c

Nuclear Physics B86 (1975) 1 3 - 6 2 . North-Holland Publishing Company

THE

REACTION

K- p ~ K- n+ n AT 3.6 GeV/c

N.A. M c C U B B I N * a n d L. L Y O N S

Nuclear Physics Laboratory, Oxford Received 7 June 1974

Abstract: By measuring 121 000 2-prong interactions on the Oxford PEPR, we obtained 9 543 events of the type K - p ~ K-rr+n. The cuts to improve the quality of the data and to reduce ambiguities with other final states are described in detail. Strong signals corresponding to the final states ~ * o (890)n and ~*o (1420)n are observed. The masses and widths of these resonances are determined. The differential cross section for ~*o (890)n is less steep than that for the reaction K+n --, K *° (890)p. The decay of the K - n + system in the 890 MeV region is analysed as a coherent mt~xture of spins 0 + and 1 - , and the density matrix elements extracted, The combination Polo d~/dt' has the sharpest t' dependence. A comparison is made with the reaction K~p ~ K * - (890)p to study the t-channel isospin contributions to the various helicity substates. The K-*r + mass spectrum appears distorted on the low side of the ~*o (1420) at low momentum transfers, thus complicating a study of this region. The ~*o (1420)n final state has a shallower t' dependence than for ~*o (890)n; this is in contrast with KiN data at higher energies. Finally we study the moments of the K-~r + system's decay distribution as a function both of mass and of momentum transfer.

1. Introduction In p r e v i o u s p a p e r s [1, 2 ] we h a v e s t u d i e d various K - p final states at 3.13 to 3.6 G e V / c . Here we p r e s e n t d a t a o n t h e r e a c t i o n K - p --> K - T r + n

(1)

at 3.6 GeV/c, for w h i c h we have 9 543 events. T h e s e were o b t a i n e d f r o m 121 116 m e a s u r e d 2 - p r o n g events; details o f K - p eleastic s c a t t e r i n g events f r o m this sample h a v e already b e e n p u b l i s h e d [2]. T h e d a t a were o b t a i n e d f r o m a 2 0 8 0 0 0 p i c t u r e e x p o s u r e o f t h e C E R N 2 m e t r e h y d r o g e n b u b b l e c h a m b e r to a 3.6 G e V / c e l e c t r o s t a t i c a l l y s e p a r a t e d K - b e a m . Details o f t h e e v e n t m e a s u r e m e n t a n d i o n i s a t i o n e s t i m a t i o n b y t h e O x f o r d a u t o m a t ic m e a s u r i n g m a c h i n e P E P R [3] are given in sect. 2. E v e n t s c o n s i s t e n t w i t h r e a c t i o n * Current address: Physics Department, University of Lancaster, Bailrigg, Lancaster, England.

14

N.A. McCubbin, L. Lyons, K - p -, K-n+n

Table 1 The 2-prong and 4-prong events (i)

(ii) (iii)

Total scanned number of 2 and 4 prong events to be measured Successfully through geometry series of programmes Events giving satisfactory output from kinematics programme

= 154 929 = 120317 = 77.7% of(i) = 114 802 = 95.4% of (ii) = 74.1% of (i)

(iv)

Events to be remeasured [(i) - (ii)]

= 34612

(v)

Events actually remeasured

= 33 492 = 96.8% of (iv)

(vi)

Remeasured events successfully through geometry series of programmes

(vii)

(v)

Remeasured events giving successful output from kinematic programme

Overall failure rate ((ii) - (iii) + (iv) - (vii))

= 27 790 = 80.2% of (iv) = 26 276 = 94.6% of (vi) = 75.9% of (iv) = 13 851 = 8.9% of(i)

(1) often also fit other K - p reactions w i t h 2-charged particles, even after ionisation i n f o r m a t i o n has b e e n used. The procedure for extracting our final K-Tr+n sample is also explained in sect. 2. The main m o t i v a t i o n for studying reaction (1) is that it provides good signals o f the ~ * o (890) and ~ , o (1420). These resonance regions are studied in sections 3 and 4 respectively. We measure the mass and w i d t h o f the resonances. The total and differential cross section for ~ , o (890)n are given, and the K.* ~ K - n + decay in this region is analysed as a c o h e r e n t m i x t u r e o f spins 1 - and 0 +. The g.*°n final state is c o m p a r e d w i t h K * - p and K * ° p . The K* (1420) region is m o r e c o m p l i c a t e d because o f the larger b a c k g r o u n d under the resonance and because o f the higher spins involved. F u r t h e r m o r e , at small m o m e n t u m transfers, the shape o f the K* (1420) appears to be distorted on the low mass side. Finally sect. 5 presents the m o m e n t s o f the K - n + system's decay distribution, as a f u n c t i o n o f mass and o f m o m e n t u m transfer. A list o f previous studies o f the K-Tr+n final state above 1 G e V / c is given in ref.

[41.

15

N.A. McCubbin, L. Lyons, K - p --, K-Tr+n

2. Event processing 2.1. Scanning and measuring

The fdm was scanned twice by conventional techniques for all interactions and for 3-prong decays of the beam K - mesons. Discrepancies between the two scans were re-examined and resolved. The 2-prong and 4-prong events were then measured on the automatic measuring machine PEPR [3]. Events which failed to give a satisfactory geometrical reconstruction were remeasured on conventional measuring machines. The loss of events through the various stages of the processing system is given in table 1. The total loss (including kinematic failures) after remeasurement is 8.9% of the 2-prong + 4-prong sample. Z2. Ionisation Apart from measuring coordinates along a track, PEPR also measures the lacunarity, or fraction of clear track, and from this an estimate of the ionisation can be made. This ionisation information can then be used to distinguish between kinematically acceptable hypotheses. Further details of how the ionisation is estimated from the lacunarity and the subsequent strategy for rejecting hypotheses are given in the appendix. Finally, after the PEPR ionisation information had been used, a further conventional ionisation scan (i.e. by human beings) was performed on those events for which a computer considered that extra ionisation information might be possible and useful. Z 3. Kinematic fitting

The kinematic hypotheses against which our 2-prong events were tested were K - p --" K - p

(a)

K - p -+ K - K + A

(g)

K-.+n

(b)

K-K+Z °

(h)

K-prr °

(c)

K-pMM

(i)

n-pK °

(d)

n-pMM

(j)

rt-n+A

(e)

n-Tr+MM

(k)

rr-n+E °

(f)

K-rr+MM

(1)

(2)

where MM denotes a missing mass above the minimum allowed for the particular reaction (i.e. corresponding to at least 2 unseen neutral particles). For the majority of events, the charged tracks are completely measured and there are 4 constraints available for testing reaction (a), ordy 1 constraint:for reactions (b)

1011 960 592 312 86 207

52 3 6 6 53 0

K-p 33 35 49 53 23 205

K-Prr° 2 38 22 51 21 206

n-PK'° 645 645 561 309 86 207

n-Tr+A 30 599 64 309 86 207

~r-*r+X° 0 9 53 153 86 207

K-K+A 0 5 25 142 64 207

K-K+Z ° 213 307 502 112 6 2

K-pMM

2 272 490 112 5 1

rr-pMM

34 7 4 1 0 0

n-n+MM

In addition to the ambiguous events listed below, there were 1 557 events giving a unique fit to K-n+n. Order n means that the event fitting K-rr+n also gave fits to n other kinematic hypotheses.

Order 1 Order 2 Order 3 Order 4 Order 5 Order 6

Total

Ambiguity matrix for a sample of 4 725 events which survived the fiducial volume and beam momentum cuts ((i) and (ii) of subsect. 2.4)

Table 2 Ambiguity table

z~

F,

17

N,A. McCubbin, L. Lyons, K - p ~ K-rr+n

to (h), and no constraints (just two inequality tests to be satisfied) for each MM reaction. The MM hypotheses were not automatically rejected in events which gave a constrained fit. A lower limit o f 1% on the confidence level o f any fit was imposed at this stage. We are interested here in events giving a fit to reaction (2b), o f which we have 21 557 examples. Ambiguities between this reaction and the others are serious, even after the ionisation information is used. The next two sections describe how an unbiassed sample o f K - r r + n events was obtained. 2.4. F u r t h e r cuts on data

In order to purify our initial K-zr+n candidates, a series o f cuts was imposed on the data. The number o f events removed at each stage is shown in brackets. (i) A fiducial cut was imposed on the interaction position within the bubble chamber for each event (4 948 events). (ii) The beam m o m e n t u m was restricted to the range 3.52 to 3.68 GeV/c (1 366 events). The ambiguity status o f a sample of K-zr+n events after imposing these first two cuts is shown in table 2. 0ii) Any event also giving a satisfactory fit to the highly constrained elastic scattering reaction (2a) was rejected (375 events).

i

80

i

I

I

J

60-

40'

20 ¸

0 0.5

I

I

1-0

1.5

M ( K ' ' n "°)

~

2.0

GcV

Fig. 1. The K - n + mass spectrum for events consistent with the K-Tr+n final state, and having either the K - or ~r+ momentum unmeasured. N is the number of events per 0.02 GeV. The size of the peak at the position of the g*o (890) enables an estimate to be made of the number of true K-~r+n events in this sample.

N.A. McCubbin, L. Lyons, K - p ~ K-lr+n

18

(iv) Any event with its positive prong stopping within the sensitive volume of the chamber was rejected; such events are essentially all elastic scatters which failed to fit the relevant kinematic hypothesis (610 events). (v) The lower limit on the confidence level for the K-~r+n hypothesis was raised from 1% tO5% (1079). (vi) Finally, we consider those events in which the momentum of one of the outgoing prongs was unmeasurable (0-C events). Many of these were caused by PEPR failing to recognise the complete length of the prong e.g. because of scratches on the fdm, confusion caused by other tracks, illumination problems, etc. and these are essentially unbiassed from a kinematic point of view. Other problems (e.g. slow dipping tracks, or fast tracks roughly parallel to other beam tracks) may involve some degree of bias. i

I

i

(GeVl¢) 4 J

I

3

"IT- momentum t

p MM area

•

\

I l°nisati°nusefut

d

\

....~iijiiJiiiii::ii9 ~siii2iiii

'

\

\

IT-IT* A Line

0

IonisatiOnusetul

I

1

\ \

2

K- momentum ~

3

GeVl¢

Fig. 2. The ambiguity plot for the K - l r + n final state. The outer curve is the kinematic b o u n d a r y for the K - n + n final state. The solid diagonal line is the line of intrinsic ambiguity with the lr-~r+A final state; the two dashed lines close to it show h o w the ambiguity line moves when the negative track's m o m e n t u m is changed by ± 1%. The shaded area d.efines the region allowed also for the K - p M M final state. Below 1.5 GeV/c, ionisation m a y be used to distinguish whether the positive track is a n + or a proton.

N.A. McCubbin, L. Lyons, K-p ~ K-n*n

19

The K - n + mass spectrum for a sample of these 0-C events is shown in fig. 1. There certainly is a g . o (890) signal which must come from either K-zr+n or K-Tr+MM final states. However, comparing the shape o f this mass spectrum with that of fig. 7 (the final sample of K-rr+n events) we see that these 0-C events are not typical of the K-rr+n final state. This is not surprising since it is impossible to perform a constrained check on any of the reactions 2(b) - 2(1), and hence these events are often consistent with a large number of these reactions. Thus, to avoid accepting a large number of spurious fits to the K-Tr+n hypothesis, these events were rejected (3 059 events). Comparing the K* (890) signals in fig. 1, in fig. 7 and in the K-n+pTr - final state (not shown), we estimate that 530 + 120 of the 0-C events are genuine K-rr+n events. This number was included in the final corrected number of K-lr+n events for the determination of the reaction cross section (see subsect. 2.6). After applying cuts (i) to (vi), we are left with 11 120 K-rr+n candidates.

2.5. Ambiguity problems The ambiguity problem after cuts (i) and (ii) of subsect. 2.4 has been summarised in table 2, and is still serious after all subsequent cuts. The main final states which have large ambiguities with K - n + n are 7r-n+A and K-pMM.

2.5.1. Ambiguity plot Before discussing our method of dealing with these ambiguities, it is instructive to examine a scatter diagram of the laboratory momenta of the two charged tracks plotted against each other. The usefulness o f this plot for 2-prong events is as follows. In fitting a well measured event to different hypotheses, the momentum vectors of the charged tracks are altered but little from their measured values. The momentum of the neutral particle is determined simply from momentum conservation. Then energy conservation can be used to see whether the particular mass assignments of the given hypothesis are consistent with the now known energies (E = V ~ + m 2) of the individual tracks. Since the energies depend only on the scalar momenta (and not on the angles) of the tracks, the scatter plot of the charged tracks' momenta is particularly suited to studying ambiguity problems in 2-prong events. The kinematic boundary of this scatter plot for the K-zr+n events is shown in fig. 2. Also shown as a solid line are those momenta for which, if we interpret the tracks as n - and n + (instead of K - and n +) then the missing mass is equal to that of the A (rather than that of the neutron) i.e. along this line there is an unavoidable ambiguity between the K-zr+n and 7r-Tr+A final states. The dashed lines close to the solid one show how the ambiguity line moves when the momentum of the negative track is changed by +1%. The region between the dashed lines is thus a crude estimate o f the ambiguity region expected, when allowance is made for the finite measurement accuracy on one of the momenta. In practice, the errors on the angles and

20

.

N.A. McCubbin, L. Lyons, K - p ~ K-lr+ n

4,

(a)

l(b)

°

Oj

@~ X: .

K-

MOM°

2o Y:

P~+

4 PiON~

E

~3. X,K

2. MOM. Y.PT+ MgM,

I

(¢)

~ % ....

: i~:!~,~

•

.

.

.

0. XiK-

.

.

.

i

.

~. MOM. Y i P I +

.

.

.

MOM.

Fig. 3. Actual ambiguity plots foi (a) unique events; (b) events ambiguous between K-~r+n and ~r-~r+A; and (c) events ambiguous between K-~r+n and K-pMM. The events are plotl;ed assuming the K-~r+n hypothesis, with K momentum along the x axis and 7r+ momentum 4. alongy. Momenta are measured in GeV/c.

on the other momenta will of course enlarge the ambiguity region. Clearly improved measurement accuracy would cut down the ambiguity region and hence the fraction o f ambiguous events. It is to be noted that ionisation measurements do little to reduce this ambiguity problem, since the positive track is a n + in b o t h hypotheses, and the negative one in general has a momentum above 0.8 GeV/c, in which region the ionisations of 7r- and K - are similar. The shaded area o f fig. 2 is the ambiguity region for K - n + n with the K - p M M final state. (The region is now an area rather than a line as the MM has a variable mass. This implies that even events measured with infinite accuracy would still be ambiguous in this region). Now ionisation is of some help as below a positive track

N.A. McCubbin, L. Lyons, K-p ~ K-rr+n

21

momentum of ~ 1.5 GeV/c, the 7r+ may be distinguishable from the final state proton. The ambiguity regions on this plot for other final states can also be found, sometimes with difficulty. In fig. 3, we show the actual scatter plots of (a) events giving a unique fit to K - n + n ; (b) events ambiguous with lr-Tr+A, and (c) events ambiguous with K-pMM. It is seen that the ambiguous events fall in approximately the regions mentioned above. (Events ambiguous with the n-n+A hypothesis in general lie to the right of the ambiguity line of fig. 2; this is related to the fact that the reaction dynamics causes events to congregate along the upper kinematic boundary.) A corollary of this is that for the unique sample there is a serious depletion of events in various regions (see fig. 3(a)), and so these unique events are certainly a biassed sample of the K - n + n final state. It is thus necessary to consider in detail how to deal with the ambiguous events. 2.5.2. Ambiguities with MM hypotheses Of the events surviving the cuts o f subsect. 2.4, 15% are ambiguous with MM hypotheses only. The K - n + mass spectrum of these events is shown in fig. 4. This looks very similar to the corresponding spectrum of the final sample (see fig. 7), and with its dominant production of K* (890) and K.* (1420) is strongly suggestive that in these ambiguous events, the charged tracks are in fact K - and rr+ and hence that the correct hypothesis is indeed K-lr+n. Further evidence that these events are indeed K-Tr+n is that they fill (without overfdling) a large gap in the ambiguity scatter plot of fig. 3(a). In addition we have estimated the cross sections for K-pMM, n-n+MM and

150

t

l

l

l

i

l

J

l

l

l

=

l

l

l

100.

50'

0 0-5

"f"-J

0.7

~ '

0.9

I

'

1-1

M ( K'/I"

°

'3

1-

)

~ " 1.7 '

1.5

1-9

Gcv

Fig. 4. The K-n + mass spectrum for events ambiguous between K-~r+n and multineutral final states. N is the number of events per 0.03 GeV. The dominant ~*o signals are strongly suggestive that the vast majority of these events are really K-~r+n.

N.A. McCubbin, L. Lyons, K - p ~ K-*r+n

22

7r-pMM as being 1-1.5 mb each [6]. As the K-Tr+n cross section is ~ 1.5 mb (see subsect. 2.6), there is no over-riding reason for supposing that these events should be considered as MM hypotheses. Thus we conclude that the 1 461 events which are ambiguous with only MM hypotheses should be included in the K-~r+n sample. For those events giving fits to K-Tr+n, MM hypotheses and to other hypotheses with only one missing neutral, the MM hypotheses are ignored and the events treated as described in subsect. 2.5.3. Our procedure of rejecting MM hypotheses in the presence of other reactions is equivalent to selecting the hypothesis of the higher constraint class.

2.5.3. Ambiguities with other constrained hypotheses At this early stage nearly 50% of the K-Tr+n fits are still ambiguous with at least one other constrained hypothesis, and almost all of these contain the 7r-~r+A combination. It is the K-rr+n/Tr-lr+A ambiguity on which we now concentrate. The cross section for the 7r-Tr+A final state is well determined from events with visible A decays. We estimate that at our momentum the cross section for ~r-~r+A (with unseen A) is 0.2 mb [6], compared with 1.5 mb for K-Ir+n. We cannot cor. rectly assign all the ambiguous events as K-Tr+n, however, since this would result in insufficient Ir-Tr+A events to give the correct rr-lr+A cross section. For this sample of events, examination of the K - n + mass spectrum (for the events considered as K-Tr+n) shows strong K* (890) production, but the 7r+A mass spectrum (for the same events but now considered as ~r-~r+A) shows some evidence of Y* (1385) production. Since the kinematic constraint imposed by the existence Of a K* (890) in the mass spectrum of the positive and negative tracks does not

i

150

I

I

I

=

I

i

I

J

100-

50-

0-0

20.10

40.0

60.10

80~0

CONFIDENCE LEVEL(IN PER CENT)

100.0 >

Fig. 5. D i s t r i b u t i o n in c o n f i d e n c e level o f t h e k i n e m a t i c fit to the K - ~ r + n h y p o t h e s i s for our final s a m p l e o f 9 5 4 3 events. N is t h e n u m b e r e v e n t s for 1%.

N.A. McCubbin, L. Lyons, K - p ~ K-rr+n

23

restrict the zr+A° mass to the region of the Y*, this is further evidence that this sample of events is a mixture o f largely K-rr+n but also some rr-rr+A. We have investigated the effect o f various selection criteria on these ambiguous events. We found it useful to examine in each case the spectra of the difference in fitted and measured momenta of the negative track (i.e. two spectra, considering the negative track first as a K - and then as a zr-), and also the above mentioned K-Tr + and zr+A mass spectra. We finally conclude that the optimum separation is provided by the following prescription: events are rejected from the K-Tr+n sample if the confidence level for any other fit is more than twice that o f the K-zr+n fit; otherwise events are accepted. This rejects a further 577 events, leaving us with a final K-zr+n sample of 9 543 events. The histogram of the K-rr+n hypothesis confidence level for these 9 543 events is shown in fig. 5, and is reassuringly flat,

2.6. Cross section We estimate the cross section for the K-rr+n final state on the basis of the 9 543 events of our final sample, the total number of observed interactions in the same amount of fdm, and a total K - p cross section [7] of 26.3 -+ 0.3 mb*. It is necessary, however, to perform several corrections. W1t-p

3,,,, O"

t K-cr+n

!

(rob)

I

0.~

0.1

3 P inc (~Vlc)

10 >

Fig. 6. The cross sections for the reactions K - p ~ K-~r+n and K+n ~ K+Tr-p above 1 GeV/c as a function o f m o m e n t u m . The K+n data have n o t been corrected for deuterium effects in the target. * Our own estimate of this cross section, based on the observed n u m b e r of events (corrected as m e n t i o n e d in the text), the density o f the hydrogen and the estimate of the beam flux from their observed 3-prong decays is 27.8 -+ 1.3 mb.

24

N.A. McCubbin, L. Lyons, K-p --, K-lr+n

(i) Although we have scanned the film for all types of interactions (except for 0-prong events without associated V°s), essentially only the 2-prong and 4-prong events have been measured and computed. Thus in order to compare the K-rr+n events with the total number, it is necessary to reduce the total scanned number for (a) those that would have failed the fiducial volume and beam momentum cuts (see subsect. 2.4, (i) and (ii)) and (b) failures in the geometry and kinematic systems of programmes. Both these factors were estimated from the measured 2 and 4 prong sample of events. (ii) We lose elastic scattering events which occur at small momentum transfer and in unfavourable azimuths. This is described in detail in ref. [2]. (iii) We use data on the 0-prong + V ° events [8] to correct for the unseen 0-prong without V ° events. (iv) There is a 5% confidence level lower limit for the K-lr+n hypothesis. (v) There are some genuine K-rr+n events among the 0-C events. (See subsect. 2.4). (vi) At the scanning stage, we reject from the 2-prong sample events in which there is a decay on a prong before it turns through 8 °. We estimate that this removes 2% of the K-lr+n events. With all these corrections taken into account, our final estimate of the K-rr+n cross section at 3.6 GeV/c is o = 1.5 +- 0.2 m b ,

(3)

where the error includes our uncertainty in the assignment of ambiguous events. Our cross section is shown in fig. 6 together with other data [4] above 1 GeV/c beam momentum. Also shown there are data [9] on the reaction K+n + K + n - p .

(4)

The cross sections for reaction (4) are uncorrected for effects resulting from the deuterium target, which could increase these values by ~ 10%.

3. The K - it* system in the 890 MeV region 3.1. Mass and width o f the ~ , o (890) The K-Tr + mass spectrum for the 9 543 events of our final sample is shown in fig. 7. Clearly prominent are the g,* (890) and the K.* (1420); the latter is considered in sect. 4. We have fitted the mass spectrum of fig. 7 in the region of the ~ , o (890) resonance by a form do dm

1-

PMom

- A [ (m 2 _ M02)2 + F2M2

]

+ B + Cm 2J

,

(5)

N.A. McCubbin, L. Lyons, K - p --, K-n+n

1000

t

1

i

I

J

I

i

I

I

I

i

25

I

t

I

BOO"

600

400.

200-

O"

0.5

0.7

0-9

1.1

1.3

M (K-fr ° )

1.5 ~

1.7

1.9

GeV

Fig. 7. The K-*r + mass spectrum from our final sample. N is the n u m b e r of events per 0.02 GeV.

Table 3 Results o f fitting K - n + mass spectrum in region o f K* (890) Mass range (GeV)

No. of bins

.,kro (MeV)

F (MeV)

F" (MeV)

No o f g,* events

x2

0.75-1.05 0.75-1.05 0.8 - 1 . 0 0.8 - 1 . 0 0.7 - 1 . 1 0.7 - 1 . 1

50 100 35 70 65 100

895.6 895.5 895.1 895.1 895.8 895.7

46.9 46.8 49.1 49.0 49.0 49.1

49.5 49.1 52.0 52.1 50.8 50.5

3416 3421 3608 3590 3563 3551

53.8 95.7 33.0 73.7 91.2 113.5

The errors o n M o are typically 0.6 MeV and on I" are 1.8 MeV. T h e c o l u m n I" refers to the fats performed with no a c c o u n t taken of the experimental resolution. T h e c o l u m n s Mo, r , No. o f K* events and x 2 all refer to fits with experimental resolution folded in. In calculating the n u m b e r o f K* events, allowance has been m a d e for events in the tails o f the g,* outside the given mass range.

26

N.A. McCubbin, L. Lyons, K - p ~ K-~r+n

where: m is the K-•r + effective mass, M o and P are the mass and width of the ~ . o (890), A is a normalisation constant, B and C are paramaters defining the non-resonant background. Fits were performed for various K-Tr+ mass ranges and bin sizes, and also with allowance for and with neglect of the experimental mass resolution. The results of these fits are summarised in table 3. We have also performed fits with a mass dependent width, and found no significant differences in the fitted parameters from the fixed width case. Allowing for the different answers obtained from the various fits, we deduce that our best estimate of the mass and width of the neutral K.* (890) are

K-p K"n

3n'd)"

Wnb

IO.3mb or 100/Jb-

30JJb

10 p,t

3

10

Pinc'

(C~Wc) Fig. 8. The cross sections as a function of incident momentum for the line-reversed reactions K-p ~ ~*o (890)n and K+n ~ K*° (890)p. Again the K+n data are uncorrected for deuterium effects.

N.A. McCubbin, L. Lyons, K --~ K-rr+n M o = 895.5 - 1.0 MeV, I"

27 (6)

= 48_+3 MeV .

These c o m p a r e w i t h the values given in ref. [5] of M o = 896.6 -+ 0.7 M e V , I~ =

51.7+-I.0MeV.

Our mass resolution calculated for events in the g.* (890) region is a b o u t 5 MeV (o o f Gaussian distribution). A l t h o u g h this is only 10% o f the K* width, it has the effect o f decreasing the value o f F b y 2-3 MeV (See table 3). Our estimate o f [' is 4 MeV b e l o w the world average o f ref. [5]; m o s t o f the experiments included in that average have n o t allowed for experimental resolution.

3.2. k *° (890)n production cross section Table 3 also shows estimates o f the total n u m b e r o f g . o (890) events. Taking into a c c o u n t n o t only the statistical errors in each fit but also the spread o f values for the different fits, we estimate that there are 3 500 -+ 150 g : o (890) events corre-

Table 4 K*°(890)n differential cross section

t' (GeV/c) 2

da/dt (mb/(GeV/c) 2)

0 -0.01 0.01-0.02 0.02-0.03 0.03-0.04 0.04-0.05 0 -0.05 0.05-0.1 0.1 -0.2 0.2 -0.3 0.3 -0.4 0.4 -0.55 0.55-0.7 0.7 -0.85 0.85-1.0 1.0 -1.2 1.2 -1.5 1.5 -2.0

3.125 2.770 3.173 2.748 2.841 2.942 2.424 1.660 1.025 0.587 0.432 0.259 0.154 0.141 0.083 0.046 0.029

-+ 0.36 -+ 0.33 -+ 0.36 +- 0.33 -+ 0.33 +- 0.24 ~ 0.24 -+ 0.12 -+ 0.10 -+ 0.07 -+ 0.05 ± 0.03 -+ 0.02 -+ 0.02 -+ 0.015 -+ 0.008 -+ 0.005

The cross sections, derived from fitting the mass spectra of fig. 9, are corrected for the tails of the Breit-Wigner, and for the unseen g~°~r° decay mode. The errors on the cross section arise from the statistical errors on the fits, but do not include the 12% overall normalis/ltion error.

N.A. McCubbin, L. Lyons, K - p --*K-~r+n

28

80

200 > L,' L9 ("4

> Ld LD 04 \

~ee

\ o9 iz Ld > Ld

z t~ > b2

I ,@ (KAPI) MASS:

1.5 T'<0.05

2.@

> Ld

04

C,,I

~\

lo0

1 .5

MASS;

0.3
KAPI)

1.0 MASS;

1.5 0.4
KAPI)

MASS;

0.55
.0 MASS:

1.5 0.7
2.'0

4e

z IM > bJ

0

0 0.5

1 .0 KAPI)

MASS;

1 .5

2.'0

J

0.5

@.05
2,0

5@-

200 > Ld L9 ('4

> LE L9 04 \ CO I'Z LE :> LL.'

1 .0 KAPI)

BO

2e0

d

@ 0.5

> LC L?,,

\ co tz LC > ,L"

40

Q

~

100

\ 09 i--.z b2 > b2

25

0

1 .0

0.5

KAPI)

MASS;

1.5

2.'0

.0

0.S

0.1
1 .5

2.'0

40-

150 > LC t.b

:>. LC Lb 04

~ \

75

\ 60 I.-Z Ld :> I1'

z w k2

i 0.5 (KAPI)

.0 MASS;

I .5 0.2
2.0

0 0.5 (KAPI)

Fig. 9.

2.0

N.A. McCubbin, L. Lyons, K - p --, K-rr+n

29

30 > W DJ \ cO I--Z kd W

30 0.5

KAPI)

30

1 .0 MASS;

1.5 0.85
Z.'@

> Ld

2>

~\

~5

cO

~4

Z W > W

\ o9 I-Z Ld > Ld

8.5

o 0,5 KAPI)

1 .0 MASS;

1 .5 1.8
z'.0

30-

KAPI)

1 .0 MASS;

1 .5 2.0
2,'0

30 > t.d ('4 t~

> Ld L~

bZ W > W

\ o') bZ W > W

i

0.5

1.0 (KAPI)

/1 ,

0.5 KAPI)

1.8 MASS;

1 o5 1.2
1.5 MASS;

2.0

T'>3,0

2.'0

30 > W

\ o9 I--Z > W

0.5

1.0

(KAPI)

MASS: +

1.5

2 .' 0

1.5
Fig. 9. The K-lr mass spectra (in GeV) for various ranges of the modified m o m e n t u m transfer t' (specified in (GeV/c) 2 under each diagram).

N.A. McCubbin, L. Lyons, K - p -+ K-rr+n

30

5-0

I

I

i

i

I

i

i

I

I

I

(a)

I

I

L

i

I

I

=

=

t

5.0

T do" dt'

1-0"

c~\

( m b l ( G c V l c ) =)

0.1

0.01 0-0

0.5

1-0 t'

I .5

2-0

(GcVlc) =

IOO0-

(b)

N = No. of events per0.1(GeVIc} Z - f o r m= 0.75 -1.05 GeV

I00

I

10

olB

t' (GcVIc)2

Fig. 10.

i

i

N.A. McCubbin, L. Lyons, K - p ~ K-~r+n

31

(C)

K" n

K-p

1 B IGeV/c] -2

0

J

2

i

|

|

t+

Pinc

i

|

i

11

10

(GeY/c)

20

----

Fig. 10. (a) The differential cross section for the ~ * o (890)n final state. The inset is for the very

small t' region. The curve A is the fit o f expression (9) to the data. Curve B is the pion propa+ 2 --2 • . gator t(t m~) , arbitrarily normalised. The dashed line C is a hand drawn curve through the 4.6 GeV/c KTn ~ K * ° (890)p data o f ref. [9d]; the normalisation is again arbitrary. (b) The differential cross section of the background under the ~ * o (890). This is plotted as the number o f background events per 0.1 (GeV/c) 2 in t' for the mass region 0.75 to 1.05 GeV in M(K-1r+). (c) The slope parameter B obtained from fitting the differential cross sections for reactions (7) and (8) by the form (12).

sponding to a cross section of 553 -+ 75/ab for the K-Tr + decay mode, and hence that the cross section for K - p -+ ~ . o (890)n,

~ . o (890) -+ K - n + or K.°rr°

(7)

is 830 -+ 110 ttb. In fig. 8 we show thi~ value, together with others at neighbouring momenta [4]. Also shown on fig. 8 are the cross sections [9] for the line-reversed reaction K+n -+ K *° (890)p,

K *° (890) ~ K+lr - or K°rr ° .

(8)

Given the scatter of individual data points for each reaction, there is little evidence at present for any difference between the cross sections for reactions (7) and (8), (although an upward correction of ~ 10% should be included in the cross sections for reaction (8) to allow for deuterium effects). 3.3. K. *° (890)n differential cross section To determine the differential cross section for neutral K.* (890) production, the K-rr + mass spectrum was fitted (as described in subsect. 3.2) for various ranges o f t'.

32

N.A. McCubbin, L. Lyons, K-p --, K-Tr+n

here t is defined by t' = 2PlP2 (1 -- cos c0, where Pl and P2 are the magnitudes of the 3-momentum vectors of the initial state proton and final state neutron respectively, both evaluated in the c.m. system, and is the angle between them. The K-rr + mass spectra in various t' ranges are shown in fig. 9. The number of resonant events in each t' region was used to deduce the differential cross section, which is presented in table 4 and shown in fig. 10(a). The curve B is the pion propagator t(t + m2) - 2 , arbitrarily normalised. A fit of the form do dt---~=A exp ( - B t ' + C t '2)

(9)

for t' less than 2 (GeWc) 2 yields B = 4.9 + 0.2 (GeV/c) -2 , (10) C = 1.3 +- 0.1 (GeV/c) -4 . Alternatively, with C set equal to zero, for the range of t' up to 0.4 (GeV/c) 2, we obtain A = 3.35 + 0.17 mb/(GeV/c) 2 , (11) B =4.8

-+0.3 (GeV/c) -2 .

Our value of B is shown, together with values at other momenta for this reaction and for reaction (8), in fig. 10(c). (The straight line there has a gradient corresponding to the shrinkage expected from the exchange of a Regge trajectory with gradient a' of 1 (GeV/c) -2.) Despite the fact that the values of B should be treated with some caution (since the identical procedures and t' ranges have not been used in the different experiments), it is clear that the K+n data has a sharper t' dependence. This is similar to the fact that at 3 GeV/c, of the two reactions K + N -~ K*(890)A(1238), it is the K + induced one which has the sharper t' dependence. (See fig. 6 of ref. [15].) The mass spectra of fig. 9 can also be used to deduce the number of background events (for the mass range 0.75 to 1.05 GeV) in each t' bin. This is Plotted in fig. 10(b), and is seen to be sharper than the resonant differential cross section: A fit of the form A exp ( - B t ' ) ,

(12)

for t' less than 0.3 (GeV/c) 2 gives B = 11.2 + 0.5 (GeV/c) - 2 .

(13)

N.A. McCubbin, L. Lyons, K - p ~ K-lr+n

33

3.4. F,* (890) density matrix elements In order to study the density matrix elements for the production of the K,* (890) resonance, we define the usual Gottfried-Jackson (t-channel helicity) and s-channel 120

i

I

i

I

i

I

'

I

,

I

'

80-.

40.

'0 -I

i 0

I -0.5

0.0

cos

120

,

I

I

0.5

1

8~

I

,

I

,

t

t

I

(b) 80-

i 40 i.J

I

-1.0

'

-0.5 cos

I

0.0 e:/

I

0-5

1-0

Fig. 11. The distribution in the cosine o f the decay angle in the J system (cos 0J). (a) For events in the ~ * o region defined as 846 to 946 MeV; and (b) for the events in (a) b u t with the background (796 to 846 and 946 to 996 MeV) subtracted. Even in (b), the forward-backward asymm e t r y is apparent.

34

N.A. ~ ' ~ ' ~ ' ~ "

L. Lyons, K - p ~ K-Tr+n

(a)

I

=

(b)

I

I

I

,

I

,

200 -

100 -

B

_

0 .0

1-5

2.0

1 .5

2.5 1.0 M (nw-)

2.11

2.5

GcV

Fig. 12. The n~r+ mass spectrum (a) for all events; and (b) for events in the ~ * o (890) region. N is the n u m b e r of events per 0.02 GeV. F r o m (b) it is clear that there is little interference between the ~ * o (890) and the zx+ (1238).

1'0.6A

I I

0.4

H-

0.2

0-0

-0.2 0.5

t

+

I

' Io?s' M(K-n')

'

1~1

'

---=,

GcV

I 1.3

Fig. 13. T h e a s y m m e t r y parameter A (defined in eq (14)) as a function of the mass of the K - n + system. The dashed vertical lines denote the masses M -+ r , where M and I~ are the mass and width of the ~ * o (890).

N.A. McCubbin, L. Lyons, K - p --, K-Tr+n

35

helicity systems. These are referred to as the J and the H systems, respectively. Both systems are defined in the rest frame o f the K* (890) resonance, so, in this frame, the initial state K - and proton and final state neutron momentum-vectors lie in a plane. F o r b o t h systems we then define a c o m m o n y axis normal to this plane, but for the J frame the z (quantisation) axis is taken along the direction o f the incident K - (i.e. antiparallel to the direction o f the t-channel exchange), whilst for the H system the z axis is antiparallel to the neutron's momentum. We then define spherical polar angles* 0J~bJoH~bH specifying the direction of the K - decay product. If the events in the g,* (890) region are a non-interfering mixture o f £ = 0 background and £ = 1 resonance, then the distribution in 0 J or OH must be symmetric**. Fig. 1 l(a) shows the cos 0 J distribution for events with m ( K - n +) in the range 0.846 GeV to 0.946 GeV. It is clearly not symmetric. Two possible explanations o f this asymmetry are: (i) Perhaps the background cannot be simply parametrised as £ = 0, and it is the background alone which produces the asymmetry. We have investigated this possibility by examining the cos 0 J distributions for the mass region 0.796 to 0.846 and 0.946 to 0.996 GeV. They are both fiat, and consequently, when we use these distributions to subtract the background in the region 0.846 to 0.946 GeV, the asymmetry persists. (fig. 11 (b)). 0i) The asymmetry could be due to kinematic reflections and/or interference caused by A + (1238) production. Fig. 12 however, shows that there is no evidence for any strong A + (1238) production in the K.* (890) region, and so this possibility can be ruled out too. We thus conclude that the asymmetry is an intrinsic property o f the K - n + system, a view which is further supported by the behaviour of the asymmetry parameter, A , as a function o f K - r r + mass (fig. 13). A is defined by A

F-B F + B'

(14)

where F(B) is the number o f events with cos 0 J greater (smaller) than zero. Consequently we parametrise the resonance region as an interfering mixture o f = 0 background and £ = 1 resonance. Similar effects have been observed for reaction (7) at 3.9 and 4.6 GeV/c [4h], and for reaction (8) [9d]. This parametrisation leads to a decay distribution*** o f the form: * We use superscript J and H to denote angles, density matrix dements and cross sections (see eq. (19)) in the J and H frames respectively. ** For a system decaying to two spin 0 particles, this symmetry is independent of any parity consideration in production or decay, and also holds for any choice ofz axis. *** Eq. (15) is sometimes written without eo and el. Care should thus be excercised in comparing density matrix elements from different experiments.

No. of events

308 292 451 331 260 183 159 115 94 81 72 64 92 63 59 41

t'range (GeV/c) 2

0 -0.025 0.025-0.05 0.05 -0.1 0.1 - 0 . 1 5 0.15 - 0 . 2 0.2 - 0 . 2 5 0.25 - 0 . 3 0.3 -0.35 0.35 - 0 . 4 0.4 - 0 . 4 5 0.45 - 0 . 5 0.5 - 0 . 5 5 0.55 - 0 . 6 5 0.65 - 0 . 7 5 0.75 - 0 . 8 5 0.85 - 0 . 9 5

0.427 0.511 0.537 0.462 0.340 0.210 0.282 0.287 0.035 -0.095 -0.067 -0.029 0.058 -0.}06 0.173 -0.061

-+ 0.063 ± 0.068 ± 0.055 ± 0.065 ± 0.072 ± 0.089 -+ 0.096 ± 0.112 ± 0.120 ± 0.135 ± 0.134 ± 0.129 ± 0.130 ± 0.147 ± 0.149 ± 0.154

el (Poo_P 11)J

2

-0.010 -0.052 0.034 -0.013 -0.024 -0.078 -0.023

0.026

-0.111 -0.096 -0.114 -0.133 -0.105 -0.048 ~0.107 -0.048

0.029 0.028 0.021 0.024 0.027 0.031 0.035 0.043 ± 0.045 ± 0.043 ± 0.048 ± 0.052 ± 0.043 ± 0.046 ± 0.051 ± 0.069

± ± ± ± ± ± ± ±

e2Re(plo)J

Table 5(a) g . o (890) density matrix dements in the Gottfried-Jackson frame

-0.061 0.024 0.046 0.096 0.108 0.075 0.113 0.131 0.171 0.275 0.258 0.169 0.159 0.260 0.151 0.249

+- 0.031 ± 0.032 ± 0.025 ± 0.029 ± 0.034 ± 0.045 -+ 0.046 ± 0.055 ± 0.060 ± 0.068 ± 0.074 ± 0.081 ± 0.064 ± 0.075 ± 0.077 ± 0.081

elPi-12 J

0.211 0.159 0.157 0.100 0.058 0.125 -0.025 0.064 0.048 0.031 -0.119 -0.001 -0.124 -0.168 0.023 -0.017

+- 0.031 ± 0.034 ± 0.027 ± 0.032 ± 0.035 ± 0.039 ± 0.044 ± 0.052 ± 0.052 ± 0.054 ± 0.056 -+ 0.062 ± 0.052 ± 0.057 ± 0.070 +- 0.077

eoel Re(pint)J

-0.059 -0.021 -0.042 -0.046 -0.053 -0.009 0.030 -0.031 0.038 -0.078 -0.050 -0.073 -0.015 0.050 -0.087 -0.067

-+ 0.019 ± 0.018 ± 0.014 ± 0.016 ± 0.019 ± 0.024 ± 0.024 ± 0.028 ± 0.032 ± 0.032 ± 0.035 ± 0.039 ± 0.033 ± 0.038 ± 0.039 ± 0.046

eOel Re(~oliont)J

I

I

$

O

0 -0.025 0.025-0.05 0.05 -0.1 0.1 - 0 . 1 5 0.15 - 0 . 2 0.2 - 0 . 2 5 0.25 - 0 . 3 0.3 -0.35 0.35 - 0 . 4 0.4 -0.45 0.45 - 0 . 5 0.5 - 0 . 5 5 0.55 - 0 . 6 5 0.65 -0.75 0.75 -0.85 0.85 -0.95

(GeV/c) 2

t' range

0.477 0.448 0.313 0.113 -0.051 -0.119 -0.175 -0.297 -0.285 -0.353 -0.355 -0.222 -0.279 -0.347 -0.367 -0.358

-+ 0.064 -+ 0.067 -+ 0.052 -+ 0.060 ± 0.067 ± 0.077 -+ 0.080 ± 0.088 ± 0.097 ± 0.103 ± 0.111 ± 0.140 ± 0.105 ± 0.122 ± 0.123 ± 0.132

e] (/20 0 --Pll )H -0.003 0.150 0.216 0.238 0.188 0.097 0.159 0.092 -0.015 0.015 0.049 -0.041 -0.008 -0.001 -0.004 -0.032

± 0.029 -+ 0.028 -+ 0.021 ± 0.023 ± 0.026 +- 0.033 ± 0.035 ± 0.043 ± 0.044 ± 0.043 ± 0.048 ± 0.050 ± 0.042 ± 0.045 ± 0.054 ± 0.066

e2 ge(Pl o )H

Table 5(b) ~ * o (890) density matrix elements in the helicity frame

-0.045 0.003 -0.029 -0.020 -0.022 -0.035 -0.039 -0.064 0.065 0.189 0.162 0.105 0.046 0.180 -0.030 0.151

-+ 0.031 ± 0.032 ± 0.027 ± 0.034 ± 0.039 ± 0.050 -+ 0.056 -+ 0.067 ± 0.074 -+ 0.085 ± 0.086 -+ 0.079 ± 0.079 -+ 0.091 -+ 0.087 +- 0.097

e1.1_12 H

0.226 0.149 0.147 0.108 0.090 0.048 -0.049 0.049 -0.051 0.109 0.076 0.102 0.038 -0.033 0.111 0.095

± 0.031 ± 0.033 ± 0.025 ± 0.028 -+ 0.030 -+ 0.035 -+ 0.037 -+ 0.041 -+ 0.045 ± 0.046 -+ 0.049 -+ 0.056 -+ 0.046 +- 0.054 ± 0.053 ± 0.065

e o e, Re(oior~t)H

-0.008 0.047 0.056 0.037 0.018 0.083 -0.009 0.043 0.039 0.019 -0.083 0.005 -0.086 -0.128 0.040 0.013

± 0.019 ± 0.019 ± 0.016 +- 0.019 ± 0.023 -+ 0.027 -+ 0.030 -+ 0.036 -+ 0.037 -+ 0.038 ± 0.040 ± 0.044 ± 0.037 +- 0.040 ± 0.050 ± 0.055

eo ~1 Re(pilnot)H

I

38

N.A. McCubbin, L. Lyons, K - p -+ K-lr+n

I

f ~oo

I

t

I

'

I

i

i

'

I

i

I

i

N 80-

60"

40-

°ol

'

0•

120

t

-

N

10080--'.

90"

180"

270"

360"

I

I

L

I

L

I

t

'

I -0-5

=

I 0-0

=

I 0.5

I

cos

e7

~

6040-

20-

0 -0

1.0

Fig. 14. The distributions in the cosine of the polar angle cos o ] and in the Treiman-Yang angle ~ J f o r events in the ~ * o (890) mass region produced at t' less than 0.95 (GeV/c) 2. N is the number of events per bin. The superimposed curves are the best fits of expression (I5) with the parameters as determined by the moments (18).

do _ A 0 + ~ dg~ 47r

% q [ - 2V~ ReO~"; sin O cos ~ + 2 R~poN cos o1

(15)

+ 3e2 [(P00 - P l l ) ( c ° s 2 0 - ] ) - P 1-1 sin20 cos2¢ - v ~ R e P l 0 sin20 cos ¢] }, where the p's are the density matrix elements. This formula is applicable for both the J and H systems.

39

N.A. McCubbin, L. Lyons, K - p ~ K-~r+n

(a) 0.50.

I -÷-

,, 0,00

I

+:+.'._.

,.-'.h.*,,.

;

J.

-

.

,

(d)

0.50 t .

,

1

.-.,,-.+ ,, , ~ ,

,

o.oo ~'~.~4=:,':t~.4-~-l~.--r" ' T - d - ,

-0-50

~ . . . . 0.50

. . . . 0,00

, 1.00

I '' ii

-0.50

. . . .

0.00

0.50l.

.';-.L.

o oo

!. '

,

...r.;~i.T+_+_,

_o..I

1 -0

O- 50

. . . .

,

0.00 , - - : - : , , - r

l'f"I

l-s

I

1 .lO0 0.00

(c)

" 1~j,~'i" , r ~!. 0,00 .

.

.

.

.

/,

~-

-+1

-r1", -,4,-I--', I T

-0.50

i~

(¢)

i

+4I

O. O0

- 0.50

'-

(b)

O. 50

0,50

' I ' O. 50

I

-÷I

. . . . . . . . . . 0.50 t' --~ ( GeVlc )~"

1-0

..J_

-t- II

L

iTt,ti , T .

.

.

0-00

J

.

.

.

.

0.50

i

1.00

t' --* (GcVle) ~ Fig. 15. Combinations of es and ps, determined as functions of momentum transfer, separately for the low (846 to 896 MeV) and for the high (896 to 946 MeV) halves of the g~o (shown as solidand dashed crosses respectively). The ordinates are as follows: (a). e2o. _. J. (b) e2p-^J (c) e~ (P~o - P Jll ), (d) e o e I p l~t.J and (e) e0 e I p~nt.J. Only for e0 e 1Rep lnt~are fllere signlfica;t differences between the two halves of the ~*o.

The p's are normalised such that P00 + 2 P l l = 1.

(16)

The amplitudes for the p r o d u c t i o n o f the 1 - resonance and the 0 + b a c k g r o u n d (in the chosen mass interval) are p r o p o r t i o n a l to e I and e 0 respectively; these are normalised such that:

0. -0.025 0.025-0.05 0,05 -0,1 0.01 -0.15 0.015-0.2 0.2 -0.25 0.25 - 0 . 3 0.3 -0.35 0.35 - 0 . 4 0.4 -0.45 0.45 - 0 . 5 0.5 ~0.55 0.55 -0.65 0.65 -0.75 0.75 - 0 . 8 5 0.85 - 0 , 9 5

(GeV/c) 2

t' range

0.713 -+ 0.056 0.765 +- 0.057 0.751 + 0.043 0.691 +- 0.051 0.585 +- 0.053 0,482 +- 0,063 0.533 +- 0.068 0.553 +- 0.086 0.360-+ 0.092 0.266-+ 0.096 0.286 -+ 0.096 0.313 -+ 0.091 0.375 -+ 0.094 0.257 + 0.107 0.460 +- 0.109 0.289 + 0.113

J Poo

-0.081 0.030 0.055 0.112 0.120 0.080 0.120 0.150 0.197 0.293 0.274 0,180 0.173 ,0.283 0.166 .0.274

PJ - 1

+- 0.041 + 0.041 ± 0.030 -+ 0.034 -+ 0.038 +- 0.048 +- 0.049 +- 0.063 +- 0.069 -+ 0.072 ± 0.079 +- 0,086 +- 0.070 +- 0.082 + 0.085 -+ 0.089

Table 6(a) Density matrix elements for the ~ * o (890) mass region in the J system

-0.148 -0,122 -0.136 -0.155 -0.117 -0.051 -0.114 -0.055 0.030 -0.011 -0.055 0.036 -0.014 -0.026 -0,086 -0.025

RePJo

-+ 0.039 -+ 0.035 +- 0.025 +- 0.028 -+ 0.030 +- 0.033 ± 0.037 -+ 0.049 -+ 0.052 + 0.046 +- 0.051 +- 0.055 -+ 0.047 -+ 0.050 + 0.056 -+ 0,076

0.487 0.391 0,428 0.288 0.19 0.53 -0.11 0.19 0.14 0.13 -0.50 0.00 -0.46 -0.62 0.08 -0.06

-+ 0.072 +- 0.084 +- 0.074 +- 0.092 -+ 0.12 -+ 0.16 -+ 0.19 +- 0,15 -+ 0.15 +- 0.23 -+ 0.24 -+ 0.26 +- 0.19 -+ 0.21 -+ 0.24 +- 0.27

~ --int,J

KeL°o0 )

-0.136 -0.052 -0.114 -0.133 -0.177 -0.04 0.13 -0.09 0.11 -0.33 -0.21 -0.31 -0.06 0.18 -0.30 -0.23

-+ 0.044 -+ 0.044 +- 0.038 -+ 0.047 + 0.063 + 0.10 +- 0.10 +- 0.08 +- 0.10 -+ 0.14 + 0.15 +- 0.16 + 0.12 -+ 0.14 +- 0.16 +- 0.16

~10 /

R e t , intx J

5-

I

t~

0.249 0.209 0.106 0.115 0.083 0.081 0.176 0.133 0.082 0.065 0.071

-0.25 -0.3 -0.35 -0.4 -0.45 -0.5 -0.55 - 0.65 -0.75 -0.85 -0.95

0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.65 0.75 0.85

-+ 0.055 -+ 0.057 -+ 0.067 -+ 0.074 -+ 0.073 -+ 0.079 -+ 0.099 +- 0.076 -+ 0.089 -+ 0.090 -+ 0.097

-+ 0.057 + 0.041 -+ 0.047 -+ 0.049

0.757 +- 0.057

0.711 0.582 0.421 0.295

-0.025

H Poo

0.025-0.05 0.05 - 0.I 0.1 -0.15 0.15 -0.2

0

t' range (GeV/c) 2

+ 0.041 + 0.032 + 0.040 -+ 0.043

- 0 . 0 3 7 -+ 0.053 - 0 . 0 4 1 -+ 0.060 - 0 . 0 7 4 ± 0.077 0.075 -+ 0.085 0.201 -+ 0.090 0.172 -+ 0.091 0.112-+ 0.084 0.050 -+ 0.086 0.196 -+ 0.099 - 0 . 0 3 3 -+ 0.096 0.166 -+ 0.107

0.004 -0.035 -0.023 -0.024

- 0 . 0 6 0 -+ 0.041

H PI--1

Table 6(b) Density matrix elements for t h e K.* (890) mass region in the H system

0.103 0.1,69 0.105 -0.017 0.016 0.052 -0.044 -0.099 -0.001 -0.004 -0.035

0.190 0.257 0.277 0.209

-+ 0.035 -+ 0.037 +- 0.049 -+ 0.051 -+ 0.046 -+ 0.051 -+ 0.053 -+ 0.046 -+ 0.049 -+ 0.059 -+ 0.107

-+ 0.035 -+ 0.025 -+ 0.027 -+ 0.029

- 0 . 0 0 4 - + 0.039

RepHo

0.20 -0.21 0.15 -0.15 0.46 0.32 0.43 0.14 -0.12 0.39 0.33

0.366 0.400 0.311 0.30

-+ 0.15 -+ 0.16 -+ 0.12 -+ 0.13 -+ 0.19 -+ 0.21 -+ 0.24 -+ 0.17 -+ 0.20 -+ 0.19 -+ 0.23

-+ 0.081 +- 0.068 + 0.081 + 0.10

0.522 -+ 0.071

Re~ioot)H

0.35 -0.04 0.12 0.12 0.08 -0.35 0.02 -0.32 -0.47 0.14 0.05

0.115 0.153 0.107 0.060

+- 0.11 +- 0.13 -+ 0.11 -+ 0.11 -+ 0.16 -+ 0.17 -+ 0.19 -+ 0.14 -+ 0.15 -+ 0.17 -+ 0.19

+ 0.047 -+ 0.044 + 0.055 + 0.077

- 0 . 0 1 8 ± 0.044

~Ke~o - - i$o n t .)H

I

I

42

N.A. McCubbin, L. Lyons, K - p --. K-lr+n

(17) By taking moments of the decay distribution, we obtain -s 4 ( 3 COS20 -- 1 > = e12(P00 -- P l l ) , --~ (sin20 cos2~ > = e21P1_l ' ---saX/~ (sin 0 cos 0 cos ~b) = e 2 R e P l 0 ,

(18)

X/{~ (cos 0 ) = e0e 1 R e p ~ , -

~

( sin 0 cos $ ) = e0e 1 R e p ~ d .

We have evaluated these moments for events in the mass range 0.846 to 0.946 GeV for various ranges of t', with the angles defined either in the J system or in the H system. The resulting products of e's and O's are presented in table 5. To demonstrate that this parametrisation of the K - n + decay is satisfactory, fig. 14 shows the distributions in cos 0 J and in the corresponding azimuthal distribution OJ (the Treiman-Yang angle) for events with t' less than 0.95 (GeV/c) 2. The superimposed curves were obtained by integrating expression (15) over $J or over cos 0 J respectively, with the parameters set equal to their values as determined from the moments. Fig. 15 shows the five parameters of eq. (18) as functions of t' for the mass regions from 0.846 to 0.896 GeV and from 0.896 to 0.946 GeV separately. We expect the moments corresponding to the 1 - resonance to be equal in these two mass regions, while the interference elements can be different. We see that the only element with significant differences between the two mass re~gions is p ~ . From our fits to the mass spectra of fig. 9, we obtain e~ and e 2 as a function of t'. (Note that, as e 2 is the fraction of resonant events in the chosen (but arbitrary) mass region, neither e 2 nor the values of table 5 should be regarded as basic constants of the K-rr + system.) Combining these with the data of table 5, we obtain the density matrix elements themselves. These are presented in table 6. The values of RePJ0 and RepH0 satisfy the consistency checks [10] that can be made when the angle of rotation about the normal to the production plane required to take the J into the H system is either 45 ° or 90 °. Furthermore our density matrix elements are substantially in agreement with the values of Aguilar-Benitez et al. at 3.9 and 4.6 GeV/c [4h]. In fig. 16 we show schematically a comparison of our density matrix elements P with those for the K+n reaction (8) at 4.6 GeV/c. (In fact ref. [9d] gives products of e and ps. For the non4nterference terms the difference is not serious since e 2 ~ 0.9, but for the interference terms, our lack of knowledge of e 0 in the K+n experiment prevents us from extracting pint from their published data.) Apart from (O00 - P 11)J there are significant differences between the two reactions.

N.A. McCkbbin, L. Lyons, K - p ~ K-~r+n

43

H system

J system ..8 +.l,

o

/,

01 - 1

-2 ~'s

*.2 Re (/:'1o} o

t l "--~1

l

0.5 t I ._}1.0

-.2

Fig. 16. Schematic diagram showing the differences between the density matrix elements for our data (solid lines) and for the K+n data of ref. [9d] at 4.6 GeV/c (broken lines). Only one line is shown for (Poo - P 1t )J as the data for the two reactions are in fair agreement. The t' scale is in (GeV/c)2.

Our interference density matrix elements all satisfy (within one standard deviation) the positivity requirement int

~<

Re(Pmo)~Pmm,

m = 0 o r 1.

The values of R e ( p ~ ) are large at small values of t', indicating significant interference between the 1 - and 0 + states. This is the same effect noted earlier in connection with the non-zero value of the asymmetry parameter A (eq. (14)). In table 7, we present values of do

% = P00 h-7' do

o = (Pll - Pl-1 )d-( ' do e+ = ( P l l + P l - : ) ~ 7 '

(19)

2.13 2.19 1.82 1.06 0.52 0.27 0.13 0.093 0.060 0.042

O.

0.025-0.05 0.05 - 0 . 1 0.1 -0.2 0.2 - 0 . 3 0.3 - 0 . 4 0.4 - 0 . 5 5 0.55 - 0 . 7 0.7 - 0 . 8 5 0.085-0.95

-0.025

ooJ

t ° range (GeV/c 2 + 0.24 + 0.25 ± 0.17 ± 0.10 + 0.07 -+ 0.05 ± 0.03 + 0.024 ± 0.015 ± 0.016

2.26 2.04 1.40 0.60 0.23 0.065 0.049 0.030 0.011 0.011

oH

± 0.25 ± 0.24 ± 0.13 +- 0.07 + 0.05 + 0.031 ± 0.021 + 0.017 ± 0.011 ± 0.015

0.68 0.25 0.14 0.11 0.14 0.058 0.046 0.032 0.015 0.012

o J_

+ 0.16 + 0.14 ± 0.09 ± 0.05 ± 0.05 ± 0.034 ± 0.023 + 0.018 + 0.015 ± 0.015

+ 0.15 + 0.14 0.59 ± 0.10 0.57 ± 0.07 0.43 + 0.06 0.26 ± 0.05 0.13 + 0.03 0.090 ± 0.019 0.066 ± 0.015 0.044 ± 0.017

0.54 0.41

trH _

Table 7 The differential cross sections (in m b / ( G e V / c ) 2 ) of eqs. (19) in the text, describing the production of the spin 1 K,* (890)

0.19 0.42 0.42 0.49 0.36 0.26 0.26 0.14 0.078 0.091

o+

± 0.15 + 0.14 + 0.11 ± 0.07 ± 0.06 +- 0.05 + 0.04 + 0.03 -+ 0.016 ± 0.019

I o,.

N.A. McCubbin, L. Lyons, K - p ~ K-n+n

45

t o-~

2

-I-

(mb/(GcY/c)) 0.1

0.3

!o.o.I.

-]-=-t-

0-03

o'2

(mb/(GeV/c)2)

0;~

o'8 t'

( OeV/c )2

003.

o:e

1'0

~_

1

0.01

0

o'z

0'.4

0'.6

0~8

1;0

T

(mb/(GeVIc)2) 0.1.

1

,--T--,

(mb/(GeV/c)21

q--

o." o,~ I

0.03

03-

0 1

0'2

o~4

o'.s

o'~

•

0.1-

oo; o;z

o:4

0'.8

o'.8

t'

(GeV/c)2

Fig. 17. The quantities o f eq. (19) of the text, plotted as a function of t'.

1'.o ~'

t'

(C-¢V/c)2

>

the first two being defined in the J and in the H system, while o+ is the same in both systems. These are plotted in fig. 17. We compare these data on quantities (19) for the ~ , o (890)n final state with those from ref. [le] on the K * - (890)p final state at 3.13 and 3.3 GeV/c beam momentum. (In order to compare them at the same value of s, they have been scaled by p~n1"95). The ratios R of these quantities in various t' ranges are presented in table 8. For isospin I exchange in the t-channel, this ratio is predicted to be 4,

~b

46

N.A. McCubbin, L. Lyons, K - p ~ K-rr+n

Table 8 Ratio of K*°]K*- production

,'

R(o )

R(o )

R(o+)

R(o )

R(o )

2.3±0.3 1.0±0.3 0.4±0.2

2.7±0.4 2.0±0.4 >2.5

0.6±0.1 0.6±0.1 0.9±0.2

2.3±0.5 1.8±0.4 >2.6

1.1±0.4 0.9±0.4 0.3±0.2

(GeV/e) 2 0 -0.2 0.2-0.6 0.6-0.95

The ratio R of the quantities oo, a_ and a+ (eq. 19) for the final states g . o (810)n and K*-(890)p e.g. da da-

R(a+)=[(Pll+Pl-1)-d~ 1g,On/IP11+P1-1)-~K,p"

Both g*o and K * - cross sections have been corrected for both Kit decay modes. For pure isospin 1 exchange, R is 4 While for isospin zero it is zero.

while for isospin zero exchange, it is zero. Absorption effects can of course alter these predictions. The value o f 000 a t low t' values is consistent with a dominanl pseufloscalar exchange contribution. The value of R for a J or a H even in the first t' bin (table 8) is, however, significantly smaller than 4, suggesting that if the pseudoscalar is a pion, then there must be absorption effects present. The SCRAM absorption model [11] predicts a dip in a H at t ' ~ 0.4 (GeV/c) 2, arising from interference between the pion pole and cut. We have no evidence for a dip or shoulder there; a H is simply very small b e y o n d 0.4 (GeV/c) 2. Furthermore in the region of the predicted dip, the ratio R is only ~ 1, which is small for a pion exchange process. The o of table 8 have been fitted by a form A e x p ( - B t ' ) . The values o f A and B and the range o f t ' for which the fits were performed are presented in table 9. The cross sections o J and a ~ satisfactorily extrapolate to consistent values at t' = 0. The Table 9 Fits of expression (11) to the differential cross sections (19) Cross section

t' range ((GeV/c)2)

A (mb/(GeV/c) ~)

a~

0.

-0.55

2.7

+

0.2

6.4 + 0.4

ooH

0

-0.4

2.8

± 0.2

10.2 ± 0.7

T

o

J

B ((GeVlc)-2)

0.025-0.95

0.24 + 0.07

3.3 ± 0.6

a

0.1

-0.95

1.0 ± 0.1

3.6 + 0.3

o+

0.1

-0.95

0.7 + 0.1

2.5 + 0.3

Total a

0

-0.4

3.4 ± 0.2

4.8 ± 0.3

N.A. McCubbin, L. Lyons, K-p ~ K-rr+n

47

values of B for o J and o n in the same reaction at 5.5 GeV/c are 7.4 + 0.8 and 12.1 + 1.3 (GeV/c) -2 respectively [4j]. It is o H which displays the sharpest t' dependence. The value of B is consistentt with that observed in K+n --> K *° (890)p at 4.6 GeV/c [9d]. Also the difference in our slopes for a H and o~ is more pronounced than in the K+n r e a c t i o n t t ; for K÷n, the values of o H and o J-are 10.9 and 9.8 -+ 0.7 (GeV/c) -2 respectively. Ref. [9d] points out that both these facts are in accordance with the SCRAM absorption model [12]. The t' dependence of crJ and cr~ are stronger for the ~ , o (890)n final state than for K * - (890)p at 3.13 and 3.3 GeV/c (where the values are 4.8 and 5.6 -+ 0.6 (GeV/c) - 2 for crJ and cr~t respectively). The slopes of o+ are, however, comparable for the two reactions (2.4 + 0.8 (GeV/c) - 2 for K * - (890)p), despite the fact that o+ for the K * - (890)p final state is dominated by isospin zero exchange, while the ~ , o (890)n final state requires isospin 1 exchange.

4. The K - n + system in the 1420 MeV region

4.1. Mass and width o f the ~ , o (1420) As seen in the K - n + mass spectrum (fig. 7), the ~ , o (1420) is strongly produced. Especially at low values of t', however, there is an indication that the shape of the g , o (1420) is distorted, with a wide shoulder on the low-mass side. This may be connected with the possible wide 0 ÷ Krr state at around 1200 MeV [5, 13]. The mass region around the peak has been fitted by a Breit-Wigner resonance Table 10 Results of fitting K - n + mass spectrum in region of ~ , o (1420) Mass range (GeV)

No of bins

t' range ((GeV/c)2)

Mo

F (MeV)

No of K,* events

x2

(MeV)

1.25-1.55 1.25-1.55 1.2 -1.6 1.2 -1.6 1.25-1.55 1.25-1.55 1.2 -1.6 1.2 -1.6

30 60 40 80 30 60 40 80

All All All All > 0.2 > 0.2 > 0,2 >0.2

1415.4 -+ 3.0 1416.1 ± 3.0 1413.2 ± 3.0 1414.3 -+3.0 1421.7 ± 4.0 1421.9 ± 4.2 1421.0 -+4.2 1422.0-+4.0

94 -+ 13 90 ± 14 106 +- 12 99 ± 12 110 -+ 18 115 -+ 18 120 ± 18 118-+ 18

1214 1144 1386 1282 781 792 858 818

28.9 62.5 39.9 84.0 22.2 64.3 29.6 87.9

The "No. of K* events" column has been corrected for those events in the tails of the resonance outside the given mass range. t For the K+n and K-p reactions (o0o -/211 ) are consistent in the J system, while for oo it is in the H system that their t' dependences agree. t t It should be remembered in making these comparisons that the K+n data are for products of e~ and the p's, while our data are for the p's themselves.

N.A. McOtbbin, L. Lyons, K - p ~ K-~r+n

48

plus a polynomial background (in fact, expression (5) with a term D m 4 added). The results of these fits are summarised in table 10. Because of the anomalous shape of the g~* (1420) at small momentum transfers, we have used the fits for t' larger than 0.2 (GeV/c) 2 to estimate our best values of the mass and width of the resonance as: M0=1421.6+

4.2MeV, (20)

P

= 116

-+18

MeV.

The effect of ignoring the experimental resolution on m(K-Tr+) is to increase P by about 5 MeV. Our values are consistent with the currently accepted world averages IS] of M 0 = 1422.8 +- 2.5 MeV, I" = 108.4-+ 6.3 MeV.

1000 K-p K'n 300

tG (/ub) 100

tI

30

Threshold ~o

Pir~ (GeVIc) Fig. 18: The cross section as a function of incident m o m e n t u m for the line reversed reactions K - p -~ g * o (1420)p and K+n ~ K *° (1420)p. The cross sections include only the Krr decay modes. The arrow denotes the threshold for the reaction.

N.A. McCubbin, L. Lyons, K - p --*K-rr+n

49

4.2. ~ ,o (1420)production cross section

From the fits with t' larger than 0.2 (GeV/c) 2, we deduce that there are 810 --- 50 events in the ~ , o (1420) peak, and hence that the cross section for K - p ~ ~ , o (1420)n,

~*o ~ KJr,

(21)

o = 192 + 26/~b,

(t' > 0.2 (GeV/c)2).

(22)

is In order to compare with previous data, we should estimate the cross section integrated over all t' values. The average number of ~ , o (1420) events in the first four fits of table 10 (made for all t') is 1 256, but these all were obtained with slightly narrower widths than our best value (eq. 20). If we extrapolate to a width of 116 MeV, we estimate the rather larger number of 1 530 events. We compromise and assume 1 430 -+ 200 ~*o (1420) events, which then gives a cross section o ~ 340 -+ 65/~b,

(all t')

(23)

for reaction (21). This is about 50/~b larger than a smooth extrapolation of the differential cross section of subsect. 4.3 would suggest.

t

t

l

i

t

,

]

I

I

I

]

I

I

'

l

,

i

,

i

5-0

d.~ 1.0

dr'

-;(mbl{GcV/¢)

=)

..~... I

I

.

i *,0 o--~..

i

0.1

__-.. ~"

I.----'t"

-'"

,

0- 01

i

0.0

r

r

I

i

I

I

I

0.5

I

]

1.0 t'

--~

I

I

i

I

I

I

I

1.5

I

t

i

2-0

(GeVIc) =

Fig. 19. T h e differential cross section for the ~ * o (1420)n final state, s h o w n as solid crosses. For comparison the differential cross section for the ~ * o (890)n final state is s h o w n as the dashed crosses.

N.A. McCubbin, L. Lyons, K - p ~ K-~r+n

50

Table 11 ~*o (1420)n differential cross section

t' ((GeV/c)2)

do /dt ~b/(GeV/c) 2)

0.2-0.4 0.4-0.6 0.6-0.9 0.9-1.2 1.2-1.5 1.5-2.0

238 ~ 30 183 +- 20 96 -+ 10 64 +- 9 55 ± 8 38-+ 5

The differential cross section for reaction (21) in the text i.e. we have corrected the observed K - n + decay mode of the ~ . o (1420) for the unseen K.°Tr° decays, but not for other decay modes. See also the comments in table 4.

The cross section (23) is plotted with other data for reaction ( 2 1 ) a s a function of the incident momentum in fig. 18. The somewhat sparse data [9] for the reaction K+n ~ K *° (1420)p,

K *° --> Klr,

(24)

are also shown there.

4.3. ~ , o (1420)n differential cross section As for the ~ . o (890)n channel, we have determined this differential cross section by fitting the individual mass spectra o f fig. 9. The results are given in table 11 and plotted in fig. 19 as the solid crosses. This differential cross section is considerably shallower than that for ~ . o (890) production, and the cross sections become comparable around t' ~ 1 (GeV/c) 2. In contrast, for higher energy K - p and K+n reac, tions, the K *° (1420) final state has at least as sharp a t dependence as that for the K *° (890). Because o f (i) the larger background under the ~ , o (1420), (ii) the low mass shoulder of the ~ . o (1420) at low t', (iii) the more complex decay angular distribution arising from the larger numer o f spin states involved and (iv) the smaller number of events (compared with the ~ . o (890)n channel), we have not attempted to determine density matrix elements for the ~ . o (1420)n final state. In sect. 5, however, we present the moments of the K - r r + decay throughout the whole K - r r + mass range, as a function o f momentum transfer.

5. The K - ~ + decay m o m e n t s In this section we present the moments o f the K-Tr + system's decay angular distribution. These moments are defined as

N.A. McCubbin,L. Lyons, K-p ~ K-lr÷n HLM = (DLMo) = ~

( YIM )"

51 (25)

As in subsect. 3.4 the decay polar angle and azimuth are determined by the decay K - vector in the K-rr + rest system with respect to axes defining the J system or the H system; thus we have two sets of moments HJLMand HIHM. In general there are no unexpected differences between the two sets of moments, so only the HJM are shown. The moments are calculated as a function of the mass of the K-lr + system, and of the modified momentum transfer t' (defined in subsect. 3.3)• Those moments showing significant structure (H10, H20, H21, H22, H30 and H40 ) are presented in fig. 20. Fig. 21 contains the values of ilL0 (for events at all t ) forL -~ 8. The following points about the moments are to be noted• (i) Hermiticity and parity conservation require all the moments to be real. Our data are consistent With this. (ii) With spin states up to ] contributing, moments with L ~< 2 J can be non-zero In the regions of the K* (890)and K.* (1420), the significantly non-zero moments have L values up to 2 and 4 respectively. (iii) At small t', H10 is positive and decreasing through the ~ . o (890) region. For S- and P-waves only, this moment is proportional to the asymmetry parameter A (see eq. (14)), and is given by H10 a [as[ lap[ cos (¢p - e s ) ,

(26)

where a s and ap are the amplitude s for s- and p-wave production and (¢p - es) is their relative phase. Now H10 goes through zero at m(K-rr +) ~ 950 MeV. Assuming that a s is non-zero there, and that ap is a Breit-Wigner amplitude withM 0 and F of 896 MeV and 48 MeV respectively, we deduce cos (¢p - es) = o,

(27)

implying Cs = 65° or 245 ° .

(28)

These correspond to the well-known "Down" and "Up" ambiguous solutions for the s-wave phase shift [9g, 14]. As in previous Krr phase-shift analyses, our data are consistent with a non-resonant s-wave in the ~ . o (890) region, but cannot rule out a narrow s-wave resonance. (iv) In the K* (1420) region, for t' less than 0.1 (GeV/c)2,HIo falls through zero, as for the K* (890), but at larger t', the structure is different. (v) The moment Re(H11 ) exhibits structure in the 890 and 1420 MeV regions, and like H10 has a zero at m(K-Tr+) ~ 0.95 GeV. (vi) In the K *° (890) region, the H2M moments are linearly related to the spin 1 density matrix elements. All three have definite structure in this mass region. In the ~ . o (1420) region, these terms arise from S-D, P-P and/or D-D interferences. Compared with the ~ , o (890), the structure in//20 holds out to larger momentum

52

N . A . M c O u b b i n , L. L y o n s , K - p

11

~ K-~r+n

1 . @

4.

tt'4L'

~.qt

Z

-1. la .4-c_

~.=~ . . . . 1 .'@ . . . . (KAPI) MASS; 1 .@,, •

1 .'~5' ' T'<~.. 1

/ 2 .' e,,

1.@ @.~

1 .@ C k'APT) MASS:

1.~3 T'<~,.

2.~. 1 h

1'

Z

J~'~+,d~J4,U I!,tJ u,'~!+{lJ !tl

z

-1

.

.

@.~ .... KAP]')

1 .'{a . . . . MASS;

1 .It5 . . . .

1

.

@

.

@.~ • KA~I)

r 1 .(~ MASS

1.S g.2
1 .{a MASS:

1 .~ 9.5
.

,

.

.

.

.

.

.

.

,

,

MASS:

@. l : T ' < ~ ? . 3

1.@

e,e

.

.

KAPT)

@. 1 , ' T ' < ~ . 3

1.~.

•.1

.

2.'~

1 2,0

, tllt~,, +, I~, q, 91, ~ ] ~ T ~

-1 .@

m

I KAPT)

I"IASS:

@.2
1.@ MASS:

1.ES 2. @.E~
1,E'

@.~5 KAPI) 1,@

~.@

~. ~

II~" ~ <*+-'+~t@i#÷#2+"b ,11.,~.t# .... . ....

1.~

....

1

1,@

/

..1 . ~ la.,~ KAPI)

n 2.l~ .~

5- 1 .(~ O.B

1 .e (KAPT) HASS:

1 ,B ALL

2.e T"

Fig. 20.

@.B

.1 .@ (FAPT) MASS:

.....

i.~:, ALL

T --~

2.@ T

53

N.A. McCubbin, L. Lyons, K - p -->K-n+n

9.5

@.S

"'t' '"Tt

7= e-I 0.~

1 ,'@ 1 .'~' I k'API) MASS; T , < ~ . I

@,%

>_,'

'

@. B . . . .

1 .hi3 . . . .

r KAPI)

1 [~ ....

MASS;

2.'i3

-r-<9.1

9.5

O/

--@. 55 @

@

@.5 K/

1.9

1.5

D

MASS;

i3.1
KAF'I) I

MASS;

9.3
gAfI)

MASS;

i3.~
2.@

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55

N.A. McCubbin, L. Lyons, K - p ~ K-~r+n

°5t i

-rrv

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0.5

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56

N , 4 . McCubbin, L. Lyons, K - p -* K - n + n iii, 1 .(3'

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Fig. 20. Some of the m o m e n t s HLM , defined in eq. (25) in the text, for the K - n + system in the J frame. The m o m e n t s are calculated as a function of the mass of the K - n + system (in GeV) and for various ranges of t' (given in (GeV/c) 2 below each plot). In each case, the m o m e n t plotted is shown on t h e y axis.

N.A. McCubbin, L. Lyons, K - p -+ K-rr+n

1.0.

0,5

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57

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Fig. 21. The momentsHL0 (L from 1 to 8) in the Jackson frame as a function ofM(K-~r +) but integrated over t'. Above about 1.6 GeV, all these moments up to H6o become significantly positive.

N.A. McCubbin, L. Lyons, K-p ---,K-lr+n

58

1.5

1.5

I11

8 -1.

0.5 . . . . ~.'z5 . . . . m ( k - , , " ) GeV

2.0

-150.5

1 25

2.0

m ( k - 'if") GeV

Fig. 22. Scatter plots of the cosine of the polar decay angle of the K - n + system against the mass of that system. The left-hand plot is for cos 0J and the right for cos 0 H. For high masses the data concentrates near cos 0 ~ +1 more strongly for cos 0 J than for cos OH. transfers; tl~s is perhaps related to the shallower t' dependence of the ~ , o (1420) production. (vii) F o r M(K-Tr +) larger than about 1.6 GeV, all HLO moments with L ~< 6 are positive and increasing. This is most simply interpreted as a direct consequence o f the increasing prominence o f the forward peaking o f the reaction K - + exchanged meson -+ K - + 7r+ ,

(29)

as the mass o f the K-•r + system increases. An alternative possibility is that it is simply a reflection of low mass structure in the nn + system. In fig. 22 are shown two scatter plots, o f cos 0 J against M(K-~r +) and o f cos 0 H against M(K-rr+). Since, for fixed M(K-Tr+), cos OH is linearly related to M2(mr+), we would expect that low mass effects in the nTr+ system would result in the cos0 H plot being more sharply peaked near cos0 ~ 1 than for the cos 0 J plot. For large values of M(K-Tr+), the opposite is the case, thus arguing against the interpretation of the rising HLO values being simply a reflection of low mass mr + dynamics, but being intrinsic to the K - n + system itself.

6. Conclusions (i) Extracting a pure, unbiassed sample o f K - r r + n events from 2-prong events in a bubble chamber experiment is difficult b u t possible at 3.6 GeV/c. (ii) The cross section for the K - n + n final state is 1.5 + 0.2 rob. (iii) The masses and ,~idths of the g , o resonances are 895.5 -+ 1.0 MeV and 48 +- ~ MeV (for the ~*o (890)); 1421.6 -+ 4.2 MeV and i 1 6 + 18 MeV (for the ~ , o (1420)). At small m o m e n t u m transfers, the ~ , o (1420) has a low-mass tail. (iv) The cross section for the ~ , o (890)n final state is 830 -+ 110 pb; that for the ~ , o (1420)n is 192 -+ 26/ab (t' > 0.2 (GeV/c)2).

N.A. McCubbin. L. Lyons, K - p ~ K - n + n

59

(v) The differential cross section for K *° (890)n in the forward direction is characterized by a slope o f 4.8 -+ 0.3 (GeV/c) -2. This is shallower than that for the reaction K÷n ~ K*0 (890)p. The background under our ~*o (890) is produced with a much sharper slope of 11.2 -+ 0.5 (GeV/c) -2. For t' larger than 0.2 (GeV/c) 2, the g , o (1420)n has a shallower t' dependence than does the g , o (890)n; this is in contrast with K* N data at higher beam momenta. (vi) The K - n + system's decay shows a significant and mass-dependent asymmetry in the region of the ~ , o (890). This requires us to treat this mass region as a coherent mixture of spins 1- and 0 ÷. (vii) The density matrix elements P00 are large at small t', consistent with a dominantly pseudoscalar exchange contribution. (viii) The density matrix elements ~00 P l l ) J for the reactions K - p --> ~ . o (890)n and K+n -~ K *° (890)p are consistent, but other density matrix elements disagree. For P l - 1 there is a sign difference for the two reactions. (ix) By comparing the ~ , o (890)n and K * - (890)p final states, we have investigated the t-channel isospin contributions to the various helicity substates. The ratio R for o~ or ~ is smaller than 4, which would be the value expected for pure pion exchange. (x) The strong absorption model SCRAM appears t 9 be capable of explaining the differences in the shapes of the differential cross sections and the density matrix elements for K *° (890) production in the K - p and K+n reactions, but we fail to observe significant structure in o~ at t ' ~ 0.4 (GeV/c) 2 . (xi) We have calculated the moments of the K - n + system's decay angular distribution as a function of mass and momentum transfer. Several of these elements exhibit interesting structure. The behaviour Of H l o is consistent with the S-wave K - n + phase shift having a value o f ~ 65 ° at M(K-1r +) of 950 MeV. The HL0 moments (L ~< 6) all go positive for M(K-zr +) larger than 1.6 GeV; this appears to be a consequence of the increasing peripheralism in the K-Tr+ system above the K*°(1420) region. -

It is a pleasure to thankMr. A.W. Lowman for participating in the experiment at the stage when the events were being measured on PEPR, and the PEPR group for their help and collaboration. We also are grateful to the other members of the Oxford bubble chamber group for many helpful discussions, and to the operations group of the CERN 2m bubble chamber for the excellent conditions provided during the taking of the data. A p p e n d i x . lonisation

In this appendix we describe how we obtained estimates of track ionisations from PEPR, and then how this information was used in trying to resolve ambiguities among the various kinematic hypotheses.

N.A. McCubbin, L. Lyons, K-p ~ K-Tr+n

60

The number o f bubbles n per unit length of track is given by

nd = loge((n + M)/M), where d is the bubble size, and H and M are respectively the numbers of "hits on bubbles" and "misses" obtained in a closely stepped scan of the PEPR spot across a section of track. We thus det'me

1 = n/nmi n = k loge((H + M)[M), where nmin is the value of n for minimum ionising tracks, and k is a constant to be determined. Then I is an estimate of (c/o) 2, where o is the velocity of the particle. Various corrections to H a n d M are necessary before the above formula can be applied in practice. (i) The fdm provides only a 2-dimensional projection of a track. This results in the finite bubble size failing in the clear regions of dipping tracks, causing an underestimation of M. We approximately correct for this by a factor in k of cos X, where h is the angle o f dip. (ii) PEPR performs its ionisation scan either horizontally or vertically on the film. Thus the spherical bubble shape will again in general cause an underestimation of M, and we have to introduce a factor of cos/3, where/3 is the angle between the track segment and the scan direction. Furthermore, when Icos/3 cos X I < 0 . 6 , the ionisation estimate for that track segment on that view is ignored. (iii) In order to distinguish between a "hit" and a "miss", PEPR requires a bubble signal above a certain threshold, which it determines by scanning clear film around the track. (iv) Various empirical factors are introduced in order to relate I correctly to c2/o 2. They include (a) parameters to make a graph o f / a g a i n s t c2/o 2 for various known tracks have a slope of unity and intercept of zero; (b) a factor to allow for saturation in the measurements for I larger than about 4; (c) a scale factor to make the errors on the ionisation estimates reasonable. The above strategy was developed by studying a large sample of 2-prong events which gave a unique fit to the highly constrained elastic scattering hypothesis [2]. It now remains to use the ionisation estimates for each track on each of the 3 views in order to decide among various possible kinematic fits to the event. The method used involved first defining a X2 for each view of an event for each successful kinematic hypothesis by

/'

N.A. McCubbin, L. Lyons, K - p ~ K-~r+n

61

where a is a factor close to unity which minimises the X2. In the above formula, the summation extends over the j tracks o f the event in that view (i.e. ] = 3 for events with 2 outgoing prongs plus a beam track), whose estimated ionisations are Ij + oj, and whose velocities according to the relevant kinematic fit are v/. Thus each hypothesis has 3 values o f the ionisation X2, one for each view. Corresponding to these are 3 confidence levels C 1 .(the largest), C 2 and C 3 (the smallest confidence level). Then in deciding between two possible interpretations of a given event, the hypothesis (denoted by the primed confidence levels below) is rejected in favour o f the unprimed one if all the following conditions are satisfied, t

(i) c 1 > 2 c 1 , P

(ii) C 2 > 0.5 C 2 , (iii) C 1 > 2%, (iv) C 2 > 0 . 1 % ,

iv)

<

If neither hypothesis is rejected in favour of the other, the event remains ambiguous between these two possibilities.. This decision-making logic is d e a r l y to a large extent arbitrary. Its justification is that it is in excellent agreement with a conventional ionisation scan of the film performed by human beings.

References [ll (a) P.A. Schreiner, D.H. Stork, A.G. Clark, D.H. Saxon and L. Lyons, Nucl. Phys. B24 (1970) 157. (b) P.A. Schreiner, D.H. Stork, R.T. Ross, A.G. Clark and L. Lyons, Nucl. Phys. B28 (1971) 85. (c) R.T. Ross, T. Buran, J.L. Lloyd, J.H. Mulvey and D. Radojicic, Phys. Letters 38B (1972) 177. (d) A.G. Clark and L. Lyons, Nucl. Phys. B38 (1972) 37. (e) A.G. Clark, L. Lyons and D. Radojicic, Nucl. Phys. B54 (1973) 432. (0 G.C. Mason and C.G. Wohl, Nucl. Phys. B58 (1973) 1. (g) A.M. Cooper, A.G. Clark and L. Lyons, Nucl. Phys. B65 (1973) 210. [2] A.W. Lowman and N.A. McCubbin, Nucl. Phys. B61 (1973) 296. [3] C.B. Brooks, P.G. Davey, J.F. Harris, J.G. Loken and C.A. Wilkinson, Machine perception of patterns and pictures, Inst. Phys. Conf. Series No. 13 p 181 (1972). [4] (a) B. Conforto, D.M. Harmsen, T. Lasinski, R. Levi-Setti, M. Rayrnund, E. Burkhardt, H. Fi/thruth, E. Kluge, H. Oberlack and R.R. Ross, Nucl. Phys. B8 (1968) 265 (0.777-1.226 GeV/c). (b) W. Graziano and S.G. Wojcicki, Phys. Rev. 128 (1962) 1868 (1.15 GeV/c). (c) J.R. Ficenec, R.I. Hulsizer, W.P. Swanson and W.P. Trower, Phys. Rev. 169 (1968) 1034 (1.33 GeV/c).

62

N.A. McCubbin, L. Lyons, K-p-~ K-~r+n

(d) M. Dickenson, S. Miyashita, D. Huwe, F. Ayer and L. Marshall, Phys. Letters 23 (1966) 505 (2.0 and 2.24 GeV/c). (e) J.R. Ficenec, H.A. Gordon and W.P. Trower, Phys. Rev. 175 (1968) 1725 (2.63 and 2.70 GeV/c). (f) A. Verglas, S. Focardi, A. Minguzzi-Ranzi, L. Monari and P. Serra, Nuovo Cimento 41A (1966) 629 (3 GeV/c). (g) B.T. Meadows, Thesis (Oxford 1966), unpublished (3.5 GeV/c). (h) M. Aguilar-Benitez et al., Phys. Rev. Letters 26 (1971) 466; Phys. Rev. D6 (1972) 11 (3.9 and 4.6 GeV/c). (i) Y.W. Kang, Phys. Rev. 176 (1968) 1587 (4.6 GeV/c). (j) F. Schweingruber et al., Phys. Rev. 166 (1968) 1317; D5 (1972) 2162 (4.1 and 5.5 GeV/c). (k) M. Deutschmann et al., Nucl. Phys. B36 (1972) 373 (10 GeV/c). (1) B.D. Hyams et al., Nucl. Phys. B7 (1968) 1 (11.2 GeV/c). (m) B. Chaurand et al., Ecole Polytechnique - Saclay - RHEL Collaboration, Phys. Letters 38B (1972) 253 (14.3 GeV/c). [5] Particle data group, Rev. Mod. Phys. 45 (1973) 1. [6] A.G. Clark, thesis (Oxford 1972), unpublished. [7] R.J. Abrams et al., Phys. Rev. D1 (1970) 1917. [8] G.C. Wohl, private communication; reL [1] (f). [9] (a) S. Goldhaber, J.L. Brown, I. Butterworth, G. Goldhaber, A.A. Hirata, J.A. Kadyk and G. Trilling, Phys. Rev. Letters 15 (1965) 737 (2.3 GeV/c). (b) S.L. Baker et al., Imperial College - Westfield Collaboration, Presented at Aix Int. Conf. on elementary particles, 1973 (2.2-2.7 GeV/c). (c) G. Bassompierre et al., Brussels - CERN - Munich Collaboration, Nucl. Phys. B16 (1970) 125 (3 GeV/c). (d) K. Buchner et al., Brussels - CERN - Munich Collaboration, Nucl. Phys. B45 (1972) 333 (4.6 GeV/c). (e) G. De Jongh et al., Brussels - Mons - Paris - Saclay Collaboration, Presented at Aix Int. Conf. on elementary particles, 1973 (8.2 GeV/c). (f) D. Cords et al., Purdue - Davis - Indiana Collaboration Phys. Rev. D4 (1971) 1974 (9 GeV/c). (g) A. Firestone, G. Goldhaber, D. Lissauer and G. Trilling, Phys. Rev. D5 (1972) 2188 (12 GeV/c). [10] L. Lyons, How is your Re Plo?, Oxford Bubble Chamber Note No. 30 (1973). [ 11] M. Ross, F.S. Henyey and G.L. Kane, Nucl. Phys. B23 (1970) 269. [12] G.C. Fox et al., Phys. Rev. D4 (1971) 2647. [13] J.L. Rosner, Hadron spectroscopy, SLAC - PUB - 1323 (1973). [ 14] M.J. Matison et al., A Study of K+Tr- scattering in the reaction K+p ~ K+*r- n + + at 12 GeV]c, LBL - 1537 (1973). [15] B. Haber et al., SABRE Collaboration, Nucl. Phys. B17 (1970) 289.