- Email: [email protected]
c K− p interactions and comparison with absorption and Regge pole models
Nuclear Physics B5 (1968) 567-581.
K*(a90)
PRODUCTION
INTERACTIONS ABSORPTION
North-Holland
AND
IN
10
GeV/c
COMPARISON
AND.REGGE
Publ. Comp.,
POLE
Amsterdam
K-p WITH
MODELS
M. ADERHOLZ, M. DEUTSCHMANN, E. KEPPEL, G. KRAUS, H. WEBER III Physikalisches Institut der Technischen Hochschule, Aachen U.GENSCH, C.GROTE, S.NOWAK, D.POSE Forschungsstelle ftir Physik Hoher Energien der De-utschen Akademie Wissenschaften zu Berlin: Zeuthen
dev
M. BARDADIN-OTWINOWSKA$ T. A. BYERgt , V. T. COCCONI, E. FLAMINIO~f~, J.D. HANSEN, G. KELLNER, U. KRUSET, M. MARKYTAN tt, D. R. 0. MORRISON, K. ZALEWSKI t-tt CERN, European Organization for Nuclear Research, Geneva D. P. DALLMAN, S. J. GOLDSACK, N. C. MUKHERJEE Physics Department: Imperial College. London A. FROHLICH, W.KlT.TEL, G.OTTER, P.PORTH, LWACEK Institut ftir Hochenergiephysik der dsterreichischen Akademie der Wissenschaften. Vienna Received 28 March 1968
Abstract: K*(890) and K*(1420) resonances are observed in 10 GeV/c K-p interactions. Masses. widths and cross sections are determined. Decay angular distributions and differential cross sections of K*(890) production are compared with the absorption model and Regge pole model. While at lower energies the absorption model predictions are in reasonable agreement with experiment. serious disagreement is observed at 10 GeV/c. Regge pole calculations including exchange of P: P’. T. p. w and A2 trajectories can fit the data but do not explain why 71exchange dominates K*‘(890) production while 0 exchange dominates K*-(890) production.
z
On leave from the University of Warsaw. $$ CERN Fellow from the University of Cambridge. Now at the International Atomic Energy Agency, Vienna. 3$$ Now at Brookhaven National Laboratory. t Now at the Universitv of Illinois. tt CERN Fellow from
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et al.
1. INTRODUCTION In the interaction of kaons with protons, K* resonances at 890 MeV and at around 1420 MeV are frequently observed. The production mechanism of these resonances can be best studied in the three particle final state NK?r, on the basis of cross sections, production and decay angular distributions. For incoming negative kaons above 2 GeV/c results on these channels have been reported at 2.1 (ref. [l]), 2.45 (ref. [l]), 2.64 (ref. [l]), 3.0 (ref. [2]), 3.5 (ref. [3]), 4.1 (ref. [4]), 5.5 (ref. [4]), and 6.0 (ref. [5]) GeV/c. For K*(890), the data usually warrant a detailed investigation, while for K”(1420) the results are in general only qualitative. In the published work it is concluded that most of the experimental facts observed for K*(890) can be described in the framework of the one particle exchange model with absorption, as introduced by Jackson and collaborators [6], when the assumptions are made that the reaction K-p -+ nK*‘(890) is dominated by pion exchange,
while the reaction
K-p -t pK*-(890) is dominated by the exchange of a vector meson. With these assumptions, the model can, in fact, describe at all energies investigated, i.e., up to 6 GeV/c, all the features of the production and decay of the K*‘(890) resonance of reaction (1). For reaction (2) the situation is complicated by the facts that in the model the energy dependence of the cross section for vector meson exchange reactions is in disagreement with experiment and that the vector meson coupling constants are not known. At energies around 3 GeV/c, however, a set of constants can be determined which allow both the production and the decay angular distributions of K*-(890) in reaction (2) to be well described. At 4.1 and 5.5 GeV/c absorption model calculations have given good fits to the decay angular distributions and reasonable fits to the production differential cross sections. As the predictions of the absorption model are strongly energy dependent and since it has been shown [7] that at high energies in pion-proton collisions, the model fails to describe various processes of quasi two-body reactions, it is interesting to investigate K* production for incoming kaon momenta above 6 GeV/c. Here we report on a study of processes in which a nucleon and a K* resonance are produced, based on an analysis of K-p interactions at (10.1 f 0.1) GeV/c, observed in about 200,000 bubble chamber pictures taken at CERN in the 150 cm British hydrogen chamber exposed in a R. F. separated beam. Total and differential cross sections have been determined both for K*(890) and K*(1420). The features of the decay angular distributions have been studied in detail for K*(890). The conclusions concerning the production mechanisms of K*(890) in 10 GeV/c K-p interactions are the following:
K*(890)
569
PRODUCTION
(a) For K*‘(890): The absorption model with pure pion exchange can describe adequately production and decay angular distributions, but predicts a cross section for reaction (1) about four times too large. (b) For K*-(890): The absorption model with a mixture of pseudoscalar and vector (w) exchange can describe some of the features of the decay of the resonance in reaction (2) if an appropriate choice of the vector meson coupling constants is made. With those constants, however, the model predicts a production differential cross section greatly at variance with the experimental one. No set of parameters can produce even approximate agreement with production and decay distributions simultaneously, and hence the model at this energy is inadequate. (c) A Regge-pole calculation including P, P’, n, P, 0 and A2 trajectories can describe most of the features of K*’ and K*- production and decay, but the reasons why the 71trajectory dominates in reaction (1) while the w trajectory dominates in reaction (2) remain to be explained.
2. EXPERIMENTAL
RESULTS
The following channels, events have been studied:
fitted from about 16 000 measured
K-p - pK-no K-P
-
~K:een
(445 events) n-
K-P - pKEtted r Kp-nKr
- +
two-prong
(a)
(183 events) z (250 events) zz (528 events).
(d)
Fig. 1 shows the (K?r) effective mass distributions for the above reactions. For reactions (a) and (d) the events in which the (nucleon + pion) system has an effective mass in the N*+(1236) band (1.12 to 1.34 GeV) were excluded. The production of both K*(890) and K*(1420) is evident in all channels. The (Kn) mass resolution is best in the four-constraint channel (b) and in channel (d), where the K and 7~tracks are directly measured and not obtained by kinematic fitting. The combined (Kr) mass distribution for channels (b) and (d) was fitted with a superposition (without interference) of two Breit-Wigner distributions z$$ and a smooth, hand-drawn background 0 Events with a visible
V” decay have been accepted in a fiducial region of the bubble chamber about twice as long as that chosen for other events. gt It is found in reaction (b) that almost all the Kots observed to decay have a lab momentum greater than 2 GeV/c. In reaction (c). where the K” is identified by kinematic fitting, the number of K” with lab momentum greater than 2 GeV/c is as expected from reaction (b), but there is an excess of events with momentum about 0.4 GeV/c. Hence events giving a fitted K” with lab. momentum less than 2 GeV/c were reassigned to other channels. zts We used the energy dependent Breit-Wigner functions as given by Jackson [13].
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K-pap
K%-
( K”seen
20
> 2
10
‘3 \ In
0
d)
cl
I
B 30K-p+pK”7r-
6 ii
(K’fitted) 250 events
372 events
=20-
lo-
Fig. 1, Effective mass distribution of the (Kn) systems in the reactions K-p - pK% ’ (a). K P- pK’?r- (b) and (c). and K-p-+ nK_n’ (d) at 10.1 GeV/c. For reactions (a) and (d) the events for which the,(pso) and (nn+) systems. respectively. are in the mass region of the N*’ isobar (1.12-1.34 GeV) have been excluded. (see fig. 2). The resulting masses and widths of K*(890) and K*(1420) are presented in table 1. Table 2 gives the cross sections for the production of reactions (1) and (2), as well as for the corresponding reactions with production of K*(1420). AI1 cross sections have been corrected for unseen decay modes. For K*(1420) the assumption was made that the branching ratio for decay into (K?T)and into all other modes is 1 : 1. It can be seen from table 2 that the cross sections for production of K*(890) and K*(1420) at 10 GeV/c are all of the same order of magnitude, between 50 and 90pb, which corresponds to about l/50 of the elastic scattering cross section and about l/350 of the total K-p cross section at the
571
K”(890) PRODUCTION
nKW* AT
0
( N **
excluded)
10 GeV/c
20
1.0
3.0
(Km1 EFF. MASS , GeV Fig. 2. Effective mass distribution of the (Kn) systems in reactions (b) and (d) fitted with two Breit-Wigner curves and the hand-drawn background shown.
Table 1 Mass and widths of K* resonances at 10 GeV/c. Resonance
Mass
Full width
K*(890)
(893 + 4) MeV
( 58 + 7) MeV
K*(1420)
(1423 f- 21) MeV
(175 + 57) MeV
same energy. The cross sections for K*(890) production at 10 GeV/c are one order of magnitude smaller than at 3 GeV/c. Fig. 3 shows a compilation of the production cross sections for reactions (1) and (2) as a function of the incident K- momentum. For reaction (2), K-p - pK*-(890), there exist several data at lower momenta and they appear to be compatible with our point at 10 GeV/c if one assumes [8] a dependence of the cross section, u, on the lab momentum, p, of the type cr = cPmcr, where c and 1yare constants. A fit to the data gives (Y= 2.01 f 0.14. For the reaction K-p - nK *‘(890), too few measurements are available to determine well the energy dependence. A fit to the data gives cy= 1.98kO.37. The solid lines in both figures are the function Q = 8.75 p-2.0. The deviations of the experimental points from the line are not necessarily of a systematic nature, i.e., a ratio of 1 : 1 for the two cross sections, independent of momentum, is quite possible. Obviously, more data are needed for the IX*’ cross section. The ratio of the cross sections for pK*- and nK*’ has some immediate bearing on the exchange mechanism that might be responsible for the production of these systems. For pure 71(or pure p) exchange in both reactions,
M. ADERHOLZ et al.
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Cross sections for (K-p -
Table 2 K* nucleon) reactions at 10 GeV/c.
Reaction
Cross section (pb)
K*-(890) + p
92 f 9
K*O(890) + n
58 2 10
K*-(1420)
54
+p
K*o(1420) A n
l
13
78 f 14
1
_
K-p--pK*-
4
2
LAB
MOMENTUM
OF
I&JENT
(890)
K-,
6
_
8u)
G*Vlc
Fig. 3. Total cross section for K-p - nK*‘(890) and K-p - pK*-(890) versus the laboratory momentum of the incoming kaon. - ref. [l] . Solid circles, Open square? - ref. [2] . - ref. [3] . Shaded square, - ref. [4] . Open triangles, Shaded triangle, - ref. [5] . Double circle: - This experiment. The solid lines are the function U(p) = 8.75 P2*0.
for instance, this ratio should be 1 :4, a figure incompatible with the experimental results. Fig. 4 shows the differential cross section,’ du/dt, for reactions (1) and (2) at 10 GeV/c. It can be seen that for nK *O, do/dt increases steadily as one moves towards small values of 1t 1, while for pK*- it goes through a
573
K*(890) PRODUCTION
ao01l
00
1
I
0.2
1
1
a4
1
1
0.6
1
1
0.8 It 1 , (GeVk)2
Fig. 4. Differential cross section. do/dt. for the reactions K p - nk“‘(890) (fig. 4a) and K-p -+ pK*-(890) (fig. 4b) at lO.lGeV/c. The dotted lines are predictions of the absorption model, the solid lines predictions of a Regge pole model with the assumptions explained in the text. bending over towards / t 1 = 0. The possimaximum at t / = 0.1 (GeV/c)2, bility that this “bending over” is caused by a loss of events in the first bins due to scanning bias has been investigated, but no indication of such an effect has been found. It is interesting to note that a similar “bending over” seems present also at 4.1 and 5.5 GeV/c (ref. [4]), while at lower energies, in particular in the large statistics experiment at 2.64 GeV/c (ref. [l]), the differential cross section is strongly peaked forwards. The forward peaking of the nK*’ differential cross section is instead observed for all K- momenta investigated. These facts will be discussed in the next section. The slopes, A, of the distributions in fig. 4 have been determined by fitting the data with the expression do/dt = k e-At in the 1t ) range indicated below. The results are: For K*‘(890):
A = (6.3 f 1.0) (GeV/c)-2
for 0.03 < it ) < 0.40 (GeV/c)2
,
For K*-(890):
A = (5.8 f 1.1) (GeV/c)-2
for 0.1
.
< IE 1 < 0.45 (GeV/c)2
574
M. ADERHOLZ et al.
A value of A = (4.8 f 0.5) for K*-(890) has been recently reported at 6 GeV/c (ref. [5]), determined by fitting the distribution up to (tj = 1.0 (GeV/c)3. No significant backwards emission of K* resonances was observed. In fact, the only example of backward production observed was one event in the mass region of the K*O(890). A similar result is reported at 4.1 and 5.5 GeV/c. The values of the spin density matrix elements, pmn, as obtained from maximum likelihood fits to the data are presented in table 3, averaged over : t\ values up to 0.3 (GeV/c)2. Fig. 5 shows the ; t j dependence of the own elements. In these calculations no background subtraction was made.
3. ANALYSIS OF THE K*(890) PRODUCTION MECHANISM WITH THE ABSORPTION MODEL 3.1. The ~~K*~syslern In the framework of the one-particle-exchange model, the production of the K*O(890) resonance in reaction (1) can proceed via the exchange of 71,P, AZ.. . . The forward peaked production angular distribution, as well as the shape of the decay angular distributions are consistent, however, with pseudoscalar (pion) exchange being the dominant process. This assumption has proved satisfactory in all experiments at lower energies, where agreement has been obtained between the experimental results and the predictions obtained using the pion exchange model with absorption as described specifically in ref. [6]. We have used this model at 10 GeV/c to calculate total and differential cross sections, as well as the p mn matrix elements and their j t ( dependence, in order to compare them with the experimental results. The pion coupling constant at the mesonic vertex was G2/4n = 0.75, deduced from the width of the K* resonance and the coupling constant at the baryonic vertex was taken to be G3/4n = 14.6. The absorption constants used were hl = 0.016, h3 = 0.01, C 1 = 0.6 and C3 = 1.0. The theoretical values of Pmn Table 3 The density matrix elements for the channels pK*-(890) and nK*O(890). pK*-(890)
nK*O(890)
Exp.
Exp.
Theory a)
PO0
0.16 f 0.05
0.60 zt 0.09
0.68
Pl> -1
0.33 * 0.05
0.16 i 0.04
0.08
RePlo
-0.03 * 0.05
-0.21 i 0.06
-0.17
a) Pure ?Texchange. The four momentum transfer t is restricted
to ) t\ < 0.3 (GeV/c)2.
K*(890) PRODUCTION
’ KJp+ n K”’ (890)
575
(a)
_ 10 GeWc -------________
REP10
l-
00
(12
a4
1 Q6
I
, 0.8 It1
1.1
J
I
,
(GeVlcl
2
Fig. 5. Dependence of the pmn density matrix elements on the squared four-momentum transfer ,t: . The dotted lines are predictions of the absorption model. the solid lines are predidtions of a Regge pole model with the assumptions explained in the text.
are compared in table 3 with the experimental values. Reasonable agreement is found. The element Poe, which should be unity for pure pion exchange without absorption, is (0.60 f 0.09) experimentally and 0.68 according to the model. The value of p o. at small momentum transfers ( j t / < 0.2 (GeV/c)2) seems to be independent of K- momentum, being (0.68 f 0.07) at 2.64 GeV/c, (0.63 f 0.12) at 5.5 GeV/c and (0.60 f 0.09) at 10 GeV/c. This constancy of the poo element may be interpreted as evidence that the mechanism of K*O production does not change drastically between 2 and 10 GeV/c. The dashed lines in fig. 5a are the calculated t dependence of the Pmn elements. Also here the agreement is reasonable. The calculated differential cross section is the dashed line in fig. 4a. The shape is satisfactorily described, however the absolute value of the cross section is too large by a factor of about four. (In the figure the curve is normalized to the data. ) As at lower energies, no evidence for an appreciable contribution of p-exchange is found at 10 GeV/c, which is of interest since the cross section due to vector meson exchange might be expected to decrease with
576
M. ADERHOLZ
et al.
energy more slowly than the cross section due to pseudoscalar exchange. This fact that at all energies the p exchange contribution to this process is negligible compared with the 7i exchange contribution, is in agreement with SU(6) predictions [9]. In conclusion, at 10 GeV/c, the absorption model with pure pion exchange can describe the main features of both the production and decay angular distributions of the K*O(890) resonance in reaction (l), but it predicts for this reaction a cross section four times too large. 3.2. The pK*- system The production of the K*- resonance in reaction (2) can be mediated not only by the exchange of n, P, A2 as for reaction (l), but also by the exchange of w, 0, as here no exchange of charge is required. Since the (~pp coupling constant is supposed to be very small, the contribution of (Dexchange is expected to be negligible. From isotopic spin consideration, both 71andp exchanges are expected to contribute to reaction (2) with cross sections only i of those contributing to reaction (1). If P exchange is found to be negligible in reactions (l), its contribution must a fortiori be unimportant in reaction (2). It must therefore be anticipated that whatever difference is observed in the experimental distributions for K*’ and K*- must derive from the effects of w exchange. The assumption that reaction (2) is produced by TIand w exchange (and the effects due to the interference of TIand w amplitudes) has produced satisfactory agreement between absorption model calculations and experimental data for all experiments up to 5.5 GeV/c. In particular the experiment at 2.64 GeV/c has indicated [lo] that the 71contribution, limited to small t ; -values, and the w contribution, predominant at large t 1-values, interfere constructively in the small jC j region, creating the strong forward peak observed in the differential cross section at that energy. As remarked in the previous section, the shape of the du/dt distribution at small t-values changes as the K- momentum increases. The observed behaviour is qualitatively consistent with the interpretation that with increasing energy, 71exchange and its interference with the w amplitude become less important and limited to smaller ; t / -values, while the w contribution becomes increasingly dominant over the whole i t j-range. The “bend-over” at small 1tl-values seen above 4 GeV/c is in fact characteristic of an exchange process involving a spin-flip by one unit. The experimental decay angular distribution for K*- is also consistent with vector exchange and so is the low value of thePoo element (0.16 f 0.05), asp.. would be zero for pure w exchange. Actually, the increasing importance of vector meson contribution as the energy increases is clearly indicated by the fact that the value of poo for small values of the four-momentum transfer (1 t ; < 0.2 (GeV/c)2) steadily decreases as the momentum of the incoming kaon increases, being 0.54 f 0.03 at 2.64 GeV/c, 0.34 f 0.08 at 3.0 GeV/c, 0.27 & 0.08 at 4.1 GeV/c, 0.22 f 0.08 at 6.0 GeV/c and 0.17 f 0.07 at 10 GeV/c. We have analysed the data for reaction (2) at 10 GeV/c with the absorption model assuming a mixture of 71and w exchange (and their interference).
K*(890) PRODUCTION
.x7-7
For the pion, the same coupling constants were used as for reacticm@., For W, the coupling constants are unknown. In the analyses reported inidilpe literature, these constants are either calculated [4] from other known coupling constants following theoretical prescriptions based on SU(6) wrnmetries [9], or are left as free parameters to be determined by,maz@imum likelihood fits to one, or all, of the same experimental distributions that one wants to compare with the model. In this latter. approach, which at the present stage of our knowledge seems the safest one, all one can do is investigate whether there exists one set of constants with which all the experimental results obtained at a given energy can be described. Whether these constants vary with energy, and the form of this variation are also important points that can throw light on the value or limitations of the model. Following the terminology of ref. [6], the constants to be determined are 5 and n, defined as:
5=f
(Gv+GT)
and
ZgG
__fGT gG’
where g and G are the pion coupling constants at the mesonic and baryonic vertices, respectively is the vector meson coupling constant at the mesonic vertex, and Gtf and GT are the vector and the tensor coupling constants at the baryonic vertex. To compare our results at 10 GeV/c with the absorption model, we have determined the constants (5, ?I) from maximum likelihood fits to the following experimental distributions and have obtained the following results: (a) From fit to the shape of the do/dt distribution: 5 = 0.2, r] = 0.2. : 5 = 0.4, q = 0.0. (b) From fit to the omn(t) distributions (c) From fit to both distributions simultaneously : 5 = 0.4, n = 0.2. In all cases, the same absorption coefficients as used for reaction (1) were introduced. It has been verified that modification of the absorption parameters, in particular of X2 which is the most arbitrary one [lo], do not change the results appreciably. Our 5 values are thus between 0.4 and 0.2, and our q values between 0.2 and 0.0. A value n = 0 is expected for pure w exchange. Donohue [lo] has made a detailed analysis of the results for reaction (2) at 2.64 GeV/c and 3.0 GeV/c, as well as of the corresponding results with positive incoming kaons. He concluded that values of 5 from 2.2 to 1.4 and of ?I from 2 to 0.5 could describe all experimental results at those energies, the best values for (4,~) at 2.64 GeV/c being (1.8, 1.15) and at 3.0 GeV/c (1.55, 0.95) obtained from fitting do/dt distributions. Fitting both decay and production distributions, the set (0.8, 0.6) was obtained at 3.5 GeV/c. At 6 GeV/c the set (0.6, 0.0) gave correct predictions for the total cross section and the density matrix elements. Fig. 6 shows the variation of 5 and 77as a function of incident K- momentum. Evidently the constants determined at 10 GeV/c differ radically from those determined at around 3 GeV/c, their dependence on the momentum, p, being about p-l. This may be taken as indication that the model, suitable at around 3 GeV/c, cannot be safely extended over a large energy range.
M. ADERHOLZ et al.
578
Fig. 6. Sets of values of the vector coupling constants functions 5 and 17determined at various momenta of the incoming kaon.
Comparison
Table 4 of density matrix elements for reaction (2) with absorption calculations for different values of g. q). 0.30
__-
exp
Pmn
-
0.60 theor 0.13a)
PO0
Pl,-1
Re PI.0
0.27 I 0.08
0.34 -c_0.05
. 0.015
: 0.05
0.34 b)
0.12 b)
I +_ ;.;;.
0.13
I f 0.07
0.07 b)
0.36 c)
0.11 C)
0.06 C)
0.07 a)
0.21 a)
0.30 a)
0.29 b,
0.43 b)
* 8.;;
+ i’;;
0.46 b,
0.22 c)
0.41 C)
0.45 c,
-0.21 a)
-0.14 a)
-0.10 a)
-0.08 b,
; i.;;
-0.13 c)
-0.02 b) -0.04 c)
a) (5.77) = (0.2, 0.2) from fit to do/dt. b) (5.17) = (0.4. 0.0) from fit topmn(t). C) (5.77) = (0.4, 0.2) from fit to do/dtand
p,,(t).
; 8.;;
-0.01 b) -0.02 c)
0.12 f 0.02
0.05b) 0.03c) 0.39a)
0.36 i 0.08
0.47b) 0.42c) -0.05a)
0.025 + 0.07
-O.Olb) -O.OlC)
K*(890) PRODUCTION I
8
K-p -
0.001
0
1
I 0.2
,
K’-
I
I 0.4
0
579
,
J
10 GeVlc
_
,
8
(890) p
I
I 0.6
I
I 0.8
1t I, (GeVlc)2 Fig. 7. Absorption model predictions for da/dt of reaction (2). with different values of 5 andq. Curve a): 5 andq determined from best fits to experimental du/dt. Curve b): 5 andT determined from best fit to the t-dependence of the density matrix elements. p&t). Curve c): 5 and 17determined from simultaneous best fit to d@/‘dt and pm&).
The comparisons of the absorption model predictions with our experimental data using the various sets of (6,~) determined from our fits are shown in table 4 and in fig. 7. It can be seen that with the (5, n) values derived from da/dt, case (a), we obtain unacceptable values of the own elements, and a poor fit to du/dt. This solution is equivalent to assuming a very small vector exchange contribution, which is in contradiction with the experimental evidence of dominance of vector exchange. The other sets of (5,~) values, cases (b) and (c), produce reasonable agreement for the ~00 and Re ~10 elements, very poor agreement for pi-l, and a completely wrong shape for du/dt. The curves dashed in figs. 4b and 5b are calculated with the set (c) of (t , q) values. In conclusion, no choice of coupling constants and of absorption parameters can bring the absorption model, in the form described in ref. [6], to produce predictions in agreement with experiment at 10 GeV/c. It is to be noted that the same conclusion, i.e., the inadequacy of the model in describing processes requiring vector meson exchange at high energies, was reached in a study of several two-body reactions induced by 8 GeV/c collisions of positive pions with protons [7].
58(h
4. REGGE-POLE
M. ADERHOLZ
CALCULATION
et al.
FOR THE PRODUCTION OF K*(890)
Regge-pole calculations have been made in an attempt to interpret the experimental data obtained at 10 GeV/c for reactions (1) and (2). For reaction (1) the r, and
‘t /. The agreement can be considered acceptable, except perhaps for the element Re ~10 for reaction (2). The results of this calculation may be summarized as follows. For the reaction (2) of K*- production, the trajectory that includes w and (Dwith no spin-flip is found to be the dominant one over the : t 1-range up to 0.7, except in the l’ery forward direction (, ti < 0.02 (GeV/c)2), where the 7~trajectory may be more important. An interpretation of why the low-lying r~ trajectory could become dominant in very forward directions has been proposed recently [12]. The trajectory, for the range 0 :t / 0.5 gives contribution two of magnitude than the w trajectory. For reaction (1) of K*’ production, the situation is very different. The x trajectory, in fact, gives the dominant contribution, overriding the higher lying trajectories. The p contribution is small and A2 gives an important contribution only for / t / > 0.4 (GeV/c)2. Interference effects are unimportant for both reactions (1) and (2). For reaction (1) it remains to be understood why the higher-lying trajectory of the p is much less important than the low-lying 7i trajectory. The fact that this is so, may be taken as indication that the p coupling constants are indeed small, as predicted by SU(6). As discussed in sect. 3, if the contribution is small in reaction (l), it must be smaller by a factor of four in reaction (2). That w should dominate in reaction (2) over A2 and 71, is consistent with the relative position of the corresponding trajectories. We are deeply indebted to the operating crews of the CERN proton synchrotron, of the 150 cm British hydrogen bubble chamber, and the constructors of the RF separated beam. We would like to thank the scanning $ Interference effects have been considered. Interference can occur only among the members of the same parity series, and hence, e.g.: 71 cannot interfere with P, P’. p. w.
K*(890) PRODUCTION
581
measuring and computing staffs at each of our laboratories. We are pleased to acknowledge helpful discussions with Dr. R. Armenteros and Professor Ch. Peyrou. REFERENCES [II J. H. Friedman and R. R. Ross. Phys. Rev. Letters 16 (1966) 485: V.P.Trower
and J.R.Ficenec,
Bull. Am. Sot. 11 (1966) 767.
121J. Badier, M. Demoulin. J. Goldberg. B. P. Gregory. C. Pelletier.
A. Rouge. B. Barloutaud, A. Derem. A. Leveque. J. Meyer. P. Schlein, A. Verglas. D. J. Holthuizen. W. Hoogland, J. C. Kluyver and A. G. Tenner. Rapport C .E.A. R-3037 (1966). (I.C.)-Oxford-Rutherford Laboratory Collaboration. [31 Birmingham-Glasgow-London N. Haque et al.. Phys. Letters 14 (1965) 338: RPP/H/3 and RPP/H/29. M. Derrick. T. Fields, D. Griffiths. L. Hyman, R. J. Jabbur. [41 F.Schweingruber, J. Loken, R. Ammar. R. Davis. W.Kropac and J. Mott. to be published. (I.C.)-MUnchen-Oxford-Rutherford Laboratory [51 Birmingham-Glasgow-London Collaboration. D. C. Colley et al., Rutherford Lab. Preprint RPP/H/25 (1967) and Nuovo Cimento 53A (1968) 522. [61 J. D. Jackson. J. T. Donohue. K. Gottfried. R. Keyser and B. E. Y. Svensson, Phys. Rev. 139 (1965) B428. F. Crijns et al.. Phys. Letters 22 (1966) VI Aachen-Berlin-CERN-Collaboration. 533. D. R. 0. Morrison, Phys. Letters 22 (1966) 528. ii; B.Sakita and K. C. Wali, Phys. Rev. 139 (1965) B1355. 1101 J. T.Donohue. Thesis: University of Illinois (1967); Phys. Rev. 163 (1967) 1349. 67-33 (1967). [Ill M. Markytan. CERN/D. Ph.II/Physics 1121 L. Jones. Phys. Rev. 163 (1967) 1523. [I31 J. D. Jackson, Nuovo Cimento 34 (1964) 1644.
K*(a90)
PRODUCTION
INTERACTIONS ABSORPTION
North-Holland
AND
IN
10
GeV/c
COMPARISON
AND.REGGE
Publ. Comp.,
POLE
Amsterdam
K-p WITH
MODELS
M. ADERHOLZ, M. DEUTSCHMANN, E. KEPPEL, G. KRAUS, H. WEBER III Physikalisches Institut der Technischen Hochschule, Aachen U.GENSCH, C.GROTE, S.NOWAK, D.POSE Forschungsstelle ftir Physik Hoher Energien der De-utschen Akademie Wissenschaften zu Berlin: Zeuthen
dev
M. BARDADIN-OTWINOWSKA$ T. A. BYERgt , V. T. COCCONI, E. FLAMINIO~f~, J.D. HANSEN, G. KELLNER, U. KRUSET, M. MARKYTAN tt, D. R. 0. MORRISON, K. ZALEWSKI t-tt CERN, European Organization for Nuclear Research, Geneva D. P. DALLMAN, S. J. GOLDSACK, N. C. MUKHERJEE Physics Department: Imperial College. London A. FROHLICH, W.KlT.TEL, G.OTTER, P.PORTH, LWACEK Institut ftir Hochenergiephysik der dsterreichischen Akademie der Wissenschaften. Vienna Received 28 March 1968
Abstract: K*(890) and K*(1420) resonances are observed in 10 GeV/c K-p interactions. Masses. widths and cross sections are determined. Decay angular distributions and differential cross sections of K*(890) production are compared with the absorption model and Regge pole model. While at lower energies the absorption model predictions are in reasonable agreement with experiment. serious disagreement is observed at 10 GeV/c. Regge pole calculations including exchange of P: P’. T. p. w and A2 trajectories can fit the data but do not explain why 71exchange dominates K*‘(890) production while 0 exchange dominates K*-(890) production.
z
On leave from the University of Warsaw. $$ CERN Fellow from the University of Cambridge. Now at the International Atomic Energy Agency, Vienna. 3$$ Now at Brookhaven National Laboratory. t Now at the Universitv of Illinois. tt CERN Fellow from
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et al.
1. INTRODUCTION In the interaction of kaons with protons, K* resonances at 890 MeV and at around 1420 MeV are frequently observed. The production mechanism of these resonances can be best studied in the three particle final state NK?r, on the basis of cross sections, production and decay angular distributions. For incoming negative kaons above 2 GeV/c results on these channels have been reported at 2.1 (ref. [l]), 2.45 (ref. [l]), 2.64 (ref. [l]), 3.0 (ref. [2]), 3.5 (ref. [3]), 4.1 (ref. [4]), 5.5 (ref. [4]), and 6.0 (ref. [5]) GeV/c. For K*(890), the data usually warrant a detailed investigation, while for K”(1420) the results are in general only qualitative. In the published work it is concluded that most of the experimental facts observed for K*(890) can be described in the framework of the one particle exchange model with absorption, as introduced by Jackson and collaborators [6], when the assumptions are made that the reaction K-p -+ nK*‘(890) is dominated by pion exchange,
while the reaction
K-p -t pK*-(890) is dominated by the exchange of a vector meson. With these assumptions, the model can, in fact, describe at all energies investigated, i.e., up to 6 GeV/c, all the features of the production and decay of the K*‘(890) resonance of reaction (1). For reaction (2) the situation is complicated by the facts that in the model the energy dependence of the cross section for vector meson exchange reactions is in disagreement with experiment and that the vector meson coupling constants are not known. At energies around 3 GeV/c, however, a set of constants can be determined which allow both the production and the decay angular distributions of K*-(890) in reaction (2) to be well described. At 4.1 and 5.5 GeV/c absorption model calculations have given good fits to the decay angular distributions and reasonable fits to the production differential cross sections. As the predictions of the absorption model are strongly energy dependent and since it has been shown [7] that at high energies in pion-proton collisions, the model fails to describe various processes of quasi two-body reactions, it is interesting to investigate K* production for incoming kaon momenta above 6 GeV/c. Here we report on a study of processes in which a nucleon and a K* resonance are produced, based on an analysis of K-p interactions at (10.1 f 0.1) GeV/c, observed in about 200,000 bubble chamber pictures taken at CERN in the 150 cm British hydrogen chamber exposed in a R. F. separated beam. Total and differential cross sections have been determined both for K*(890) and K*(1420). The features of the decay angular distributions have been studied in detail for K*(890). The conclusions concerning the production mechanisms of K*(890) in 10 GeV/c K-p interactions are the following:
K*(890)
569
PRODUCTION
(a) For K*‘(890): The absorption model with pure pion exchange can describe adequately production and decay angular distributions, but predicts a cross section for reaction (1) about four times too large. (b) For K*-(890): The absorption model with a mixture of pseudoscalar and vector (w) exchange can describe some of the features of the decay of the resonance in reaction (2) if an appropriate choice of the vector meson coupling constants is made. With those constants, however, the model predicts a production differential cross section greatly at variance with the experimental one. No set of parameters can produce even approximate agreement with production and decay distributions simultaneously, and hence the model at this energy is inadequate. (c) A Regge-pole calculation including P, P’, n, P, 0 and A2 trajectories can describe most of the features of K*’ and K*- production and decay, but the reasons why the 71trajectory dominates in reaction (1) while the w trajectory dominates in reaction (2) remain to be explained.
2. EXPERIMENTAL
RESULTS
The following channels, events have been studied:
fitted from about 16 000 measured
K-p - pK-no K-P
-
~K:een
(445 events) n-
K-P - pKEtted r Kp-nKr
- +
two-prong
(a)
(183 events) z (250 events) zz (528 events).
(d)
Fig. 1 shows the (K?r) effective mass distributions for the above reactions. For reactions (a) and (d) the events in which the (nucleon + pion) system has an effective mass in the N*+(1236) band (1.12 to 1.34 GeV) were excluded. The production of both K*(890) and K*(1420) is evident in all channels. The (Kn) mass resolution is best in the four-constraint channel (b) and in channel (d), where the K and 7~tracks are directly measured and not obtained by kinematic fitting. The combined (Kr) mass distribution for channels (b) and (d) was fitted with a superposition (without interference) of two Breit-Wigner distributions z$$ and a smooth, hand-drawn background 0 Events with a visible
V” decay have been accepted in a fiducial region of the bubble chamber about twice as long as that chosen for other events. gt It is found in reaction (b) that almost all the Kots observed to decay have a lab momentum greater than 2 GeV/c. In reaction (c). where the K” is identified by kinematic fitting, the number of K” with lab momentum greater than 2 GeV/c is as expected from reaction (b), but there is an excess of events with momentum about 0.4 GeV/c. Hence events giving a fitted K” with lab. momentum less than 2 GeV/c were reassigned to other channels. zts We used the energy dependent Breit-Wigner functions as given by Jackson [13].
M. ADERHOLZ et al.
570
K-pap
K%-
( K”seen
20
> 2
10
‘3 \ In
0
d)
cl
I
B 30K-p+pK”7r-
6 ii
(K’fitted) 250 events
372 events
=20-
lo-
Fig. 1, Effective mass distribution of the (Kn) systems in the reactions K-p - pK% ’ (a). K P- pK’?r- (b) and (c). and K-p-+ nK_n’ (d) at 10.1 GeV/c. For reactions (a) and (d) the events for which the,(pso) and (nn+) systems. respectively. are in the mass region of the N*’ isobar (1.12-1.34 GeV) have been excluded. (see fig. 2). The resulting masses and widths of K*(890) and K*(1420) are presented in table 1. Table 2 gives the cross sections for the production of reactions (1) and (2), as well as for the corresponding reactions with production of K*(1420). AI1 cross sections have been corrected for unseen decay modes. For K*(1420) the assumption was made that the branching ratio for decay into (K?T)and into all other modes is 1 : 1. It can be seen from table 2 that the cross sections for production of K*(890) and K*(1420) at 10 GeV/c are all of the same order of magnitude, between 50 and 90pb, which corresponds to about l/50 of the elastic scattering cross section and about l/350 of the total K-p cross section at the
571
K”(890) PRODUCTION
nKW* AT
0
( N **
excluded)
10 GeV/c
20
1.0
3.0
(Km1 EFF. MASS , GeV Fig. 2. Effective mass distribution of the (Kn) systems in reactions (b) and (d) fitted with two Breit-Wigner curves and the hand-drawn background shown.
Table 1 Mass and widths of K* resonances at 10 GeV/c. Resonance
Mass
Full width
K*(890)
(893 + 4) MeV
( 58 + 7) MeV
K*(1420)
(1423 f- 21) MeV
(175 + 57) MeV
same energy. The cross sections for K*(890) production at 10 GeV/c are one order of magnitude smaller than at 3 GeV/c. Fig. 3 shows a compilation of the production cross sections for reactions (1) and (2) as a function of the incident K- momentum. For reaction (2), K-p - pK*-(890), there exist several data at lower momenta and they appear to be compatible with our point at 10 GeV/c if one assumes [8] a dependence of the cross section, u, on the lab momentum, p, of the type cr = cPmcr, where c and 1yare constants. A fit to the data gives (Y= 2.01 f 0.14. For the reaction K-p - nK *‘(890), too few measurements are available to determine well the energy dependence. A fit to the data gives cy= 1.98kO.37. The solid lines in both figures are the function Q = 8.75 p-2.0. The deviations of the experimental points from the line are not necessarily of a systematic nature, i.e., a ratio of 1 : 1 for the two cross sections, independent of momentum, is quite possible. Obviously, more data are needed for the IX*’ cross section. The ratio of the cross sections for pK*- and nK*’ has some immediate bearing on the exchange mechanism that might be responsible for the production of these systems. For pure 71(or pure p) exchange in both reactions,
M. ADERHOLZ et al.
572
Cross sections for (K-p -
Table 2 K* nucleon) reactions at 10 GeV/c.
Reaction
Cross section (pb)
K*-(890) + p
92 f 9
K*O(890) + n
58 2 10
K*-(1420)
54
+p
K*o(1420) A n
l
13
78 f 14
1
_
K-p--pK*-
4
2
LAB
MOMENTUM
OF
I&JENT
(890)
K-,
6
_
8u)
G*Vlc
Fig. 3. Total cross section for K-p - nK*‘(890) and K-p - pK*-(890) versus the laboratory momentum of the incoming kaon. - ref. [l] . Solid circles, Open square? - ref. [2] . - ref. [3] . Shaded square, - ref. [4] . Open triangles, Shaded triangle, - ref. [5] . Double circle: - This experiment. The solid lines are the function U(p) = 8.75 P2*0.
for instance, this ratio should be 1 :4, a figure incompatible with the experimental results. Fig. 4 shows the differential cross section,’ du/dt, for reactions (1) and (2) at 10 GeV/c. It can be seen that for nK *O, do/dt increases steadily as one moves towards small values of 1t 1, while for pK*- it goes through a
573
K*(890) PRODUCTION
ao01l
00
1
I
0.2
1
1
a4
1
1
0.6
1
1
0.8 It 1 , (GeVk)2
Fig. 4. Differential cross section. do/dt. for the reactions K p - nk“‘(890) (fig. 4a) and K-p -+ pK*-(890) (fig. 4b) at lO.lGeV/c. The dotted lines are predictions of the absorption model, the solid lines predictions of a Regge pole model with the assumptions explained in the text. bending over towards / t 1 = 0. The possimaximum at t / = 0.1 (GeV/c)2, bility that this “bending over” is caused by a loss of events in the first bins due to scanning bias has been investigated, but no indication of such an effect has been found. It is interesting to note that a similar “bending over” seems present also at 4.1 and 5.5 GeV/c (ref. [4]), while at lower energies, in particular in the large statistics experiment at 2.64 GeV/c (ref. [l]), the differential cross section is strongly peaked forwards. The forward peaking of the nK*’ differential cross section is instead observed for all K- momenta investigated. These facts will be discussed in the next section. The slopes, A, of the distributions in fig. 4 have been determined by fitting the data with the expression do/dt = k e-At in the 1t ) range indicated below. The results are: For K*‘(890):
A = (6.3 f 1.0) (GeV/c)-2
for 0.03 < it ) < 0.40 (GeV/c)2
,
For K*-(890):
A = (5.8 f 1.1) (GeV/c)-2
for 0.1
.
< IE 1 < 0.45 (GeV/c)2
574
M. ADERHOLZ et al.
A value of A = (4.8 f 0.5) for K*-(890) has been recently reported at 6 GeV/c (ref. [5]), determined by fitting the distribution up to (tj = 1.0 (GeV/c)3. No significant backwards emission of K* resonances was observed. In fact, the only example of backward production observed was one event in the mass region of the K*O(890). A similar result is reported at 4.1 and 5.5 GeV/c. The values of the spin density matrix elements, pmn, as obtained from maximum likelihood fits to the data are presented in table 3, averaged over : t\ values up to 0.3 (GeV/c)2. Fig. 5 shows the ; t j dependence of the own elements. In these calculations no background subtraction was made.
3. ANALYSIS OF THE K*(890) PRODUCTION MECHANISM WITH THE ABSORPTION MODEL 3.1. The ~~K*~syslern In the framework of the one-particle-exchange model, the production of the K*O(890) resonance in reaction (1) can proceed via the exchange of 71,P, AZ.. . . The forward peaked production angular distribution, as well as the shape of the decay angular distributions are consistent, however, with pseudoscalar (pion) exchange being the dominant process. This assumption has proved satisfactory in all experiments at lower energies, where agreement has been obtained between the experimental results and the predictions obtained using the pion exchange model with absorption as described specifically in ref. [6]. We have used this model at 10 GeV/c to calculate total and differential cross sections, as well as the p mn matrix elements and their j t ( dependence, in order to compare them with the experimental results. The pion coupling constant at the mesonic vertex was G2/4n = 0.75, deduced from the width of the K* resonance and the coupling constant at the baryonic vertex was taken to be G3/4n = 14.6. The absorption constants used were hl = 0.016, h3 = 0.01, C 1 = 0.6 and C3 = 1.0. The theoretical values of Pmn Table 3 The density matrix elements for the channels pK*-(890) and nK*O(890). pK*-(890)
nK*O(890)
Exp.
Exp.
Theory a)
PO0
0.16 f 0.05
0.60 zt 0.09
0.68
Pl> -1
0.33 * 0.05
0.16 i 0.04
0.08
RePlo
-0.03 * 0.05
-0.21 i 0.06
-0.17
a) Pure ?Texchange. The four momentum transfer t is restricted
to ) t\ < 0.3 (GeV/c)2.
K*(890) PRODUCTION
’ KJp+ n K”’ (890)
575
(a)
_ 10 GeWc -------________
REP10
l-
00
(12
a4
1 Q6
I
, 0.8 It1
1.1
J
I
,
(GeVlcl
2
Fig. 5. Dependence of the pmn density matrix elements on the squared four-momentum transfer ,t: . The dotted lines are predictions of the absorption model. the solid lines are predidtions of a Regge pole model with the assumptions explained in the text.
are compared in table 3 with the experimental values. Reasonable agreement is found. The element Poe, which should be unity for pure pion exchange without absorption, is (0.60 f 0.09) experimentally and 0.68 according to the model. The value of p o. at small momentum transfers ( j t / < 0.2 (GeV/c)2) seems to be independent of K- momentum, being (0.68 f 0.07) at 2.64 GeV/c, (0.63 f 0.12) at 5.5 GeV/c and (0.60 f 0.09) at 10 GeV/c. This constancy of the poo element may be interpreted as evidence that the mechanism of K*O production does not change drastically between 2 and 10 GeV/c. The dashed lines in fig. 5a are the calculated t dependence of the Pmn elements. Also here the agreement is reasonable. The calculated differential cross section is the dashed line in fig. 4a. The shape is satisfactorily described, however the absolute value of the cross section is too large by a factor of about four. (In the figure the curve is normalized to the data. ) As at lower energies, no evidence for an appreciable contribution of p-exchange is found at 10 GeV/c, which is of interest since the cross section due to vector meson exchange might be expected to decrease with
576
M. ADERHOLZ
et al.
energy more slowly than the cross section due to pseudoscalar exchange. This fact that at all energies the p exchange contribution to this process is negligible compared with the 7i exchange contribution, is in agreement with SU(6) predictions [9]. In conclusion, at 10 GeV/c, the absorption model with pure pion exchange can describe the main features of both the production and decay angular distributions of the K*O(890) resonance in reaction (l), but it predicts for this reaction a cross section four times too large. 3.2. The pK*- system The production of the K*- resonance in reaction (2) can be mediated not only by the exchange of n, P, A2 as for reaction (l), but also by the exchange of w, 0, as here no exchange of charge is required. Since the (~pp coupling constant is supposed to be very small, the contribution of (Dexchange is expected to be negligible. From isotopic spin consideration, both 71andp exchanges are expected to contribute to reaction (2) with cross sections only i of those contributing to reaction (1). If P exchange is found to be negligible in reactions (l), its contribution must a fortiori be unimportant in reaction (2). It must therefore be anticipated that whatever difference is observed in the experimental distributions for K*’ and K*- must derive from the effects of w exchange. The assumption that reaction (2) is produced by TIand w exchange (and the effects due to the interference of TIand w amplitudes) has produced satisfactory agreement between absorption model calculations and experimental data for all experiments up to 5.5 GeV/c. In particular the experiment at 2.64 GeV/c has indicated [lo] that the 71contribution, limited to small t ; -values, and the w contribution, predominant at large t 1-values, interfere constructively in the small jC j region, creating the strong forward peak observed in the differential cross section at that energy. As remarked in the previous section, the shape of the du/dt distribution at small t-values changes as the K- momentum increases. The observed behaviour is qualitatively consistent with the interpretation that with increasing energy, 71exchange and its interference with the w amplitude become less important and limited to smaller ; t / -values, while the w contribution becomes increasingly dominant over the whole i t j-range. The “bend-over” at small 1tl-values seen above 4 GeV/c is in fact characteristic of an exchange process involving a spin-flip by one unit. The experimental decay angular distribution for K*- is also consistent with vector exchange and so is the low value of thePoo element (0.16 f 0.05), asp.. would be zero for pure w exchange. Actually, the increasing importance of vector meson contribution as the energy increases is clearly indicated by the fact that the value of poo for small values of the four-momentum transfer (1 t ; < 0.2 (GeV/c)2) steadily decreases as the momentum of the incoming kaon increases, being 0.54 f 0.03 at 2.64 GeV/c, 0.34 f 0.08 at 3.0 GeV/c, 0.27 & 0.08 at 4.1 GeV/c, 0.22 f 0.08 at 6.0 GeV/c and 0.17 f 0.07 at 10 GeV/c. We have analysed the data for reaction (2) at 10 GeV/c with the absorption model assuming a mixture of 71and w exchange (and their interference).
K*(890) PRODUCTION
.x7-7
For the pion, the same coupling constants were used as for reacticm@., For W, the coupling constants are unknown. In the analyses reported inidilpe literature, these constants are either calculated [4] from other known coupling constants following theoretical prescriptions based on SU(6) wrnmetries [9], or are left as free parameters to be determined by,maz@imum likelihood fits to one, or all, of the same experimental distributions that one wants to compare with the model. In this latter. approach, which at the present stage of our knowledge seems the safest one, all one can do is investigate whether there exists one set of constants with which all the experimental results obtained at a given energy can be described. Whether these constants vary with energy, and the form of this variation are also important points that can throw light on the value or limitations of the model. Following the terminology of ref. [6], the constants to be determined are 5 and n, defined as:
5=f
(Gv+GT)
and
ZgG
__fGT gG’
where g and G are the pion coupling constants at the mesonic and baryonic vertices, respectively is the vector meson coupling constant at the mesonic vertex, and Gtf and GT are the vector and the tensor coupling constants at the baryonic vertex. To compare our results at 10 GeV/c with the absorption model, we have determined the constants (5, ?I) from maximum likelihood fits to the following experimental distributions and have obtained the following results: (a) From fit to the shape of the do/dt distribution: 5 = 0.2, r] = 0.2. : 5 = 0.4, q = 0.0. (b) From fit to the omn(t) distributions (c) From fit to both distributions simultaneously : 5 = 0.4, n = 0.2. In all cases, the same absorption coefficients as used for reaction (1) were introduced. It has been verified that modification of the absorption parameters, in particular of X2 which is the most arbitrary one [lo], do not change the results appreciably. Our 5 values are thus between 0.4 and 0.2, and our q values between 0.2 and 0.0. A value n = 0 is expected for pure w exchange. Donohue [lo] has made a detailed analysis of the results for reaction (2) at 2.64 GeV/c and 3.0 GeV/c, as well as of the corresponding results with positive incoming kaons. He concluded that values of 5 from 2.2 to 1.4 and of ?I from 2 to 0.5 could describe all experimental results at those energies, the best values for (4,~) at 2.64 GeV/c being (1.8, 1.15) and at 3.0 GeV/c (1.55, 0.95) obtained from fitting do/dt distributions. Fitting both decay and production distributions, the set (0.8, 0.6) was obtained at 3.5 GeV/c. At 6 GeV/c the set (0.6, 0.0) gave correct predictions for the total cross section and the density matrix elements. Fig. 6 shows the variation of 5 and 77as a function of incident K- momentum. Evidently the constants determined at 10 GeV/c differ radically from those determined at around 3 GeV/c, their dependence on the momentum, p, being about p-l. This may be taken as indication that the model, suitable at around 3 GeV/c, cannot be safely extended over a large energy range.
M. ADERHOLZ et al.
578
Fig. 6. Sets of values of the vector coupling constants functions 5 and 17determined at various momenta of the incoming kaon.
Comparison
Table 4 of density matrix elements for reaction (2) with absorption calculations for different values of g. q). 0.30
__-
exp
Pmn
-
0.60 theor 0.13a)
PO0
Pl,-1
Re PI.0
0.27 I 0.08
0.34 -c_0.05
. 0.015
: 0.05
0.34 b)
0.12 b)
I +_ ;.;;.
0.13
I f 0.07
0.07 b)
0.36 c)
0.11 C)
0.06 C)
0.07 a)
0.21 a)
0.30 a)
0.29 b,
0.43 b)
* 8.;;
+ i’;;
0.46 b,
0.22 c)
0.41 C)
0.45 c,
-0.21 a)
-0.14 a)
-0.10 a)
-0.08 b,
; i.;;
-0.13 c)
-0.02 b) -0.04 c)
a) (5.77) = (0.2, 0.2) from fit to do/dt. b) (5.17) = (0.4. 0.0) from fit topmn(t). C) (5.77) = (0.4, 0.2) from fit to do/dtand
p,,(t).
; 8.;;
-0.01 b) -0.02 c)
0.12 f 0.02
0.05b) 0.03c) 0.39a)
0.36 i 0.08
0.47b) 0.42c) -0.05a)
0.025 + 0.07
-O.Olb) -O.OlC)
K*(890) PRODUCTION I
8
K-p -
0.001
0
1
I 0.2
,
K’-
I
I 0.4
0
579
,
J
10 GeVlc
_
,
8
(890) p
I
I 0.6
I
I 0.8
1t I, (GeVlc)2 Fig. 7. Absorption model predictions for da/dt of reaction (2). with different values of 5 andq. Curve a): 5 andq determined from best fits to experimental du/dt. Curve b): 5 andT determined from best fit to the t-dependence of the density matrix elements. p&t). Curve c): 5 and 17determined from simultaneous best fit to d@/‘dt and pm&).
The comparisons of the absorption model predictions with our experimental data using the various sets of (6,~) determined from our fits are shown in table 4 and in fig. 7. It can be seen that with the (5, n) values derived from da/dt, case (a), we obtain unacceptable values of the own elements, and a poor fit to du/dt. This solution is equivalent to assuming a very small vector exchange contribution, which is in contradiction with the experimental evidence of dominance of vector exchange. The other sets of (5,~) values, cases (b) and (c), produce reasonable agreement for the ~00 and Re ~10 elements, very poor agreement for pi-l, and a completely wrong shape for du/dt. The curves dashed in figs. 4b and 5b are calculated with the set (c) of (t , q) values. In conclusion, no choice of coupling constants and of absorption parameters can bring the absorption model, in the form described in ref. [6], to produce predictions in agreement with experiment at 10 GeV/c. It is to be noted that the same conclusion, i.e., the inadequacy of the model in describing processes requiring vector meson exchange at high energies, was reached in a study of several two-body reactions induced by 8 GeV/c collisions of positive pions with protons [7].
58(h
4. REGGE-POLE
M. ADERHOLZ
CALCULATION
et al.
FOR THE PRODUCTION OF K*(890)
Regge-pole calculations have been made in an attempt to interpret the experimental data obtained at 10 GeV/c for reactions (1) and (2). For reaction (1) the r, and
‘t /. The agreement can be considered acceptable, except perhaps for the element Re ~10 for reaction (2). The results of this calculation may be summarized as follows. For the reaction (2) of K*- production, the trajectory that includes w and (Dwith no spin-flip is found to be the dominant one over the : t 1-range up to 0.7, except in the l’ery forward direction (, ti < 0.02 (GeV/c)2), where the 7~trajectory may be more important. An interpretation of why the low-lying r~ trajectory could become dominant in very forward directions has been proposed recently [12]. The trajectory, for the range 0 :t / 0.5 gives contribution two of magnitude than the w trajectory. For reaction (1) of K*’ production, the situation is very different. The x trajectory, in fact, gives the dominant contribution, overriding the higher lying trajectories. The p contribution is small and A2 gives an important contribution only for / t / > 0.4 (GeV/c)2. Interference effects are unimportant for both reactions (1) and (2). For reaction (1) it remains to be understood why the higher-lying trajectory of the p is much less important than the low-lying 7i trajectory. The fact that this is so, may be taken as indication that the p coupling constants are indeed small, as predicted by SU(6). As discussed in sect. 3, if the contribution is small in reaction (l), it must be smaller by a factor of four in reaction (2). That w should dominate in reaction (2) over A2 and 71, is consistent with the relative position of the corresponding trajectories. We are deeply indebted to the operating crews of the CERN proton synchrotron, of the 150 cm British hydrogen bubble chamber, and the constructors of the RF separated beam. We would like to thank the scanning $ Interference effects have been considered. Interference can occur only among the members of the same parity series, and hence, e.g.: 71 cannot interfere with P, P’. p. w.
K*(890) PRODUCTION
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measuring and computing staffs at each of our laboratories. We are pleased to acknowledge helpful discussions with Dr. R. Armenteros and Professor Ch. Peyrou. REFERENCES [II J. H. Friedman and R. R. Ross. Phys. Rev. Letters 16 (1966) 485: V.P.Trower
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