Spin-rotation measurements in π−p → K0Λ

Nuclear Physics B222 (1983) 389-410 © North-Holland Publishing Company

SPIN-ROTATION MEASUREMENTS IN 'n'-p~K°A K.W. BELL 1, J.A. BLISSE'I~, T.A. BROOME, H.M. DALEY, J.C. HART, A.L. LINTERN, R. MAYBURY, A.G. PARHAM, B.T. PAYNE, D.H. SAXON, T.G. WALKER and J.B. WHITTAKER

Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 OQX, UK Received 8 March 1983 The first measurements of spin-rotation in meson-baryon scattering in the resonance region are presented. These measurements, for the reaction ~--p-, K°A, confirm the main predictions of a previous partial-wave analysis. Comments are made on resonant couplings in the reaction •r-p -* K°A.

1. Spin-rotation This paper reports on measurements of spin-rotation in the reaction ~r-pl' ~ K °A' at seven momenta between 1.34 and 2.24 GeV/c. These complement our earlier measurements of differential cross section and polarisation at 22 momenta from 0.93 to 2.38 GeV/c [1, 2]. Such complete polarisation information is not available in any other meson-baryon reaction, and in the reaction ~r-p-~ K°A exists only at 5 GeV/c and for a restricted range of momentum transfer near the backward direction [3]. The availability of spin-rotation measurements places extra constraints on partial-wave analysis. The experiment described here was performed using a target with protons polarised parallel to the incident direction, and used the A -~ p~r- decay to analyse the final state baryon spin. The target polafisation increases the physical observables in the reaction from two, obtainable with an unpolarised target, to three. The analysis methods used here have been described in a previous paper [4]. For clarity the technique is outlined briefly here. Scattering processes of the type 0-½+~ 0-½+ can be described in terms of a scattering matrix

M = f +ign .or, where f is the non-spin-flip amplitude, g is the spin-flip amplitude, n is the normal to the production plane, and ~ are the Pauli spin matrices, f and g are complex functions of c.m. energy, E, and scattering angle, 0. There are thus four real numbers 1 Present address: DESY-F1, Notkestrasse 85, 2000 Hamburg 52, Germany. 389

390

K. W. Bell et aL/ Spin-rotation measurements

defining the reaction at a given (E, 0). One, the overall phase, is unobservable. For an unpolarised target the differential cross-section

Zo--Ill = +

Igl 2 ,

and the final-state polarisation, parallel to n, is P = - 2 Im

(f*g)/(lfl2+ Igl=).

Both Io and P are invariant under the transformation

(f:t= ig) ~ exp {+ie (O))(f + ig), where e is an arbitrary real function of 0. This continuum ambiguity mixes high and low partial waves, and a unique partial-wave decomposition is impossible without additional assumptions, such as truncation of the partial-wave expansion [5] or a specific ansatz for the high partial waves [6]. If either of these is performed, the Barrelet ambiguity [6, 7], in which a finite set of solutions is obtained, remains. This is usually resolved by appeal to dominance by well-known resonances [1], or analyticity [8, 9]. With the aid of spin-rotation measurements, a more direct approach is possible. The formalism of Kelly et al. [10] defines a spin-rotation angle, 18, such that

( f - i g ~ =tan_l [ - 2 Ref*g'~ 18 - - a r g \ f + i g ] ~ Ifl=-Igl = J" Measurement of 18 then removes these ambiguities. 18 has a simple physical interpretation. In this experiment the target polarisation, Pt, is parallel to the beam direction, Iv. The final state polarisation vector is Pf = en + P t x / - ~ - - ~ (~ c o s 18 + n × 'IT sin 18).

The final state polarisation, projected onto the interaction plane, is equal to the initial state polarisation, multiplied by ~/~Z-p"Z, and rotated away from its initial direction by an angle 18. It is this phenomenon which allows 18 to be defined as a spin-rotation angle. The behaviour is illustrated in fig. 1. The parameters A and R are sometimes defined such that IoA - Iff-lgl

=,

/ o n - 2 Re (f'g).

Then A = (1 _ p 2 ) 1 / 2 c o s 3 ,

R = -(1 _p2)1/2 sin 3 ,

pE+A2+R2=

1.

This analysis is cast in terms of the variables (P, 18) rather than (P, A, R ) for several reasons [4], which we list below. (i) Knowledge of (P, 18) specifies completely the final state A polarisation (for a given initial state).

391

K. W. Bell et al. / Spin-rotation measurements

n =TI;x K

~

\

p

,/ POLARISATION IN cm FRAME DIRECTION

INI TIAL

FINAL STATE

t~

Pr

PT ~_p2 cos~ =

n x~

0

!PT~JI-p2 sin~3

n

0

P

PT A

=-PT

R

Fig. 1. Initial and final state polarisation vectors for the case of a target polarised parallel to the incident beam. Definitions valid in the c.m. frame.

(ii) /~ is determined from the direction of the largest a s y m m e t r y of A-decay in the production plane, not f r o m its magnitude. ~ is therefore not sensitive in first order to errors in estimating background subtraction. The p a r a m e t e r s A and R are most naturally found from the magnitude of the a s y m m e t r y and are therefore sensitive to background subtraction.

392

K. W. Bell et al. / Spin-rotation measurements

(iii) P and/~ have uncorrelated errors, as/~ is determined from the direction of an asymmetry in the production plane, and P from the magnitude of an asymmetry in the orthogonal direction. P and/3 are determined experimentally from the decay A ~ p~r-, for which the angular distribution of the proton, in the A c.m. frame, is given by --=--dN 1 (1 + a p dO 4~r

•

Pf)

where p is a unit vector along the proton direction and a is the A decay parameter (a = 0.642 [11]).

2. Experimental details The experiment was performed in an unseparated negative beam derived from the 7 GeV proton synchrotron, Nimrod, at the Rutherford Appleton Laboratory. The apparatus is illustrated in fig. 2, with a "typical" event overlaid. Much of the apparatus was the same as that used in a previous experiment and has been described before [2]. We therefore give only an outline description here. The beam had a momentum spread of 0.8% and each beam particle had its trajectory and momentum measured by a telescope of twelve I mm pitch MWPCs. There were typically 150 000 particles in a 700 ms spill. About 8% of events had two or more beam tracks and were rejected in the analysis. Electrons in the beam were vetoed by a low-pressure freon Cerenkov counter in the upstream part of the beam. A beam particle was defined in the event trigger by a signal in a beam counter, no signal in a halo veto counter and signals in the central portions of the last two beam chambers. For normal running a polarised target of 1, 2 propanediol (C3HsO2), of volume 35 cm 3, was used [12]. For about a third of the running a carbon target was substituted for background studies. The targets were mounted inside a short superconducting solenoid which produced a field of 2.5 T at the target. The coil was unusual in having a very wide opening angle (60 ° cone half-angle) to permit the escape of particles over a wide range of scattering angles. Target polarisations in excess of 80% were achieved over long runs. The polarisation was monitored to an accuracy of better than 1% over the entire running period. Both magnetic field and target polarisation directions were reversed periodically throughout the running. An interaction producing a neutral final state was defined by the absence of hits in a veto counter completely covering the exit cone from the target. The trigger for the reaction ~r-p ~ K °

+

[->7r+1r-

A

L "tr-p,

demanded a "beam. veto. (4 downstream particles)" coincidence. The "four

K. W. Bell et al.

/ Spin-rotation measurements

393

Time of flight /'-/

Optical spark ~ chambers,N~ Low- mass sp.chambers

[

2mm.~itch MWPCs n*

I

m

lmm pitch MWPCs

],I-

To spectrometer

\ 0too

Solenoid ryostat

c

Veto counter

Fig. 2. The central part of the apparatus. The 24 time-of-flight trigger counters form a ring covering the region up to 60° cone half-angle as seen from the target. The beam spectrometer and downstream spectrometer are not shown [2]. A notional event is indicated, ignoring track curvature in the field.

d o w n s t r e a m particles" r e q u i r e m e n t was o b t a i n e d f r o m a ring of 24 time-of-flight counters and a M W P C system. T h e principal detectors for o u t - g o i n g tracks were two m o d u l e s of optical spark c h a m b e r s placed as close to the m a g n e t as possible. M a n y d e c a y vertices were u p s t r e a m of these c h a m b e r s and in the strong magnetic field. T h e analysis hinges on the accurate reconstruction of the vertices, yet the extrapolation f r o m optical data in a relatively w e a k field to the vertex in the strong field was difficult. In o r d e r

394

K. W. Bell et al. / Spin-rotation measurements

tO improve the vertex determination eight low-mass magneto-strictive read-out spark chambers [13] were placed in the exit cone of the magnet. The read-out of these chambers had to be remote (outside the magnetic field) and this restricted the read-out to one plane per chamber. The extra measurements did, however, lead to a significant improvement in the vertex reconstruction and reduction in error matrix correlations. The measuring accuracy for sparks detected by read-outs at both ends of the magneto-strictive wands was 0.6 mm. These chambers were followed by the optical spark chambers. The first module was 1.3 m × 1.3 m in area with ten 1 cm gaps, and the second 2.25 m × 2.25 m with eight 1 cm gaps separated by 2 cm spaces. Lead-oxide vidicon cameras were used to read out the optical chambers. The position and intensity of each spark were recorded. In order to convert these digitisings into space points, two cameras at +5 ° to the normal were used to scan the side view, and two more the top view. The requirement to resolve the individual gaps of the smaller module leads to a limitation of the field of view such that the whole of the larger module could not be scanned by these cameras. Another two cameras, normal to the faces and with a wider field of view, were used to ensure full coverage of the larger module. The cameras were calibrated using grids at the front and rear of the modules which were exposed during special runs. Corrections were made for spark intensity effects and the drift of calibrations with time [14]. Forward-going particles were detected in the MWPC chambers of 2 mm pitch (4 planes, each measuring one coordinate) and a downstream spectrometer, as in the previous experiment [2].

3. Event reconstruction The first step in event reconstruction was to remove camera distortions. Digitisings from different cameras were then associated into space points. In the first instance the four high-resolution cameras were used and sparks reconstructed which were seen in all four views (a constrained fit can be made). Techniques were developed to handle cases where two sparks were not resolved in one view. Note that, because four cameras were used rather than three, there were no " b a d " directions of overlap or ambiguity. Sparks far out in the larger optical chamber were reconstructed using two main and one auxiliary cameras, or, in the corners, two auxiliary cameras only (in which case the reconstruction was unconstrained). Measuring errors were typically 0.6 mm on a 4-view spark. The next phase was to link these space points into chains corresponding to a single charged particle. This task was greatly complicated by the fringe field of the polarising magnet, which had axial symmetry and extended at several k G throughout most of the optical chambers. There were two main effects. (a) Displacement o f sparks from the true particle trajectory due to drift in the electric and magnetic fields.

395

K. W. Bell et al. / Spin-rotation measurements

(b) Distortion of particle trajectories. It was completely inadequate even for recognition purposes to describe trajectories by straight lines. In fact the field, although very inhomogeneous and with an unfavourable orientation, did provide a momentum measurement with an error A p / p ~ 0.8p (p in GeV/c). After correction for spark displacement the sparks and MWPC digitisings were linked into chains, special care being taken to handle ambiguous cases. For identification in the optical chambers a weighted line-fit method was devised to follow the curvature of the tracks. Sometimes extrapolation across the gap between the two chambers was difficult and a procedure was devised for linking chains together. After chain making, unassociated camera digitisings were examined and, where appropriate, associated with chains. Details are given elsewhere [15]. Tracks were fitted by integrating the equations of motion

1/2,

cpx" = e (x ' y ' B , - (1 + x '2)By + y 'Bz) (1 + x'2 + Y,2)

cpy" = e ((1 + y '2)B x - x 'y 'By - x 'Bz)(1 + x ,2 + Y,2)1/2,

where primes denote differentiation with respect to z (the beam direction). The values of X2 for the track fit, and its first and second derivatives with respect to the track parameters (x, y, x', y' at fixed z, and e / p c ) were used in an iterative fit, which generally converged after four or five iterations [16]. The method was motivated by the approach of Myrheim and Bugge [17], but in our case none of the field components or derivatives could be neglected. Facilities were incorporated to reiect badly measured points. The tracks so reconstructed were extrapolated upstream into the low-mass chambers, and digitisings were associated with them [15]. Candidate vees were then made out of pairs of tracks, provided that a combination of vees could be made which satisfied the trigger, and were consistent with the correct charge assignments. Vertex fits were made, and these and their error matrices used as input to kinematic fitting. It was verified by Monte Carlo studies that, although the vertex coordinates and outgoing momenta were highly correlated and the momenta poorly measured, the error matrix provided an accurate representation of the X2 surface in the neighbourhood of the true solution. This allowed the separation of kinematic fitting from the magnetic field analysis and vertex fitting. Kinematic fits were made to the hypothesis ~r-p ~ K°A using charge and momentum information (and the full error matrix) from vertex-fitting in a 9-constraint fit with both geometric and kinematic constraints.

4. Separation of ~'-Pt --~K°A events from background Various processes can give rise to the two-vee topology characteristic of this reaction: ~--p ~ K ° A from free protons, or from those bound in carbon or oxygen nuclei in the propanediol (and hence unpolarised), and 1r-p ~ K°2~° from both free

K. W. Bell et al. / Spin-rotation measurements

396

1780 MeVlc INTERACTION POINT

CUT

.J-L PROPANEDIOL DATA

03

lJ

100

I,--

Z W > W

CARBON DATA NORMALISED TO SAME INCIDENT FLUX

X2 < 40

xF

X

X

x

X X X

X

X

X J

0

,,

X, X

,

L

1

100 mm

Fig. 3. The reconstructed interaction point coordinate along the beam direction, at 1780 MeV/c. Results from propanediol and carbon target runs. (Carbon data rescaled to same incident beam on target.)

and bound protons. Other processes, such as 7r-p-~K°A~ "°, do not contribute significantly. The wanted process, , r - p ~ K°A from a free proton, was selected by the kinematic fitting. The background was reduced by cuts requiring the interaction point to be within the target, and by a cut on the X 2 of the kinematic fit. Fig. 3 shows the z coordinate of the reconstructed primary production vertex at 1 7 8 0 M e V / c beam momentum, selecting events with a X2 for the reaction ~r-p(free)-* K°A less than 40. A broad peak at the target location and a narrower one at the veto counter are seen, corresponding to their depths, 32 mm and 6 mm respectively. (The veto counter was slightly inefficient, particularly for reactions in it leading to neutral final states.) Subsidiary downstream vertices could be identified with interactions on matter in the d e t e c t o r . Also shown in fig. 3 is the same distribution for interactions on a carbon target, renormalised according to the target

K. W. Bell et al.

/ Spin-rotation measurements

397

mass and number of beam particles. The difference in target signals, and the similarity of signals from the veto counter (which contains free protons) is striking. Fig. 4 shows the X2 distribution of events with vertices falling in the target cut, again for propanediol and carbon runs. Detailed Monte Carlo simulation of the

1780 MeVlc

X 2 DIST.

200

I=--L PROPANEDIOL DATA

/

CARBON DATA NORMALISED TO SAME INCIDENT FLUX

CUT

u~ b--

1

z LU > LU

100

MONTE CARLO ESTIMATE OF ~ADDITIONAL BACKGROUND. K Y FROM H TARGET

m

0

50

Fig. 4. X2 distribution of events from interactions in the target showing propanediol and carbon data, and ¢r-p (free) -* K I Monte Carlo as a band above the carbon data. The wanted ¢r-p (free) -* Kit data should lie above this band within the propanediol data distribution.

398

K. W. Bell et al. / Spin-rotation measurements

apparatus was made [18], and in this instance used to study the backgrounds. The X 2 distribution from Monte Carlo carbon events is in good agreement with that shown. The calculated contribution from lr-p(free)-~K°,Y ° is shown as a band above the carbon-target results. Based on inspection of such X 2 distributions, a X 2 cut was chosen and all events below the X 2 cut were assigned to the K ° A final state. From the X 2 distributions of the data and those derived from Monte Carlo rr-p(free)-, K°A, we conclude that, at 1780 M e V / c , for a X 2 cut of 30 (used for the results quoted in this paper), the fraction of events which are genuinely ~--p(free)--, K°A is 81 ± 2%, and the fraction which are from the K°,Y° state is 9% (from free or bound protons). The corresponding figures at 1 3 4 0 M e V / c are 9 1 + 2% and 1.5%, and at 2240 M e V / c 77 + 2% and 15%. The errors represent the uncertainties in the Monte Carlo and the residual discrepancies between Monte Carlo and data X 2 distributions. We conclude that we have observed predominantly the wanted process ~r-pt ~ K °A. As discussed below, the results do not depend on an accurate knowledge of these background fractions. Loss of events involving low-momentum particles was investigated. No significant difference between data and Monte Carlo was observed in the numbers of lowmomentum pions or protons. This represents an improvement on the situation in the previous experiment [2] which is due to the ability of the track-finding procedure to follow tracks deviating from a straight line. The determination of P and/3 was performed both with and without momentum cuts of 70 M e V / c for pions and 300 M e V / c for protons. There were significant differences only in the bin 0.9 < cos 0 < 1.0. The results quoted below used these cuts. The final event sample contained between 700 and 1000 events at each momentum: 1.34, 1.52, 1.71, 1.78, 1.88, 2.00 and 2.24 G e V / c .

5. Extraction of P and ~ values: elimination ot biases P and B were determined at each energy for bins of 0.1 in cos 8 from the A ~ p~rdecay angular distribution, following the procedure of Saxon and Whittaker [4]. We define polar and azimuthal angles ~ and ~ in the A rest frame such that the proton flight direction p has components, p • n = cos 7 ,

p • K = sin ~ cos ~b,

p • (n x K ) = sin ~7 sin $ ,

where K is a unit vector in the kaon direction. Then the angular distribution in sect. 1 becomes. 4~-

d2N = 1 + a (P cos 71 + Ptx/1-S-~ sin n cos (~ - 0 - $ ) ) , d cos r/dO

The observed angular distribution is modified by acceptance losses. Let the

K. W. Bell et al. / Spin-rotation measurements

399

apparatus acceptance be

W = W ( O , cos-o,,b,K),

0
where K labels the magnetic field polarity (1< = +1). Then define

A(o)=ff

W(0, cos , , ~b, K = 1) dcos ~ d~b,

Bl(O)= I f cos rlW dcos rl ddp/A(O) , B2(0) =

f f sin 7/cos (~b +O)W dcos ~t dd:/A(O),

B3(0) =

I I sin 7/sin (~b +O)W dsin ~/d~b/A(O),

i.e. B1, B2, B3 are the first moments of the acceptance. Typical Monte Carlo calculations of A, B1, B2 and B3 are shown in fig. 5. The acceptance, A, is a few percent because of the branching ratios of the decays [11] and the loss of decays upstream of the veto counter. The moments are smoothly varying functions of angle, and substantially smaller than the maximum possible values (-1 ~
L(P, S, fl) = Y~In (NdD~), i

where the sum runs over all events in a given cos 0 bin. The signal purity factor, S, is the fraction of events which are K°A on free hydrogen (0 < S < 1). Here

Ni = 1 +a(P cos ~i + S P [ , f i - : ~ sin r/i cos (0i +~bi - f l ) ) , D~ = 1 + a (B1Px ~+ SP[ ~/T:-~ [B2 cos ~ +B3 sin fl]). In the case B 21,2,3 << 1, approximated by the apparatus used here, the contribution to the likelihood from D~ is

- a ( B 1 P ~i Ki+ S ' ~ - Z - ~ [B2 COS~-+ B3 sin ~] ~/PI).

400

K. W. Bell et al. / Spin-rotation measurements i

I

I

A .05

I

i

,

i

' I

I i

!

REV FIELD -.25

B1 .25 -

0

B2 0

'}

i

-.25

'}

f

~t B3 0

f

{

{

t

{

{

--.25

I

-0.5

0.5

0.0

1.0

cos O Fig. 5. Event acceptance (A) and bias moments (Bb B2, B3), calculated by Monte Carlo for data at 2000 MeV/c, as a function of c.m. scattering angle, cos 0.

K. W. Bell et al. / Spin-rotation measurements

401

Thus, for equal samples of data with both field polarities (Y~iKi =0) and both polarisations (Y~iP~ = 0), the values of B1.2.3 have no effect on the answer. Roughly equal quantities of data were taken in these conditions, to minimise these acceptance biases. However, as a further check, the analysis was repeated using each magnet polarity separately and each polarisation orientation separately, and the discrepancies calculated. This showed that the bias on P and/3 arising from this source was negligible. The question of biases arising from backgrounds (S < 1) was also investigated. It was found that the values of P and/3 obtained and their errors were insensitive to assumed values of the purity factor S; no significant differences were obtained with S = 0.8 or S = 1 (cf. the measured value S = 0.81 + 0.02 at 1780 MeV/c given in sect. 4 above). Any contribution to the anisotropy of the A-decay azimuth angle distribution, ~b, from interactions on bound protons should be due only to random fluctuations. A study was made in which data taken with a carbon target were analysed as though they had been taken with a target of PT = 0.8. The systematic error in /3 due to the background from bound protons was estimated from the variation of the likelihood function with/3, for the 1880 MeV/c and 2000 MeV/c data. RMS errors of between 30 and 90 mrad were found in the different cos 0 bins, which are negligible after addition in quadrature to the statistical errors on /3. Similar results are expected at the other beam momenta. This verifies the assertion, made earlier, that the measurement of/3 is not sensitive to errors in background subtraction. Any bias due to K,Y production from polarised protons can readily be estimated. Consider a sample of events of fraction f from K,Y and ( 1 - f ) from KA. (From Monte Carlo estimates, f = 0.05 at 1780 MeV/c.) Then the final state A polarisation in the production plane is P, qr]-Z~Ka (1--f) from KA and --}P,f,~Z-~K~ from K,Y. The factor -~ arises from depolarisation in the ,Y°~Ay decay. The angle between these is unknown, so that the RMS deviation of the resultant from the KA polarisation vector is given by 1 _f/{(1 --PK~)/( 2 1 --PKa)} 2 1/2 • 342 1 The factor in brackets is only rarely large, so that a typical deviation is 30 mrad, negligible in comparison with the measuring errors. The K ~ fraction can, however, bias P as this is determined from the magnitude of the asymmetry component normal to the production plane. (The factor ~/~-z-P~ in the likelihood is effective in constraining P only when P is close to 1, as can be deduced from insensitivity of the fit to the value of S.) It is expected that P(measured) = fP(true), with a small scatter resulting from the K~ polarisation. Such an effect was looked for in the data by changing the g2 cut from 30 to 15. This removed 30% of KA

TABLE 1 Measured values of P and/3 cos 0 1340 MeV/c - 0 . 2 to - 0 . 1 - 0 . 1 to 0.0 0.0 to 0.1 0.1 to 0.2 0.2 to 0.3 0.3 to 0.4 0.4 to 0.5 0.5 to 0.6 0.6to 0.7 0.7 to 0.8 0.8 to 0.9 0.9 to 1.0 1520 MeV/c - 0 . 2 to - 0 . 1 - 0 . 1 to 0.0 0.0 to 0.1 0.1 to 0.2 0.2 to 0.3 0.3 to 0.4 0.4 to 0.5 0.5 to 0.6 0.6 to 0.7 0.7 to 0.8 0.8to 0.9 0.9 to 1.0 1710 MeV/c - 0 . 1 to 0.0 O.Oto 0.1 0.1 to 0.2 0.2 to 0.3 0.3 to 0.4 0.4 to 0.5 0.5 to 0.6 0.6 to 0.7 0.7to 0.8 0.8 to 0.9 0.9 to 1.0 1780 MeV/c - 0 . 2 to - 0 . 1 - 0 . 1 to 0.0 0.0 to 0.1 0.1 to 0.2 0.2 to 0.3 0.3 to 0.4 0.4 to 0.5 0.5 to 0.6 0.6 to 0.7 0 . 7 t o 0.8 0.8 to 0.9 0.9 to 1.0

/3 (deg)

62 + 45 62+49 884-30 484-51 914-43 904-55 974-26 74±51 -1254-130 -7±45 --59±91

P (this experiment)

0.14 4- 0.56"~ 0.454-0.40) 0.434-0.33 0.834-0.20 0.524-0.31 0.884-0.15 0.674-0.18 0.924-0.11 0.994-0.08 0,824-0.20 0.984-0.14 0.844-0.29

P (refs. [1, 2])

P (combined

0.45 .4-O. 16

0.43 4- O.14

0.534-0.17 0.824-0.15 0,674-0.14 0.824-0.14 0.834-0.1'2 0.874-0.11 1,174-0.09 1.154-0.09 1.044-0.10 0.374-0.18

0.514-0.15 0.824-0.12 0.64+0.13 0.85±0.10 0.78±0.10 0.894-0.08 1 . 0 7 , 0.06 1.094-0.08 1.024-0.08 0,504-0.15

-84±27 1074-25 77±22 1194-58 104±25 954-46 914-46 ---1234-29 -106±56

0.794-0.50 -0.034-0.41 0.384-0.30 0.174-0.24 0.314-0.30 0.674-0.19 0.914-0.11 0.784-0.17 0.994-0.06 0.96:t:0.13 0.734-0.19 0.454-0.28

0.304-0.44 -0.584-0.40 0.25±0.32 0.534-0.30 0,084-0.31 0.984-0.23 0.934-0.22 1.4 ±0.2 1.3 4-0.2 0,974-0.22 1.0 ±0.2 0.554-0.25

0.50±0.33 -0.30±0.29 0.32±0.22 0.314-0.19 0.194-0.21 0.784-0.14 0.914-0,10 1,04±0,13 1.014-0.06 0.964-0,12 0,854-0,14 0.50±0,19

1194-51 1384-42 1164-42 874-47 704-28 554-29 -16±32 --161±72 -1024-34 -1784-49

-0.524-0.49 -0.634-0.29 -0,754-0.24 -0.094-0.34 -0.244-0.26 0.304-0.28 0.50±0.25 0.89±0.20 0.944-0.14 0.41±0.32 0,194-0.45

-0.184-0.65 - 1 . 9 ±0.6 -0.924-0.34 -0.204-0.34 0.074-0.34 0.184-0.38 0.66±0.28 0.804-0.25 1.1 ±0.2 0.934-0.22 0.574-0.26

-0.404-0.38 -0,874-0.26 -0,804-0.20 -0,154-0.24 -0.13±0.21 0.26±0.22 0,574-0.19 0.854-0.15 0.99±0.11 0.75±0.18 0.484-0.22

0.02 ± 1.43 -0.674-0.32 -0.624-0'.35 -0.66±0.30 -0.384-0.28 -0.094-0.26 0.34±0.22 0.434-0.27 0.80±0.25 0.51±0.23 0.97±0.10 0.89±0.30

-- 1 . 3 +0.3 -0.59±0.31 -0.73±0.38 -0.59±0.28 -0.19±0.28 0.59±0.24 0.914-0.20 0.84±0.19 0,834-0.19 0.97±0.18 0.62±0.18

0.02 ± 1.43 -1.03±0.22 -0.604-0.23 -0.694-0.24 -0.49±0.20 -0.144-0.19 0.464-0.16 0.734-0.16 0.824-0.15 0.704-0.15 0.97±0.09 0.70±0.15

109 ± 81 171±38 1054-41 131±48 944-45 234-30 854-32 734-40 -384-55 -674-35 -1704-107

K. W. Bell et al. / Spin-rotation measurements

403

TABLE 1-...-continued cos 0

0 (deg)

1880 M e V / c -0.2 to -0.I -0.I to 0.0

0.0 to 0.1 0.1 to 0.2 0.2 to 0.3 0.3 to 0.4 0.4 to 0.5 0.5 to 0.6 0.6 to 0.7 0.7 to 0.8 0.8 to 0.9 0.9 to 1.0 2000 MeV/c -0.2 to -0.1 -0.1 to 0.0 0.0 to 0.1 0.1 to 0.2 0.2 to 0.3 0.3 to 0.4 0.4 to 0.5 0.5 to 0.6 0.6 to 0.7 0.7 to 0.8 0.8to 0.9 0.9 to 1.0 2240 MeV/c O.Oto 0.1

P (this experiment)

P (refs. [1, 2])

P (combined)

178±49 53±86

-0.47±0.50 -0.32±0.45

-1.4 ±0.6 -1.2 ±0.3

-0.85±0.38 -0.92±0.24

15±44 -172±53 101±23 63±27 50±21 56±42 9±27 -39+43 -97±41 -151±70

-0.73±0.30 -0.79±0.26 -0.21±0.26 0.01±0.24 0.34±0.21 0.36±0.25 0.16±0.27 0.74±0.20 0.69±0.25 0.92±0.17

-1.0 ±0.3 -1.3 ±0.2 -0.06±0.30 -0.04±0.26 -0.04±0.24 0.13±0.27 0.55±0.23 0.63±0.23 0.77±0.20 0.81±0.19

-0.86±0.21 -0.99±0.16 -0.14±0.20 -0.01±0.18 0.18±0.16 0.25±0.19 0.39±0.18 0.70±0.15 0.73±0.16 0.87±0.12

-49±61 -144±73 139±31 59+29 83 ± 37 72±25 12±32 14±26 61±37 -121±31 --

-0.61±0.53 -0.97±0.18 -0.50±0.52 -0.67±0.25 -0.70±0.19 -0.51 ± 0.24 0.00±0.26 -0.41±0.23 0.36±0.22 0.52±0.22 0.52±0.24 0.93±0.25

-0.50±0.56 -1.6 ±0.6 -0.91±0.43 -0.76±0.39 -0.84±0.31 -0.45 ± 0.29 -0.77±0.24 0.10±0.26 0.17±0.27 0.58±0.32 0.43±0.21 0.46±0.19

-0.55 ±0.38 -1.02±0.17 -0.74±0.33 -0.70±0.21 -0.74±0.16 -0.49 ± 0.18 -0.40±0.18 -0.19±0.17 0.28±0.17 0.54±0.18 0.46±0.16 0.63±0.15

-72±37

0.1 to 0.2 to 0.3 to 0.4 to

0.2 0.3 0.4 0.5

76±40 -168±92 32±32 71±52

-0.41±0.44 0.05±0.54 -0.91±0.32 -0.57±0.27 -0.85±0.22

--0.18±0.45 -1.1 ±0.3 -0.71 ±0.31 -0.86±0.22

-0.41±0.44 -0.09±0.34 -0.99±0.21 -0.63±0,20 -0.85±0.16

0.5 to 0.6 to 0.7 to 0.8 to 0.9to

0.6 0.7 0.8 0.9 1.0

30±44 30±96 1±29 --143±123

-0.83±0.21 -0.80±0.32 -0.11±0.30 1.00±0.15 0.97±0.30

-1.0 ±0.2 -0.56±0.25 0.33±0.22 1.0±0.2 0.37±0.16

-0.92±0.15 -0.65±0.20 0.18+0.18 1.00±0.12 0.50±0.14

e v e n t s b u t h a l v e d t h e K Z fraction. W i t h i n an e r r o r of 3 % on an e x p e c t e d shift of 5 % n o effect was seen. W e c o n c l u d e t h a t n o scaling of P d u e to K S c o n t a m i n a t i o n is justified, b u t t h a t a s y s t e m a t i c e r r o r o n P s h o u l d b e q u o t e d , z i p = 0 . 0 1 5 P at 1340 M e V / c

rising to 0 . 0 9 P a n d 0 . 1 5 P at 1780 a n d 2 2 4 0 M e V / c

respectively.

This e r r o r is n o t i n c l u d e d in t h e e r r o r s g iv e n below. T o s u m m a r i s e , w e h a v e l o o k e d f o r biases o n t h e P a n d / ~ / r e s u l t s f r o m i n c o r r e c t e v a l u a t i o n of t h e a c c e p t a n c e , a n d f r o m c o n t a m i n a t i o n by u n w a n t e d p r o c e s s e s , e i t h e r f r o m i n t e r a c t i o n s o n b o u n d p r o t o n s , o r f r o m t h e r e a c t i o n ~ - - p --) K°,Y °. T h e r e

404

K. W. Bell et al.

/ Spin-rotation measurements

is a resulting systematic error on P, as stated above, but no significant bias or additional error on/~. Table 1 shows the measured values of P at the seven incident m o m e n t a , and compares them with the results of our previous experiments [1, 2]. They are statistically compatible and we therefore quote also a combined value which is shown in fig. 6. Table 1 and fig. 7 show the measured values of ~, expressed in the range - 1 8 0 " to 180". There are no previous m e a s u r e m e n t s of/3 for comparison.

¢

13L,O MeV/c

1520

I

I

I

•

\

"I

I

"I

0

Tt-p --~K°A P v cos e

0

Fig. 6. Polarisation measurements at the various beam momenta. Results from this experiment combined with refs. [1, 2]. The curves show the fit of ref. [2] (dashed line), and of this analysis (solid line).

K. W. Bell et al. / Spin-rotation measurements

405

0 1880

.

T

I

-1

0

lZ- p .-.~ Ko A

13 v cos

"N -1

O

I 0

Fig. 7. Spin-rotation measurements at the various beam momenta. The curves show the prediction of ref. [2] (dashed line), and of this analysis (solid line).

From comparison of the behaviour of P and/~ as a function of cos 0, in figs. 6 and 7, it can be seen that at cos O = + 1 both P and/3 are zero (spin-flip amplitude g = 0). Also when P goes close to +1,/3 changes rapidly by 180 °, as expected. These measurements of/3 form the kernel of this paper.

6. Partial-wave analysis A partial-wave analysis of these data, together with our earlier measurements on P and do-/dO [1, 2] has been made. No other data were used as there are inconsistencies within the world data set which tend to mask the physics. (See also refs. [6, 19].) The data set used has measurements of P and dot/d/2 at 22 momenta from 931 to 2340 M e V / c , and of/3 at seven momenta. In this analysis fits were made to the combined measurements of P from this and our earlier work.

406

K. W.

Bell et al. / Spin-rotation measurements

The dashed curves on figs. 6 and 7 show the predictions of the results of the analysis of ref. [2], without any further optimisation. The measurements of P are described well by the prediction. This is not surprising, as P has been measured previously. The level of agreement between measured and predicted values of is significant, in view of the remarks of sect. 1. The overall g 2 is 1115 for 795 degrees of freedom (x2/DF = 1.40), and for the spin-rotation measurements X2 = 124 for 72 bins (x2/bin = 1.72). It is clear that this prediction from our previous partial-wave analysis represents the new measurements well. We decided, therefore, to look for improved fits in the neighbourhood of the results of our previous work. An energy-dependent partial-wave analysis was performed exactly as described in refs. [2, 6]. Nonresonant and higher waves were represented by a reggeised K*-exchange model [6]. The preferred solution is shown in table 2. It has g 2 = 1072 overall and ~2 = 86 for the spin-rotation data. The results of the fit are indicated by a solid line on fig. 8. We also show in table 2 resonance parameters from ~rN analyses [8, 9], from QCD models [20], and couplings predicted by SU(6)w [21]. The KA branching ratios given in table 2 were obtained using ~'N couplings from refs. [8, 9]. The sign and phase conventions are as given in ref. [2]. No errors are quoted on our results in table 2. We believe that the energydependent partial-wave analysis technique adopted is not capable of delivering meaningful errors, as it does not take into account systematic errors due to the choice of parametric form. From studies of runs in which parameters are altered, we have concluded that disagreements in mass or width of under 0.1 GeV are probably not significant. Coupling magnitudes are broadly valid to +30% and phase differences to 45 °. There is also the possibility of an overall phase error altering slowly as a function of energy, so that phase differences are much more reliable when compared over small than over large energy gaps. More sophisticated analysis techniques which yield a meaningful error, such as those used in ~rN--> 7rN analyses [8, 9], are not suitable, given the statistical accuracy of the experimental data. The argand diagrams for waves up to H19 are shown in fig. 8. We make the following observations about the partial waves. $11, P13, D~3, D15: we find good fits using the standard masses and widths. The signs of the couplings are all relatively real and positive, as required by SU(6)w, and of the magnitude expected from SU(6)w. The magnitudes of the SH and D13 couplings are of particular interest. In SU(6)w these are assigned to 48[70, 1-] states and hence should decouple from KA, unless mixed with the 28[70, 1-]S~1 and D13 states. In practice the SH coupling is found to be large, and the D~3 coupling small. This has been explained by the QCD hyperfine interaction, as used by Isgur and Karl [20, 22]. The one-gluon exchange term becomes an effective diquark hamiltonian Hhyp= A ~ q r ( S l • S 2 8 3 ( r ) + ~ (3(S~ " P)(S2 " : ) - S I

• $2)).

K. W. Bell et al. / Spin-rotation measurements

407

TABLE 2 Fitted resonance parameters

$11 this analysis Cutkosky Hoehler Isgur & Karl Litchfield Pll this analysis Cutkosky Hoehler Isgur & Karl P13 this analysis Cutkosky Hoehler Isgur & Karl Litchfield D~3 this analysis Cutkosky Hoehler Isgur & Karl Litchfield D~3 this analysis Cutkosky Hoehler D15 this analysis Cutkosky Hoehler Isgur & Karl Litchfield D~5 this analysis Cutkosky Hoehler FI7 this analysis Cutkosky Hoehler GI7 this analysis Cutkosky Hoehler G19 this analysis Cutkosky Hoehler H19 this analysis b) Cutkosky Hoehler

Mass (GeV)

Width (GeV)

~/~x'

Phase

Branching ratio

1.68 a) 1.65 ± 0.03 1.67±0.01 1.66

0.12 a) 0.15 ± 0.4 0.18±0.2

-0.22

0")

8%

1.73~) 1.70 ± 0.05 1.72±0.01 1.70 1.69 a) 1.70±0.05 1.71±0.02 1.70

0.54 0.09 ± 0.03 0.12±0.02

-0.145 +0.16

-23 °

13%

-0.09

-21"

5%

1.65") 1.67 ± 0.03 1.73 ± 0.02 1.75

0.06 a) 0.09 ± 0.04 0.11 ± 0.03

1.92 11.88±0.10 [2.07±0.08 2.08 + 0.02 1.67 a) 1.67+0.01 1.68±0.01 1.67

0.32 0.19±0.06 0.30±0.10 0.26 + 0.04 0.15 a) 0.16±0.02 0.12+0.15

1.90 2.18 ± 0.08 2.23 ± 0.03 1.99 a) 1.97±0.05 2.00±0.15 2.17 a) 2.20±0.07 2.14 ± 0.01 2.25 a) 2.25 ± 0.08 2.27±0.02 2.25 2.23 ± 0.08 2.20±0.01

0.13 0.4 ± 0.1 0.31 + 0.05 0.30 a) 0.35±0.12 0.35±0.10 0.25 a) 0.50+0.15 0.39 ± 0.03 0.30a) 0.30 ± 0.04 0.48±0.12 0.30 0.50 ± 0.15 0.36±0.30

a) Fixed in the final fit. b) Omitted from the final fit.

0.13 a) 0.12±0.07 0.19±0.03

-0.07 -0.012

-0.012 +0.04

21"

0.2%

-100"

2.1%

-0.01

-64*

0.1%

0.0 -0.03

2°

1.4%

+0.01

-63 °

0.2%

-0.02

-58 °

0.3%

-0.02

-8 °

0.3%

+0.02

37 °

0.2%

408

K. W. Bell et.al. / Spin-rotation measurements

0.2

$11

L/

P13

0.1

I

0.1

0.1

°,3

(

I

-0.1

o11

o11 '

l

Dis 1:15

I

1

.05

.05

-.0~ .05

.05

%

0s

G19 H19

).05

D5

0

I

.05

(

1

.05

-.05

Fig. 8. Argand plots for *r-p~K°A. The Fls and H 1 9 a r e described by the partial-wave projection of the K*-exehangeterm. This term is shown, dashed, in the F17 and Gi9 plots. The contact term mixes the $11 states substantially ( - - 3 0 ° mixing angle). The tensor term does not mix the D13 states substantially. The D~5 state is also assigned to the 48[70, 1-] and therefore predicted to have a very small coupling, as observed. However, no acceptable fit was obtained without this resonance. PH: as we found before [2], the width of resonance is not in good agreement with that found in ,rN analyses. Attempts to produce a good fit with a narrow PH plus a third-order polynomial background, or by adding a PH (2100) as suggested by IrN analysis, were not successful. The SU(6)w status of the Pl1(1710) is not settled. Hoehler assigns it to a 48[70, 2+], which would decouple from KA. This

K. W. Bell et al. / Spin-rotation measurements

409

raises the interesting possibility that we are observing a different state from the normal P 11(1710). One candidate would be a hybrid (qqqg) baryon. The lowest-lying such state would be a Px~ state with a mass which could be in this region, with another PI~ and P13 state lying a few hundred MeV higher [23]. Such a state might well be broad [24], and would couple with comparable strengths to both strange and non-strange channels [25]. DI3, DIs: We find a need for a second D13, possibly consistent in mass and width with one found by Cutkosky, and a second D15. Attempts to fit with a D13 at 2.2 GeV instead of or in addition to this state were not compelling. It is of interest to compare the similarity of the argand plots to the ~ r - p o ~ ° n analysis of Baker et al. [26]. F17, G~7, G19, H19: acceptable fits are found using standard values for masses and widths, and all the couplings are of similar size. Since removal of the G17 resonance produces a dramatic degradation of the fit, this state is required in K°A. The other couplings are not on such a strong footing. Removal of the Ft7, G~9 and H19 resonances (replacing them in turn with a reggeised K*-exchange background) results in X 2 changes of +2, +10 and - 1 4 respectively. The H19 state is therefore not required by this analysis and is not in the best fit shown. However, we have listed it in the table for the following reason. The argand plots for the F17 and G19 waves are very similar with and without the resonances. The K* exchange argand loops are shown in fig. 8, indicated by a dashed line. It is therefore not surprising that the changes in X 2 on adding resonances in these waves are modest, as there is little phenomenological difference. We do not require couplings to F15 (1.68) or F1s(1.88). This analysis does not bear directly on the uniqueness of the above solution. However, we remark that the X 2 fit to the new results (the spin-rotation data) is acceptable, both for the initial and final fits, so that the scope for very different solutions has been limited. In conclusion, we have measured for the first time spin-rotation angles in the reaction ~r-p-* K°A. The results obtained are broadly consistent with our previous partial-wave analysis. A new partial-wave analysis yields additional information on resonance couplings. This experiment would not have been possible without the dedication of the support staff of the Rutherford Appleton Laboratory; in particular we wish to thank the polarised target group, the Nimrod operating crew, Physics Apparatus Group and the Computing Division.

References [1] R.D. Baker et al., Nucl. Phys. B141 (1978) 29 [2] D.H. Saxon et al., Nucl. Phys. B162 (1980) 522 [3] P. Astbury et al., Nucl. Phys. B99 (1975) 30

410

K. W. Bell et al. / Spin-rotation measurements

[4] D.H. Saxon and J.B. Whittaker, Z. Phys. C9 (1981) 35 [5] D. Atkinson, Proc. Conf. on baryon resonances, eds. R.T. Ross and D.H. Saxon (Oxford, 1976) p. 189 [6] R.D. Baker et al., Nucl. Phys. B126 (1977) 365 [7] E. Barrelet, Proc. Conf. on baryon resonances, eds. R.T. Ross and D.H. Saxon (Oxford, 1976) p. 175; Nuovo Cim. 8A (1972) 331; D.M. Chew, Phys. Rev. D18 (1978) 2368 [8] R.E. Cutkosky et al., Phys. Rev. D20 (1979) 2804, 2839 [9] (3. H6hler et al., Physik Daten 12-1 (1979) [10] R.L. Kelly, J.C. Sandusky and R.E. Cutkosky, Phys. Rev. D10 (1974) 2309 [11] Particle Data Group, Phys. Lett 111B (1982) 1 [12] R.W. Newport et al., AIP Conf. Proc. no 51 (Argonne, 1978) p. 48, presented by D.H. Saxon, M. Bail, P.T.M. Clee, N. Cunliffe and J. Simkin, Proc. 5th Int. Conf. on magnet technology, eds. N. Sacchetti et al. (Rome, 1975) p. 606 [13] H.M. Daley, Rutherford Report RL-82-086 [14] R. Maybury and H.M. Daley, Rutherford Report RL-82-085 [15] R. Maybury and H.M. Daley, Rutherford Report RL-82-087 [16] J.C. Hart and D.H. Saxon, Rutherford Report RL-83-006 [17] J. Myrheim a~d L. Bugge, Nucl. Instr. Meth. 160 (1979) 43 [18] J.B. Whittaker, Rutherford Report RL-80-101 (1981) [19] M. Neveu, Proc. Conf. on baryon resonances, ed. R.T. Ross and D.H. Saxon (Oxford, 1976) p. 99 [20] N. Isgur and (3. Karl, Phys. Lett 72B (1977) 109; R. Koniuk, Proc. 4th Int. Conf. on baryon resonances, ed. N. Isgur (Toronto, 1980) p. 217 [21] P.J. Litchfieid, R.J. Cashmore and A.J.G. Hey, Proc. Conf. on baryon resonances, eds. R.T. Ross and D.H. Saxon (Oxford, 1976) p. 477 [22] A.J.(3. Hey, Proc. 4th Int. Conf. on baryon resonances, ed. N. Isgur (Toronto, 1980) p. 223 [23] E. Barnes and F.E. Close, Phys. Lett. 123B (1983) 89 [24] F. de Viron, Louvain preprint UCL-IPT-82-34 [25] F.E. Close and S. Monaghan, Phys. Rev. D23 (1981) 2098; A.K.A. Maciel and J.E. Paton, Nucl. Phys. B197 (1982) 201 [26] R.D. Baker et aL, Nucl. Phys. B156 (1979) 93