in fact be quite safe in attributing most of the subtract the so-called background, but I also, in answer to peak one observes to the p (1470). another question, said that to define the background with the 11 CLA model would be entirely wrong because the CLA model very often does give you prominent resonances in one way or Metzger: the other. So I would really suggest that if you do subtract I wish to ask a question with respect to the specific example the background in one way or the other in terms of a freely that you have shown to suggest the use of the CLA model as drawn curve, you should probably do precisely what you did background. You have drawn a CLA background on the now, namely just take a look at the picture and draw some­ YK mass distribution from the 4.6 and 5.0 GeV/c Brook­ thing with your imagination and not use this CLA thing. haven-Syracuse experiment and have suggested that the CLA Kaon Reactions 267

peaking at high mass values somewhat lessens the statistical 26. R. C. Arnold, Phys. Rev. Letters 14 (1965) 657. significance of the 5'(2430) resonance. Have you calculated 27. K. P. Pretzl and K. Jgi, CERN Theory Preprint TH-1021 (1969). 28. BN L Rochester., Carrol ct al., Paper submitted to Vienna the CLA background for 3.9 GeV/c? For, naively, I would Intcmational Conference on High Energy Physics (1968), Phys. expect the CLA shape at 3.9 GeV/c to be similar to that at Rev. Letters 21(1968)1282 and University of Rochester Report 4.6 GeV/c, namely that it would also show peaking at the 875- 254 ( 1968). high mass values. But in the BNL-Syracuse data at 3.9 GeV/c, 29. C. Daum ct al., Nucl. Phys. B7 (1968) 19. 30. T. Lasinski, Paper 385. where phase space ends below 5'(2430), no peaking is observed 31. C. Michael, Wisconsin preprint. at high mass values. And if the CLA does not give the back­ 32. CERN, C. Bricrnan ct al., private communication. ground at 3.9 GeV/c, why should it give the background at 33. Arnsterdam-Nijmegen Collaboration, paper 175. 4.6 GeV/c? 34. CERN-Zl'lrich Collaboration, P. Astbury ct al., Phys. Letters 23 ( 1966) 396. 35 . R. D. Mathews, Nuclear Physics ll 11 (1969) 339. 36. M. Krammer and K. Maor, Tel-Aviv preprint TAUP-78-69, Morrison: submitted to Nuclear Physics. The calculation was done only at 4.6 GeV/c where the statis­ 37. T. Hofmokl and M. Szeptycka, submitted to Nuclear Physics. tics were best. It has not been done at 3.9 GeV/c, but we 38. College de France-Saclay-Impcrial College-Westfield College, London, Collaboration, J. M. Brunet et al., Paper 7 l. can try it.* 39. Saclay-Amslerdam-Dologna-Rehovoth-EcolePolytechniqueCol­ Iaboration, Paper 55. 40. Saclay-Collcge de France-Imperial College-Westfield College, London, Collaboralion, J. A. Danysz ct al., Paper 70. References 41. CERN-Brussels Collaboration, G. Bassompicrre et al., sub­ mitted to Nuclear Physics. 1. CERN-IHEP Collaboration, J. V. Allaby et al., Paper 309 sub­ 42. Aachen-Berlin-CERN-London-Vienna Collaboration, M. Ader­ mitted to Lund Conference (1969). holz et al., N uclcar Physics B7 ( 1968) l l I. 2. V. Berger, M. OJlsen and D. D. Reeder, University of Wisconsin 43. Aachen-Berlin-CERN-London-Vienna Collaboration, M. Ader­ preprint C00-881-159 and V. Berger, Topical Conference on holz et al., Nuclear Physics B5 (1968) 567. High Energy Collisions of Hadrons, CERN Report 68-7, Vol. 44. M. Markytan, Nuclear Physics B 10 ( 1969) 193. 1, (1968) 3. 45. G. V. Dass and C. D. Froggatt, Rutherford Preprint RPP/A 47 3. Aachen-Berlin-CERN-London-Vienna Collaboration, private (1969). communication. Note that it is a guesstimate as not all channels 46. A. Bialas and K. Zalewski, Nuclear Physics B6 (1968) 465. have been measured. 47. Brussels-CERN Collaboration, W. De .Baere ct al., submitted to 4. E. Flaminio, J. D. Hansen, D. R. 0. Morrison, CERN-HERA Nuclear Physics. reports, (to be published). 48. Aachen-Berlin-CERN Collaboration, M. Aderholz et al., 5. D. R. 0. Morrison, Phys. Letters 22 (1966) 528. Nuclear Physics B8 (1968) 503. 6. Cabibbo et al., Phys. Letters 22 (1966) 336. 49. CERN-Brnxelles-MUnchen Collaboration, G. Bassompierre et 7. Stanford-SLAC, W. L. Lakin, R. Hofstadter, E. B. Hughes and al., Paper 139. L. Mandansky, Bull. of Am. Phys. Soc. 14 (1968) 592 and private 50. D. D. Reeder and K. V. L. Sarma, Phys. Rev. 172 (1968) J 566. communication. 51. Purdue University, W. L. Yen et al., Phys. Rev. Letters 22 (1969) 8. Karlsruhe-CERN Collaboration, J. Engler et al., Phys. Letters 963. 2713 (1968) 599. 52. S.A. B.R.E. Collaboration, R. Barloutaud ct al., Nuclear Physics 9. CERN, .T. Allaby et al., Phys. Letters, 28B (1968) 67. B9 (1969) 493. 10. CERN-Holland Collaboration, C. Daum et al., Nuclear Physics 53. Brookhaven-City College of New York Collaboration, private B6 ( 1968) 273. communication from Kwan Lai. 11. Saclay-CERN Collaboration, J. Banaigs et al., Paper 67. 54. G. Bellcttini, Proc. of 14th International Conference on High 12. B. N. L.-Rochester Collaboration, J. Owen et al., Phys. Letters Energy Physics, Vienna (1968) page 329. 28B (1968) 61. 55. S.A.13. R. E. Collaboration, Paper 89 l submitted to the Vienna 13. CEN-Saclay, College de France, Imperial and Westfield Colleges Conrercnce (1968) (unpublished). London Collaboration, J. A. Danysz et al., Paper 72. 56. Birmingham-Ed in burgh-Glasgow-London Collaboration, pri­ 14. R. Dolen, D. Horn and C. Schmidt, Phys. Rev. 166 (1968) 1768. vate communication from D. C. Colley. 15. Saclay, 0. Guisan et al., Phys. Letters 18 (1965) 200. 57. Carnegie-Mellon University, private communication from 16. C. Lovelace, paper 140 contributed to tl1is conference. G. Yckulieli and Argonne Labornlory, private communication 17. A. I. Akheizer and M. P. Rckalo, Inst. for Theoretical Physics, from B. Musgrave. Acad. of Sciences of Ukrainian SSR, preprint No. NT

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