Partial-wave analysis of K−p → π∓Σ± (1385) between 1775–2170 MeV including new data below 1960 MeV

Nuclear Physics B143 (1978) 189-231 © North-Holland Pubhshmg Company

PARTIAL-WAVE ANALYSIS OF K - p "* n ; ~ + ( 1 3 8 5 ) BETWEEN 1 7 7 5 - 2 1 7 0 MeV INCLUDING NEW DATA BELOW 1960 MeV

Rutherford Laboratory - Imperial College Collaboration W. CAMERON, B. F R A N E K , G.P GOPAL, G.E. KALMUS, A.C. McPHERSON and R T ROSS *

Rutherford Laboratory T.C. BACON, I BUTTERWORTH, R W.M. HUGHES, P NEWHAM, R A. STERN and R.M. WATERS

Imperial College, London Received 1 March 1978

New data are presented for the reacUon K - p ~ A~r+n- at 11 energies between 1775 and 1957 MeV m the centre-of-mass New values for the masses and widths of the ~-+(1385) are gwen The differential cross sections and the complete spm density matrices for the reactions K - p --} 7r+-~(1385) were extracted from these data using also the information from the A decay An energy-dependent partial-wave analysis has been carried out over the c m range 1775-2170 MeV also usmg data from an earher experiment. Comparisons between the observed resonant amplitudes and SU(3) and SU(6)W ®0(3) predlcUons have been made

1. Introduction The reactmn K - p ~ Air+ 7r~plr-

(1)

has been investigated at 11 incident m o m e n ta between 0.96 and 1.355 GeV/e. The quas~ two-body processes K - p -} rr- •+(1385),

(2)

1r+~-(1385),

(3)

* Present address Unwerslty of Michigan, Physics Department, Ann Arbor, Mtchlgan 48109, USA 189

190

Rutherford Laboratory - Imperial College Collaboration/K-p -* n~ ~± (1385)

dormnate reaction (1) and data for these channels have been extracted using a four variable fitting technique. The new high-statistics data have then been combined with those of the CRSS Collaboration over the momentum range 1.263 to 1.843 GeV/c [1], and a partialwave analysis has been carried out over the c.m. energy range 1775 to 2170 MeV.

2. Data

The new data for the reaction K - p ~ Arr+n -

used m this analysis come from an exposure of the CERN 2m HBC to a K - beam at 11 equally spaced incident momenta between 0.96 GeV/c and 1.355 GeV/c. Only events with two outgoing charged particles and seen neutral decay have been used. Detads of the exposure, scanning and measuring, beam calibration and cross-section normahsation are gwen m an earher pubhcatlon [2]. Events with two-prong plus V ° topology arise not only from reaction (1) but also from reactions K - p ~ K°prr~r+rr-,

(4)

K - p ~ Z°rr+rt -

l_, A~, ~prr- .

(5)

Kinematical amblgmties between reactions (1) and (4) were resolved on the basis of lomsaUon measurements. Events which were kmematically ambiguous between reaeUons (1) and (5) proved overwhelmingly to be from reaction (1), as may be seen from the distribution of the missing mass to the rrrr system (fig. 1). Also when ambiguous events from any missing mass region of fig. 1 are assigned to reaction (5) a marked amsotropy m the Z ~ A'), decay angular distribution Is observed. Accor&ngly, all ambiguous events have been assigned to reaction (1). In order to correct for biases m the data, the following cuts and weights were applied. (a) A cut of 0.3 cm (Imm) was apphed to the projected decay length of the A and the remaining events were each weighted by the inverse probabdlty that the A would decay between lmm and the boundary of the fiduclal volume. P = e x p ( - l l / f ) - exp(-12fi),

(6)

where ll = lmm/COS or, o~is the &p of the A, 12 is the potentml decay length from the

Rutherford Laboratory - Imperial College Collaboration/K-p -~ Ir~~±(1385)

191

1100t I 90C zLU 70C LLI

,, 50£ 0 Zo 30C 10C i

12

14

MISSING MASS-SQUARED (GeV/c2)2---~ Ftg 1 The mlssmg mass-squared distribution to the rr+rr- system for (A) unique A0~r+Trevents, (B) umque r-O~r+~r- events, (C) events which are ambiguous between AOrr+zr- and ~01r+zr-

production vertex to the boundary of the fiduclal volume and l = pcT/Mwith T(A) = 2.61 × 10 - l ° s [3] a n d p a n d M are the momentum and mass of the A. (b) Losses of A's due to slow particles from the A decay were corrected for by imposing minimum momentum cuts. These correspond to cuts in the cos 8 distribution where 8 IS the angle between the decay track in the rest frame of the A and the A direction. A minimum momentum cut of 54 MeV/c was chosen for the plon but no cut was necessary for the proton A weight W = 2/(1 - cos 81) was applied to the remaining events where 81 is the value of 8 corresponding to a 54 MeV/c plon from the observed A. The posslblhty of a loss of events with the decay plane perpendicular to the chamber window was investigated. No such loss was observed. The final weight for each event includes scanning and throughput efficlencles. Numbers of events remaining after the cuts together with the average weight and the value of the cross section for reaction (1) at each of the incident momenta are gwen in table 1. The total number of events used was 23 885 The cross section as a function of momentum is shown m fig. 2 and is in good agreement with the results of earher experiments [ 4 - 6 ] . Dahtz plots, together with their projections are shown in fig. 3 for the lowest, central and the highest incident momenta. The prominent features to be seen are two bands corresponding to the ~ - ( 1 3 8 5 ) and the ~+(1385) resonances. Some p production is also present at higher energies The An + and ATr- mass-squared distributions in the region of the Z-+(1385) (1 68
1775 1796 1815 1833 1852 1870 1889 1907 1926 1941 1957

0 960 1 005 1 045 1 085 1 125 1 165 1 205 1 245 1 285 1 320 1 355

1508 1350 2235 1970 2058 2214 2182 2593 2668 2195 2912

No of events after cuts

1 26 1 25 1 26 1 24 1 22 1 22 1 22 1 21 1 21 1 23 1.20

Average weight

1 26 1 12 1 29 0 97 0 98 0.95 0.88 0 90 0 84 0 82 0 74

_+0 12 -+ 0 12 -+ 0 11 -+ 0 09 _+0 09 -+ 0 08 _+0 08 -+ 0.07 +- 0.06 -+ 0.07 -+ 0 05

o [ K - p --* 1r-E+(1385)] (rob)

1 98 1 99 2 06 1 90 1 76 1 54 1 43 1 24 1.09 1 03 0 91

_+ 0 17 +- 0.19 -+ 0 15 -+ 0 15 _+ 0 13 -+ 0 11 -+ 0 11 _+0 09 -+ 0 07 -+ 0 08 -+ 0 06

a [ K - p ~ lr+~-(1385)] (mb)

0 85 0 94 1 16 1 06 0.92 0 68 0 73 0 67 0 71 0 76 0 70

-+ 0 11 -+ 0 13 -+ 0 11 -+ 0 11 _+0 09 _+0.07 -+ 0 08 _+0 07 -+ 0.06 -+ 0 07 _+0 05

a [ K - p ~ Alr+lr-(LIPS)] plus o [ K - p --* pA ] * (mb)

-~ A n + n - ]

409-+017 405_+018 4 51 _+0.16 394_+015 366_+013 317_+011 304_+011 2.81 -+ 0 09 2 64 _+0.08 2 61 _+0.09 235_+007

(mb)

o[K-p

* The cross sections determined for the LIPS and pA 0 have been added together as it was found difficult to separate them rehably.

c m. energy (MeV)

Beam momentum (GeV/c)

Table 1 Values of cross sections for the A0~r+~r- final state and for processes contributing to It at the 11 incident beam m o m e n t a

H

H-

+1

I

Va

I

bo

Rutherford Laboratory - Imperial College Collaboratton / K - p ~ n~F,±(1385)

++++

50

E

40

(.J w o3

30

J~

U3 0 E U

'~

+

! ~

I

,

-...,'

,~-

Ref

+.

-

193

5

'+'++

20

10

< L

09

08

io

;~

12

i

13

,,

BEAM MOMENTUM (GeV/c)

F i g 2 K - p --* AO~r+~r - c r o s s s e c t i o n as a f u n c t i o n o f i n c i d e n t m o m e n t u m

M ~ ( A n -) 2.60

2.40

2.20

2.00

1.a0

1.60

15

4;

i

' Cs

i

i

105

i

135

105

Inc. K- MomentL~n = 0.960 GeV/c M2(A~')

.V.

75

C

M2(A7 + )

qn (GeVlcZ) 2 1508 Events

,

F i g 3a

1.60

L 1.80

~

~

L ~ ,

i

2®

2'.20 2'.40 2.60

M2(A [+)

Rutherford Laboratory - Imperial College Collaboration / K - p -~ n~~±(1385J

194

distribution a relativistic Brelt-Wlgner shape superimposed on a linear background. Three different forms of the resonance shape have been tried" a relativistic BreitWlgner [7] shape with energy independent width (FIT 1), the form used by Holmgren et al. [8] (FIT 2), and a P wave relativistic Brelt-Wlgner [7] (FIT 3) The results are given in table 2. The experimental resolution of approximately 2 MeV has been considered in the fits. In all three cases, higher order background forms have been tried but did not result in any significant improvement. However, they have an influence on the resonance parameters, especially the width and this uncertainty has been included in the quoted errors. As can be seen from table 2 and as confirmed by other experiments [8,9], good fits to the A~ ± spectra could not be obtained using a P wave Breit-Wigner form (FIT 3) A satisfactory description of the data is given by the other two forms of the resonance shape. However, we prefer the form with energy independent width since that gwes the simplest description of the data. The values obtained are in excellent agreement with the average values pub-

~(A~-)

3.00

~1_ 2.60 ~ 24O 2.80

2.00

I

I

I"

j___I

1 80

1.60

,~--~i 25 7'5

'

d5

'

~5

'

m'

'

175 Inc. K- Momentum = 1.165 GeV/c MZ(A.-) .V. M~(A4 ÷) In (GeV/cZ)z

125 75

2214 Events

25y Fig

3b.

~

M

z (A ~*)

1.60 1.80 2 00 2.20 2.40 2.60 2.80 3.00

Rutherford Laboratory - Imperial College Collaboration/K-p -* I r ~ +(1385)

195

M2(An - ) 3.21]

2.80

240

2.00

]--

1.60

1

J

J 7

7 i

30

t

|

i

90

L

i

150

i 210

i

L 270

270 Inc. K- Momentum = 1.355 GeV/c MZ(A~-)

.V.

210

MZ(AT*) 15(]

an (GeV/c2) 2 90

2912 Events

30 Flg. 3c.

M2(A ~+ ) 60

2.00

2 40

2.80

3.20

Fig. 3 Dahtz plots of M 2 ( A n -) versus M 2 ( A n +) and proJectlons at 0.960, I 165 and 1.355 GeV/c K-

incident

momenta

for the reaction

K-p

~ A0n+~r -

lished m the Particle Data Group tables [10] and represent by far the best determination of these parameters to date.

3. Extraction of the n~E ±(1385) channels In order to extract It;Z±(1385) channels, reactxon (1) has been considered as an incoherent sum of Lorenz invariant phase space and the three reactions" K - p ~ lr-Z+(138S),

(2)

K - p ~ 1r+~-(1385),

(3)

K - p -~ p A .

(7)

196

Rutherford Laboratory -Impertal College Collaboration / K - p -* ~ ~+(1385) z,o0 -

i

300 -~n E > (D

200--

"6 O

Z

100--

: : ,- ,T :T 68

1 78

188

1 98

TM

2 08

(A°vr +) Effectwe m a s s - s q u a r e d

2 18

(GeV/¢ 2)

2

500 -

4OO

t 300 >

"6

200

O

Z

100 ---I-

168 (A°n-)

I

,

178

1

i

188

I

198

I

I

i

208

I

218 2 2

Effedlve mclss-squored (GeV/c) --~

Fig. 4. (a) An+ and (b) A n - mass-squared distributions m the reg:on of the I;(1385) resonance The curves are the result of the FIT 1 described m the text, the dashed line indicates the background under the resonance

The coefficients of the Legendre polynomial expansaons of the differential cross sections and the real parts of the dens]ty matrix elements for the quasi two-body processes are extracted mmultaneously [ 11 ]. The fact that the data are well fitted at all energies by an incoherent production model suggests that interference effects are small. A set of one-dimensional projections for a typical m o m e n t u m (1.245 GeV/c) together with the results of the fit are shown m fig. 5 The probablhty distribution W for reactions (2) and (3) is gwen by

1

do

W(cos0* 0, 4~,M2) = 3 n B(M 2) ' o dcos 0*

Rutherford Laboratory - Imperial College Collaboration / K - p ~ n~ ~+-(1385)

197

Table 2 Masses and widths of the Z+(1385) This experiment

x2/NDF

Mass (MeV/c 2)

17 (MeV/c 2)

Number of events above background

FIT 1

X+ X-

1381 9 -+ 0 3 1387 6 -+ 0 3

35 5 +- 1 9 39 2 +- 1 7

79 5/96 111/96

6900 9720

FIT 2

X+ X-

1383 5 -+ 0 4 1389 4 -+ 0 4

36 3 -+ 1 9 41.1 -+ 1 9

102/96 115/96

6730 9640

FIT 3

Z+ Z-

1382 2 -+ 0 4 1388 3 -+ 0 4

37 5 -+ 2 1 44 0 -+ 2 0

152/96 155/96

7000 10100

Parttcle data table values

2;+ Z-

Mass (MeV/c 2)

(MeV/c 2)

13825-+05 13866-+ 1.2

352-+ 1 7 424+-42

F

V!(!3 + c°s2°) + 2(~ - cos20) 033(cos 0") x L2

(8) - ~ - ~ sin 20 cos ~ Re P31(cos 0 " ) - ~

sin20 cos 2~ Re 0 3 _ 1 ( c o s 0*

,

where 0* Is the centre-of-mass scattering angle o f the pion, 0, ~ are the decay angles m the helicxty frame o f the I~(1385), M 2 is the m v a n a n t (Art) mass squared and B ( M 2) is the relativistic Brelt-Wlgner f o r m n o r m a h s e d to u n i t y over the available phase space and w i t h an e n e r g y - i n d e p e n d e n t w i d t h for the ~ ( 1 3 8 5 ) . The expression m square brackets describes the I~(1385) decay distnbutxon m terms o f the d e n m y m a t r i x elements 033, Re 031 and Re 0 3 - 1 which themselves are f u n c t i o n s o f production angle. F o l l o w i n g the formalism set out by D e e n [12] * the differential cross section and the denstty m a t r i x e l e m e n t s for reactions (2) and (3) are e x p a n d e d m

* We believe that the system of axes for the decay of the A from the 2;(1385) used in his report is inconsistent and we therefore use the following the z axis ts along the direction of the A In the ~(1385) rest frame, and t h e y axis is defined asy = (z' × z)/t(z' X z)l where z' is the direction of the Z(1385) In the overall c m system

198

Rutherford Laboratory - Imperial College Collaboratmn / K - p -* ~r~.+(1385)

,ooi ,,.~.

cos~ ,oo~

~oo~ I ~ ol -I

I 0

t

^~. cos.., ,oo~

~oot~ ~

,,,

]

I

o,

-1

300t

MASS2

,

L

~ooV~ ,

0

,

1

I A~° MASS2

200 100I 0/

0

> O O Z

,5OO 400 300 200 100 0 -1

3OO

~

-I

300 t

0

I

~

s2

200t

R" R"

'°if14

02 04 06 (GcVI¢2)2

300t

16 22 2.6 30 (GcVI¢2)2

A~"

'°~I

.

14 16 22 26 3,0 (GeVIc2)2

COSeiT,ij_'

,°°I~ 0

!

I~'~- ~01t-

200 ~.

2R

cose^

'°°oI~ ;,, 0I ,, II -1

|~I -I

0

300f

300[

AI~"

Aft,"

~I~* ]

'°:f0 .........1~

.......

' ,'

~A

Z O 0 ~

200

1~

^~"

3ooI

200~

100 0 0

o

10:f . . . . . . . 2~

0

1~

2~

Fig. 5 The four one-variable distributions for each of the two-particle combinations at 1 245 GeV/c K - me]dent momentum The curves were obtained by Monte Carlo integration using the fitted values of the A, B, C, D coefficients

Legendre polynomial series" do dcos 0* = 2~'X2 ~AtP~t (cos 0"), l

(9)

A0 * 100

668.+064 6 35 ± 0 67 7 75 ± 0 65 6 16 +- 0.57 65350.57 6.64 ± 0.55 642-+055 6 92 -+ 0 52 6 75 -+ 0 4 9 6 77 -+ 0.55 6415045

Beam momentum (GeV/c)

0960 1 005 1 045 1 085 1125 1 165 1205 1 245 1 285 1 320 1355

Table 3(a)

001±010 0.07 -+ 0 13 0 15 .+ 0 10 0.21 -+ 0 12 026-+011 0 17 -+ 0 10 008-+0.10 0 46 -+ 0.09 0 30 .+ 0.09 0 64 +- 0 09 066-+0.08

A1/A0

005.+012 0.60 .+ 0.15 0 89 .+ 0.11 1.21 -+ 0 13 10050.13 0 85 ± 0.12 0.74-+012 0.64 +- 0 10 0 57 .+ 0 10 0.37 .+ 0.10 0.73+-0.09

A2/A0

-0.49-+014 - 0 45 .+ 0 18 - 0 66 .+ 0.13 - 0 78 -+ 0.17 -0795015 - 0 . 5 6 +- 0.14 -0.61-+014 - 0 . 4 1 -+ 0 13 - 0 60.+ 0 12 - 0 49 .+ 0 12 -052-+0.11

A3/A0

-044.+016 - 0 43 ± 0 20 - 0 70 .+ 0.15 - 0 50 -+ 0.20 -046-+018 - 0 46 ± 0 16 -044-+016 - 0 47 -+ 0 15 - 0 4 7 .+ 0 14 - 0 85 +- 0 14 -0.72.+013

A4/A0

Table 3 Values of the coefhcmnts A O,AlIA O, BI/A O, Ct/A O, DI/A O, Ella O, FI/A O, Gl/A O, Hl/A 0 for K - p ~ lr-~+(1385)

A7/A0

021-+021 0.24 ± 0 26 0.16 -+ 0 20 - 0 40 -+ 0.25 0 06 +- 0.23 0 00 +- 0.21 - 0 31 -+ 0.21 0.18 -+ 0 18 - 0 10 -+ 0 18 0 02 -+ 0.19 0 13 +- 0.17

A6/A0

- 0 33 ± 0.19 0 04 -+ 0.24 - 0 38 ± 0 19 011.+024 001.+021 - 0 . 0 8 .+ 0 19 - 0 05 ± 0 19 0 13 ± 0.17 006-+017 - 0 43 -+ 0 17 - 0 . 1 0 -+ 0 16

A5/A0

0.09 -+ 0.18 - 0 20 ± 0 23 002.+017 - 0 18 -+ 0.22 - 0 27 -+ 0 20 - 0 . 0 0 + 0 17 0.13 + 0 18 - 0 . 0 7 -+ 0 16 0 07 .+ 0.15 - 0 . 3 8 .+ 0.16 - 0 . 2 2 ± 0 15

I

=I.H t~ H-

I

t~

027+-0.03 019-+004 022+-003 0 21 -+ 0 03 0 24 -+ 0 03 025-+0.03 0.22 -+ 0 03 028-+0.03 0 28 -+ 0 03 035+-003 034+-003

0960 1.005 1.045 1.085 1.125 1.165 1 205 1245 1 285 1320 1355

C1/A0 * 100

10 15 -+ 3 51 100-+341 522-+262 -001-+323 090+-298 -905-+274 - 7 37 -+ 2 90 - 7 04 -+ 2 75 - 8 02 +- 2.70 - 2 58 +- 2 97 - 5 47 +- 2 56

Beam momentum (GeV/c)

0 960 1.005 1045 1085 1.125 1165 1 205 1.245 1 285 1.320 1 355

Table 3(c)

B0/A0

Beam momentum (GeV/c)

Table 3(b)

7.08 +- 2.87 5.39+-324 989+-2.58 994+-3.29 1153+-295 1044+-2.75 8 72 -+ 2 79 3 14 -+ 2 53 - 0 . 9 4 +- 2 42 - 1 69 +- 2 62 - 9 . 5 8 +- 2 36

C2/A0 * 100

0.22-+006 020+-007 036+-006 0 4 1 +- 0 07 0 36 +- 0 07 032-+006 0.31 -+ 0.06 036+-005 0 30 +- 0.05 041-+006 043-+0.05

B1/A0

- 0 26 +- 2 36 225+-269 583+-214 -055-+277 6.01-+2.49 -2.06-+235 - 3 . 4 1 +- 2 33 - 2 43 +- 2.01 - 4 08 +- 1.90 - 4 09 +- 2.12 --4 28 +- 1 87

C3/A0 * 100

0.23+-007 -027-+009 -021+-007 - 0 06 -+ 0.08 - 0 05 -+ 0 08 -0.18-+0.07 - 0 05 -+ 0.07 010+-0.06 - 0 . 0 6 -+ 0 06 0.07+-007 008-+006

B2/A0

- 3 . 1 4 +- 2 04 -025+-2.21 209+- 181 224+-238 156+-214 418-+205 5 19 -+ 2 01 3 22 +- 1 77 3 08 +- 1 70 5 80 +- 1.74 2.34 +- 1 61

C4/A0 * 100

-024-+008 -014-+011 -0.11-+008 - 0 18 +- 0 10 - 0 13 +- 0.10 -0.25-+009 - 0 20 -+ 0.09 -0.18-+008 - 0 23 +- 0 08 -022-+008 -017-+007

B3/A0

1 41 -+ 1 80 340-+200 -051-+162 1 14+-219 291_+1.93 081-+180 0.07 +- 1 82 3 89 -+ 1 59 2 96 -+ 1 54 - 0 59 -+ 1.53 1 00-+ 1.44

C5/A0 * 100

003-+010 -004-+012 -030-+010 - 0 31 -+ 0 12 - 0 15 -+ 0 11 -033+-010 - 0 22 +- 0 10 -011-+009 - 0 . 1 2 +- 0 09 -027-+0.09 -024+-008

B4/A0

- 0 . 6 2 -+ 1 67 -165+-200 -I 14+-147 224-+204 -2.89-+186 -078+-166 1 45 -+ 1 68 - 0 43 -+ 1 43 1 10 -+ 1 39 1 37 +- 1 38 1 77 +- 1.34

C6/A0 * 100

005+-011 -0.07+-014 005-+011 0 02 -+ 0 13 - 0 14 +- 0.12 - 0 . 1 1 +- 0.11 0.01 -+ 0.11 -014-+010 - 0 03 -+ 0 10 -017-+0.10 -014+-009

B5/A0

- 0 . 1 7 -+ 1 51 025+- 1 8 2 069+- 1 3 4 196-+ 1 9 2 061+-183 -175-+153 - 0 54 -+ 1.57 - 1 . 1 0 +- 1 36 - 0 . 7 6 -+ 1 24 0 34 -+ 1 29 - 0 48 -+ 1 24

C7/A0 * 100

-010-+0.11 -017+-015 005+-012 - 0 01 -+ 0 14 - 0 00-+ 0 13 -0.12-+011 - 0 13 -+ 0 12 -003-+010 - 0 04 +- 0 10 -028-+011 0.03-+010

B6/A0

0.00 -+ 0 12 - 0 01 +- 0 16 0.02 +- 0 13 - 0 . 0 4 +- 0 15 0.03 -+ 0 14 - 0 . 0 4 +- 0.13 012_+013 013+-012 001+-011 0 03 -+ 0 12 -001-+011

B7/A0

+~

I

I+

t~

I

bO O O

0.960 1.005 1 045 1 085 1 125 1 165 1.205 1 245 1 285 1 320 1 355

momentum (GeV/c)

Bealn

E2/A0 * 100

160-+089 2 15 +_ 1.01 162+_079 1 93 -+ 0 90 3 03 -+ 0 85 3 21 +_0 78 240-+080 1 71 +_0 71 2.27 +_0 71 1 27-+080 0 79 -+ 0 68

D3/A0 • 100

E3/A0 * 100

0.64-+059 1 94 -+ 0 65 207+_054 0 24 +_0 61 1 06 -+ 0 58 0.19 -+ 0 52 -072-+054 - 0 36 -+ 0.47 - 0 08 -+ 0 46 052+_054 0 37 -+ 0.45

D4/A0 • 100

441-+ 12.15 - 8 17+_ 9.89 059+_778 1180-+12.14 -300+_1017 -4.95+_860 - 0 2 9 + _ 9.69 - 8 04+_ 8.84 - 0 3 2 + _ 7 2 6 - 1 7 19+_11.72 -12.33-+ 1 1 3 2 -8 48+_917 - 1 1 44 -+ 11 47 - 1 3 93 -+ 10 53 1 20 +_9 00 - 1 4 96+_1008 219+_ 9 5 8 - 1 5 0 1 - + 8 " 2 0 -2107-+1102 -917-+1069 -843+_891 -1082-+ 1014 -085-+ 928 508-+771 - 1 2 31+- 10.32 - 3 63-+ 8 8 3 1.95+_715 -2076+_1142 -1725-+1002 -9.28+_821 - 0 6 3 + _ 10.27 153+_ 9 4 1 141-+749

E l / A 0 * 100

652+_158 7 53 -+ 1 60 553-+ 1 15 0 88 +_ 1.25 3 31 +_ 1 26 5 02 -+ 1.19 478-+ 1 27 1 80 +_ 1 12 0 81 +_ 1.15 197+- 1 2 7 0 08 +_ 1 02

0960 1 005 1045 1 085 1 125 1.165 1205 1 245 1.285 1320 1 355

Table 3(e)

D2/A0 • 100

Beam momentum (GeV/c)

Table 3(d)

-085+_701 -5 39-+685 002+_6.05 680-+777 - 6 10 +_ 7 96 1162+_703 731+_7.69 3.75-+6.74 402+_636 -0.86+_650 -172+_643

E4/A0 * 100

049+_042 0 56 -+ 0 47 000-+039 0.54 +- 0 44 0 30 +_0 41 0 18 +_0 39 -0.33+_039 0 13 -+ 0 34 0 09 +_0 34 -015+_038 0 31 +_0 32

D5/A0 • 100

-2.79+_6.32 250-+614 371-+5.39 5.09±723 1.10 -+ 7 51 - 8 35+_649 716-+6.87 758-+613 4.01+_5.54 588-+616 058-+571

E5/A0 * 100

032+_031 - 0 14 +_0 36 044+_0.30 - 0 30 +_0 34 - 0 19 +_0.32 - 0 39 -+ 0 30 -043-+029 - 0 17 -+ 0.26 0.02 +_0 26 -0.25+_028 0 04 -+ 0 24

D6/A0 • 100

563-+556 484+_627 3 3 4 - + 5 19 -159-+673 - 8 96 -+ 6.99 474-+5.51 456-+637 -7 08-+566 - 4 50-+4.99 -095-+5.51 004+_5.20

E6/A0 * 100

-006-+025 - 0 . 3 3 -+ 0 29 -014-+024 - 0 . 0 5 +_0 27 - 0 . 3 3 -+ 0 25 - 0 01 +_0 24 -005-+024 - 0 16 +_0 21 0 08 +- 0.20 018-+023 0 02 -+ 0.19

D7/A0 • 100

- 3 83 +- 5 23 409+_602 2 62 -+ 4.86 - 4 . 3 1 +_6 13 328_+671 - 2 57 +_4 99 0 58 -+ 6 00 099-+ 5 15 059-+472 376+-491 4 36 -+ 4.85

E7/A0 * 100

I+

+1

I

¢

I

t~ ~a

- 5 07 _+4 08 - 4 99 _+3 75 - 3 . 3 0 _+ 2.64 - 2 06 _+ 3 05 - 1 . 0 3 _+2 85 - 5 25 _+ 2 72 - 4 8 1 _+ 2 8 7 - 3 . 0 6 +_ 2 65 - 5 45 +_ 2 73 - 4 53 _+ 2 78 -342_+231

0 960 1.005 1 045 1.085 1 125 1 165 1.205 1.245 1 285 1 320 1 355

G1/A0 * 100

- 1 7 67 +- 14.13 - 1 25 ± 13 73 - 0 . 9 8 -+ 10 08 10 6 2 - + 1 3 3 0 5 56 _+ 12 24 15 5 6 _ + 1 0 6 6 13.95 _+13.49 5 76 _+ 10.81 1 90 _+ 10 25 1449_+ 9 5 7 -753- + 947

Beam momentum (GeV/c)

0 960 1 005 1 045 1 085 1 125 1 165 1 205 1 245 1 285 1 320 1.355

Table 3(g)

F 2 / A 0 * 100

Beam momentum (GeV/c)

Table 3 ( 0

553 - 1 6 34 - 7 66 - 1 5 40 -0.09 - 1 7 04 -4.31 -4.98 -1.19 5 24 - 2 25

- 1 24 0.33 -1.07 -2.08 - 1 93 -2.13 -1.71 -0.28 - 1 19 - 1 53 -0.79

- 5 08 ± 10 71 7-09 -+ 11.88 - 4 72-+ 9.92 11 42 ± 12.22 0 88 ± 11 78 17.57 -+ 10.84 6 36 -+ 10 92 -082_+ 859 525+- 7 9 6 7.16 -+ 7 4 2 262+- 7 7 9

0.19 ± 0.78 0.06 +_ 0.82 011_+077 - 0 . 2 7 -+ 0 91 - 1 07 -+ 0.75 004-+076 0.09 -+ 0 70 - 0 42 ± 0 62 0 44 -+ 0.61 - 0 56 -+ 0.65 027+_057

F 6 / A 0 * 100

910-+ 8 9 4 -224- + 971 111+_ 8 2 3 - 1 3 57 +_ 10 17 3 I 0 ± 10 99 -17.28-+ 9 58 - 8 70-+ 9.98 -148 + - 794 - 4 . 3 9 -+ 6.82 - 3 11 +- 6 19 5.46 ± 6 56

G 4 / A 0 * 100

1 19 -+ 1.08 - 1 . 0 1 -+ 1 08 - 0 . 1 8 _+ 0 99 - 0 57 +_ 1.19 0 46 _+ 1 01 - 0 41 ± 0 99 -055_+093 - 0 . 3 9 -+ 0.78 0 09 -+ 0.81 0.41 -+ 0.89 0 40 +_ 0 76

F S / A 0 * 100

G 3 / A 0 * 100

_+ 1.52 +_ 1 50 _+ 1.33 ± 1.62 _+ 1 40 _+ 1.30 +_ 1 28 _+ 1.10 _+ 1.13 -+ 1 25 +_ 1 06

F 4 / A 0 * 100

+- 13 32 ± 14 27 ± 1105 _+ 14 49 +- 13 11 _+ 1 1 8 3 _+ 13 01 -+ 10.30 ± 990 ± 912 ± 949

G 2 / A 0 * 100

057_+227 1875238 - 0 45 _+ 1 90 - 0 96 -+ 2 32 0 4 6 _+ 2 05 - 1 . 1 3 _+ 1 92 0.14 -+ 1.90 0 6 9 -+ 1 68 - 0 77 -+ 1 75 0.94 _+ 1 79 - 0 51 -+ 1 56

F 3 / A 0 * 100

+ 0.63 -+ 0.66 +- 0 6 2 -+ 0.70 -+ 0.60 -+060 -+055 + 049 -+048 -+051 +- 0 4 6

- 0 56 - 7.78 1 18+- 9 1 3 - 0 79 -+ 7.30 3.03 -+ 9.69 - 0 . 4 8 +_ 10 20 8 70 + - 8.66 - 7 63 -+ 9 09 - 9 . 0 9 -+ 7.29 - 2 96 -+ 6 30 - 5 95 -+ 5.72 3.21 +- 5 99

G 5 / A 0 * 100

0.11 0 06 037 0.12 0 26 -0.02 0 05 -0.39 - 0 39 -0.03 0 64

F 7 / A 0 * 100

- 1 . 2 7 -+ 7 34 - 7 . 0 7 +- 9.35 1 96 + 7.24 1.69 + 8 95 14.46 +_ 9 53 - 3 . 3 2 -+ 7.98 - 7 . 9 0 x 8 38 765+-660 215---567 - 0 57 -+ 5 18 5.00 -+ 5.40

G 6 / A 0 * 100

3.62+675 -6.20 + 9 11 i -0.53 + 6.98 4, -H -2.89 + 8 09 -034-+928 3 . 1 4 + _ 7 1 8 "-~ -744-+807 ~ - 3 . 5 7 +_ 5.64 0.03 -+ 5 22 - 3 . 7 0 +- 4 55 - 3 . 6 2 -+ 5.13

G 7 / A 0 • 100

I

g:

O

H3/A0 • 100

039-+113 0.11-+108 -0.87-+072 -103-+074 -028-+076 -0.16-+077 -1.04-+080 -0.37-+071 - 0 . 0 1 -+ 0 69 - 0 . 4 2 -+ 0 82 -013-+064

Beam momentum (GeV/c)

0.960 1.005 1 045 1.085 1 125 1 165 1 205 1 245 1.285 1.320 1 355

Table 3(h)

-066-+0.49 -0.72-+051 -0.30-+041 -051-+046 003-+0.42 005-+041 -044-+043 -010-+037 - 0 . 1 8 ~ 0.35 - 0 . 4 5 -+ 0 41 -0.51-+035

H4/A0 • 100

-023-+027 -003-+0.30 -014-+0.25 013-+0.28 -025-+025 002-+023 -009-+024 017-+0.21 - 0 04 -+ 0.20 0 17 -+ 0 25 -002-+021

H5/A0 • 100

-0.19-+017 -0.21-+019 -005-+016 0.01-+0.18 010-+016 008-+015 009-+016 011-+0.13 - 0 03 -+ 0 13 0.06 -+ 0.15 0.01-+013

H6/A0 • 100

008-+011 0.06-+012 -0.04-+0.11 0.11-+012 -000-+011 0.08-+011 0 10-+ 0.11 -0.05-+009 - 0 02 -+ 0 09 0 03 -+ 0 10 005-+0.09

H7/A0 • 100

M

I

14-

44

I

A0 • 100

10.44-+091 11.27-+105 12.31 _+0 92 1201_+096 11.69 ± 0 88 1076-+079 1044_+080 958_+067 8 73 _+ 0.59 8 54 -+ 0 6 6 778_+052

Beam momentum (GeV/c)

0.960 1005 1 045 1085 1.125 1165 1205 1245 1 285 1 320 1355

Table 4(a)

-011-+008 014_+009 0 31 -+ 0 07 0.55-+008 0 56 _+ 0 08 061_+007 077-+007 074_+ 0 0 7 0 82-+ 0 07 0 82 -+ 0 09 069_+007

A1/A0

Table 4 As for table 3 for K - p ~ Ir+l~- (1385)

-015-+009 -006-+011 0.30 _+0 09 031-+009 0 36 -+ 0 09 024_+009 026_+009 027-+0.08 0 30-+ 0 08 0 75 -+ 0 10 058_+008

A2/A0

032-+017 - 0 10 -+ 0 18 - 0 03 -+ 0 15 006_+016 - 0 10 -+ 0 15 - 0 . 1 0 -+ 0 15 - 0 09 -+ 0 15 - 0 . 2 4 -+ 0 14 001-+015 - 0 48 -+ 0.16 - 0 31 -+ 0 14

-+ 0 15 -+ 0.16 ± 0.14 -+ 0 14 -+ 0 14 -+ 0.13 -+ 0 13 -+ 0 13 -+ 0 13 -+ 0 15 -+ 0 13

- 0 09 - 0 14 - 0 51 -0.07 -0.13 - 0 40 -0.28 - 0 35 - 0 20 - 0 37 - 0 18 - 0 60 - 0 38 - 0 30 -0.42 - 0 42 - 0 42 - 0 45 - 0 58 -0.59 - 0 74 - 0 62

039-+012 022-+013 043-+011 022-+011 - 0 05 -+ 0 11 010-+011 - 0 25 -+ 0 11 - 0 . 0 4 -+ 0 10 - 0 13 -+ 0 10 - 0 09 -+ 0 11 - 0 20 -+ 0 10

-+ 0 13 -+ 0 14 -+ 0 12 -+ 0.13 -+ 0 12 -+ 0 12 -+ 0 12 -+ 0.11 -+ 0 12 -+ 0 13 -+ 0 12

A6/A0

A5/A0

A4/A0

A3/A0

0.00 - 0 05 - 0 08 0.19 0 08 -0.13 -0.03 - 0 03 - 0 14 - 0 14 -0.11

A7/A0

-+ 0 18 -+ 0 19 -+ 0 16 -+ 0 17 -+ 0.16 -+ 0 16 -+ 0 17 -+ 0 15 -+ 0 15 -+ 0 17 -+ 0 15

I

+1 PI N-

I

- 0 19 -+ 0 05 - 0 16 5 0 05 - 0 06 5 0 04 - 0 04 -+ 0.05 - 0 11 _+ 0 05 - 0 03 _+ 0 05 0 0 7 5 0 05 0105004 0 145 0 0 4 009-+005 007_+004

0.26 5 0 03 029-+003 025-+002 0215003 0235003 0275002 027-+002 023-+002 023+_002 0225003 025_+002

0 960 1 005 1 045 1 085 1 125 1 165 1 205 1 245 1 285 1 320 1 355

C2/A0 * 100

0585235 1 4 7 5 2 44 059-+212 1485221 0 16 5 2 16 2225214 5 41 -+ 2 18 7.09 5 2 10 13 80 5 2.12 16 42 5 2 48 13 08 5 2 19

C1/A0 * 100

6715295 8635302 9675250 9645259 10.01 5 2.53 9795249 14 49 5 2 59 18 82 -+ 2 49 14 52 5 2 50 12 97 5 2 66 9 14 5 2 39

Beam momentum (GeV/c)

0 96O 1 005 1 045 1 085 1 125 1 165 1 205 1 245 1 285 1 320 1 355

Table 4(c)

B1/A0

B0/A0

Beam momentum (GeV/c)

Table 4(b)

10 21 08 18 10 24 13 10 08 05 07

-+ 0 50 50 5 0 50 -+ 0 50 5 0 50 -+ 0 _+0

06 06 06 06 06 05 06 05 05 06 05

- 3 14 5 1 85 1.41 5 2.07 0 69 5 1.67 1 0 5 5 1 74 0 03 5 1.73 3.00 5 1 71 3.40-+ 1 72 3.61 5 1 70 3 68 5 1 66 4265208 230-+182

C3/A0 * 100

-0 -0 -0 -0 -0 -0 -0 -0 -0 -0 -0

B2/A0

- 1 58 0 46 - 1 20 1.14 - 1 54 - 2 13 - 1 57 -1.03 - 4 08 - 1 60 -0.57

5 1.68 5 1 77 5 1 44 5 1 57 5 1 52 5 1.47 5 1 52 5 1.45 -+ 1.49 5 1 77 5 1 57

C4/A0 * 100

0205008 0085008 0 13 -+ 0 07 002-+007 - 0 06 -+ 0.07 - 0 09 5 0 07 - 0 18 5 0 07 - 0 11 5 0 06 - 0 14 5 0 06 - 0 08 5 0 07 - 0 18 5 0 06

B3/A0

0 08 -0.46 - 4 06 - 0 68 -1.39 -2.15 - 2 36 - 1 34 - 2 66 - 2 63 - 3 69

-+ 1.48 -+ 1 57 5 1 30 5 1.40 5 1.33 -+ 1 32 5 1 36 5 1 29 5 1 29 5 1 56 5 1.38

C5/A0 * 100

- 0 . 2 5 5 0.08 - 0 16 5 0 09 - 0 03 5 0.08 002_+008 0055008 002_+007 - 0 . 0 6 5 0 08 - 0 08 5 0 07 - 0 13 _+0 07 - 0 17 5 0 08 - 0 11 5 0 07

B4/A0

- 0 11 -+ 1 21 - 0 79 5 1 36 - 0 51 5 1.12 - 0 02 5 1.25 - 1 56 -+ 1 16 0 72 5 1.11 0 8 8 5 1 11 - 0 01 5 1.09 - 0 12 + 1 13 0175133 0 34 5 1.18

- 0 40 5 1.31 2 17 -+ 1 4 4 - 1 . 5 7 -+ 1 23 0.65 -+ 1 31 - 0 76 5 1 23 0 3 7 5 120 - 0 55 5 1 21 - 0 67 5 1 16 - 1 68 5 1 18 - 2 50 5 1 46 - 2 48 -+ 1.24

- 0 . 0 2 5 0 11 009-+012 0 11 5 0.10 - 0 02 5 0 10 0 08 -+ 0 10 0.00 -+ 0 10 0.04 5 0.10 0025009 0035009 - 0 10 -+ 0 10 - 0 03 5 0 09 0115010 0035011 - 0 06 -+ 0 09 001_+009 0 06 5 0.1~ 0 06 5 0 09 001-+009 003_+009 - 0 02 5 0 09 - 0 10 5 0 10 - 0 03 5 0 08

C7/A0 * 100

B7/A0

B6/A0

C6/A0 * 100

- 0 . 0 5 5 0 09 0 08 -+ 0 10 - 0 . 1 7 5 0 08 019-+008 010-+009 - 0 00 -+ 0 08 - 0 12 -+ 0 08 - 0 13 5 0 08 - 0 07 5 0 08 - 0 11 -+ 0 0 9 002-+008

B5/A0

I

b~

I+

=i+i

I

Beam

0.960 1.005 1.045 1 085 1 125 1 165 1 205 1 245 1 285 1 320 1.355

momentum (GeV/c)

-6.68 - 1 2 30 - 1 0 86 -9.85 -5.54 - 9 41 -7.34 - 3 91 - 4 74 - 3 O1 497

± 11 41 ±11 29 ± 8.64 ± 9.36 ± 905 ± 9.89 ± 912 ± 915 ± 9.10 ± 9.60 ± 872

E l / A 0 * 100

7 2 9 ± 1 38 6 45 ± 1 40 5 13 ± 1.08 3 9 9 5 1 12 5 14 ± 1.12 3 62 ± 1.10 3 96 ± 1.12 2 46 ± 1 03 3.93 ± 1 06 3 24 ± 1 09 2 72 -+ 0.97

0.960 1.005 1.045 1 085 1.125 1 165 1 205 1 245 1.285 1 320 1.355

Table 4(e)

D2/A0 * 100

Beam momentum (GeV/c)

Table 4(d)

- 0 10 -1.50 - 0 55 - 0 32 -4.32 - 7 82 - 3 44 10 24 1 22 - 0 88 7.34

± ± ± ± ± ± ± ± ± ± ±

8 64 8.73 7 07 7 48 7 44 7.51 7 64 7 82 7 40 8 60 7.27

E2/A0 * 100

- 0 22 -+ 0.79 0185077 0.95 -+ 0.63 030±065 1.08 ± 0.66 0 55 ± 0.64 0 53 ± 0.66 - 0 51 ± 0.62 - 0 50 -+ 0.65 - 0 34 ± 0.72 - 1 13 ± 0.62

D3/A0 * 100

4.33 ± 6.55 0.30 ± 7 35 5.78 ± 5 58 - 8 . 5 3 ± 5.97 5 48 ± 6 26 - 1 57 ± 6 36 1 . 4 0 ± 6 08 - 3 35 ± 5 96 2.07 ± 5.89 - 5 83 ± 7.08 084±601

E3/A0 * 100

0.49 ± 0.48 0365050 0.32 ± 0 42 0 62 ± 0.43 1.05 ± 0 44 0.63 ± 0 42 0.34 ± 0 42 0 59 ± 0.41 0 79 ± 0.42 1.13 ± 0.49 0 94 ± 0 4 2

D4/A0 * 100

---453 -5 83 -1 94 -4 68 -8 53 -5 52 -1.93 -3 75 2 57 -2.57 -5 04

± ± ± ± ± ± ± ± ± ± ±

5 95 6 59 4.95 5 40 5.40 5 27 5.27 4 97 4.85 5.85 5 14

E4/A0 * 100

0.49 ± 0 34 - 0 14 ± 0 36 033±030 0555030 0705032 0 32 ± 0.30 0205030 0.30 ± 0.29 0205030 0505035 - 0 19 ± 0 29

D5/A0 * 100

2375545 3105536 1 23 -+ 4.44 0.30 ± 4.93 2 70 ± 4.89 - 0 70 ± 4 76 6 88 ± 4 79 - 0 44 ± 4 72 - 1 52 ± 4.39 1 2 9 ± 5.13 1.02 ± 4 6 8

E5/A0 * 100

- 0 32 ± 0.27 - 0 29 ± 0.27 0 59 -+ 0.23 0385024 0.23 ± 0 24 0 07 ± 0.23 0.32 ± 0 23 024±022 0215022 0 . 1 5 ± 0 26 0105022

D6/A0 * 100

3.09 0.09 -0.53 -0 58 -5 16 0.43 3 42 -0 79 - 4 09 3.78 -0.51

± 4.76 ± 4.78 ± 4 II ± 4.45 ± 4.52 ± 4.31 ± 4.18 ± 4 17 ± 4 04 ± 4.63 ± 4.17

E6/A0 * 100

- 0 . 0 0 -+ 0.21 0 12 ± 0.21 0235018 - 0 . 0 7 ± 0 19 - 0 . 0 4 ± 0.19 0.21 ± 0.18 - 0 . 0 5 ± 0 19 0.04 ± 0 17 0.05 ± 0 17 - 0 28 ± 0 20 - 0 07 ± 0 18

D7/A0 * 100

-1.98 - 7 03 4 31 -0.41 - 2 23 0 10 2 84 0 32 -5.04 3.74 - 3 02

± 4.33 ± 4 63 ± 3.94 ± 4.31 ± 4.32 ± 4.12 ± 3.87 ± 3.76 ± 3.82 ± 4.40 ± 4.00

E7/A0 * 100

t~

H-

I

¢

8 q I

O~

495-+345 253-+349 1 68 -+ 2 61 3 31 -+ 2 76 3 30 -+ 2 75 310-+264 261-+271 343_+258 2.64 _+ 2.55 131-+267 093-+232

0960 1.005 1 045 1 085 1.125 1165 1205 1245 1.285 1320 1355

G1/A0 * 100

21.63-+ 13 98 - 4 21-+ 10.37 1082-+1173 -559-+1064 828_+ 1 0 5 2 - 1 1 18-+ 9 2 5 23 5 9 _ + 1 0 9 9 4.86_+ 9 9 5 437_+1081 -3 26-+1011 I081_+1027 -1.04_+ 9 7 3 -146_+1028 -9.21_+ 9 2 4 409-+ 1108 -1190-+ 1008 991_+1108 873_+ 9 7 4 17 72 -+ 10 36 7 12 _+ 10 68 -0.51_+ 9 1 5 -4.36-+ 909

0 96O 1.005 1 045 1.085 1 125 1 165 1 205 1.245 1 285 1 320 1 355

G2/A0 * 100

-027_+ 191 -199_+196 1 54 _+ 1.56 - 0 04 -+ 1 66 1.69 -+ 1 61 121-+ 1 6 0 222-+1.59 313_+1.57 3.19 -+ 1.58 539_+184 459_+ 1 5 5

F 3 / A 0 * 100

Beam momentum (GeV/c)

Table 4(g)

F 2 / A 0 • 100

Beam momentum (GeV/c)

Table 4 ( 0

- 7 27-+8.41 5.89_+941 -1.71_+715 16 7 3 _ + 7 8 0 -8.61_+8.22 640_+807 0.99-+769 439_+778 071-+752 15 96 _+ 9 06 -8.15_+768

G 3 / A 0 * 100

-090_+122 047-+129 2 37 _+ 1.04 0 91 -+ 1 07 0 53 -+ 1 04 0 8 3 - + 1.06 1.92-+104 2.29-+1.04 1.06 _+ 1.03 169_+126 106_+104

F 4 / A 0 * 100

188-+747 441-+794 103-+602 474-+728 230_+724 275-+666 138_+702 091-+634 -153-+652 2 51 _+ 7 50 -0.70_+677

G4/A0 * 100

-056-+086 029-+092 0 33 _+ 0 73 - 0 . 2 3 -+ 0 75 - 0 . 3 7 -+ 0 75 029-+073 040_+074 044_+073 0.26 -+ 0.75 100-+090 034_+073

F 5 / A 0 * 100

-5 98-+6.80 231_+660 -1105_+5.41 2.07_+669 -193_+634 -050_+591 -7 06_+610 -0.56_+594 828_+569 0 69 _+6 35 - 6 8 4 - + 6 10

G 5 / A 0 * 100

-022_+069 036-+068 0.22 -+ 0 54 0 01 -+ 0 59 0 42 _+ 0 55 026+-056 -0.01_+058 025-+055 0 15 ± 0.57 0.37-+065 038_+0.57

F 6 / A 0 * 100

-3 37-+6.22 062_+608 151_+507 001_+6.21 222_+590 068_+5.58 -8 59-+520 -046_+540 612_+546 1.09 -+ 6.15 -134_+5.24

G 6 / A 0 * 100

001_+054 051-+054 - 0 11 -+ 0 43 - 0 . 3 2 -+ 0.46 0 24 -+ 0.46 -0.25-+045 -009-+047 011+-0.44 0.23 _+ 0.44 -0.34_+0.51 -037_+047

F 7 / A 0 * 100

018-+569 186_+582 -2 71_+485 3.17-+595 350-+578 146-+540 -4 69-+4.58 070-+4.91 793_+517 - 4 77 _+6 05 3.36-+501

G 7 / A 0 * 100

O

14-

1

g

I

q

t~

0 960 1 005 1.045 1 085 1 125 1 165 1 205 1 245 1 285 1 320 1 355

momentum (GeV/c)

Beam

Table 4(h)

- 2 48 +- 0 94 -141+-092 - 2 01 +- 0 74 - 1 82 +- 0 74 - 2 45 +- 0 70 -217+_075 - 1 67 +- 0 73 -141+_067 -188+-069 - 0 77 -+ 0 68 -1.03+_062

H3/A0 • 100

0 22 -+ 0 43 018+-0.41 - 0 34 -+ 0.34 - 0 04 +- 0.35 - 0 24 -+ 0 33 -042+_035 - 0 30 +_0.35 -051+_0.32 -044+_034 - 0 37 +_0 37 -029+_031

H4/A0 • 100

- 0 23 +- 0 22 -0.39-+022 0.02 +- 0 20 0 07 +- 0.20 - 0 . 0 9 +- 0 19 -017_+020 - 0 12 +_0.19 -026+_0.19 -015+_019 - 0 20 +_0.22 -019-+0.18

H5/A0 • 100

- 0 08 +- 0 14 002+-014 - 0 . 0 4 +- 0 12 0 19 +- 0 12 0.03 +- 0 12 011+_012 - 0 00 +_0 12 -014-+012 010-+012 - 0 14 +- 0 14 - 0 0 0 + - 0 11

H6/A0 * 100

- 0 . 0 1 +- 0.09 002+-010 0 01 +- 0 08 -0.05 +- 0 08 0 12 +- 0 08 006+_0.08 0 02 +_0 08 011+_008 004+-0.08 - 0 03 +- 0.09 -001+-008

H7/A0 • 100 I

I

I+

t~ O oo

Rutherford Laboratory - Imperial College Collaboration/K-p -~ *r~~+(1385)

209

do 033 dcos 0* - 27rA2 ~B/P~/(cos 0 " ) , 1

do O* = 2nX2 ~1 CtPl(cos 0 " ) , Re Pai dcos do 0* - 2hA 2 ~ D i e t 2 ( c o s 0 " ) , Re 03-1 dcos l Similar expansions were used for reaction (7). For all reactions the highest value of I used was 7. The expansion coefficients extracted by ttus procedure were checked against the results of the moments programme developed by Litchfield [13]. The results from the two methods were found to be m satisfactory agreement. Data from the parity vlolatmg decay of the A were used together with the results of the above extraction to determine the remaining four independent elements of the density matrix (Ira P3i, Im 03-1, Im P I - 1 , Im 03-3). These elements were again expanded in Legendre polynomial series. do = 27rX2 ~ ElP1 (cos 0 ' ) , Im P3I dcos 0* l do = 2~'~2 ~ F / P t 2 ( c o s 0 " ) , Im P3-1 dcos 0* 1

da

Im P l - 1 dcos O*

_ 2rrR2 ~ G t P ] ( c o s 0 " ) , 1

d---L---°- 2rrX~ ~3/4~P~(cos 0"),

Im P a - a dcos 0*

(10)

1

and the coefficients Et, Ft, Gt and Hi (later referred to as polansatxon coefficients) up to order 7 were calculated by the orthogonal moments method [12] The complete set of coefficients for reactions (2) and (3) are given in tables 3 and 4 and some of the more significant coeffmlents are shown In figs. 6 and 7 together with data from the CRSS [14] * collaboration.

4. Partial-wave analysis

There is substantial overlap between the data from the CRSS collaboration [1] and those from this experiment Following our previous practice [15], we have * Data su mmary tapes for the reaction K - p ~ A~r*n- were made avmlable to us by the CRSS CollaboraUon These were analysed using the m e t h o d s described for the present data

Rutherford Laboratory - Imperial College Collaboration/K-p ~ ~r~~±(1385)

210

Centreofmossenergy(GeV) .

,

1,eoo

,

,

1,9oo,

,

,

2,ooo,

,

,

z,loo,

,

i 800

_

i 900

~ ooo

~ 1oo

As/Aox 102

'°i] Al/A°x 102

t

t

,~ 5S.

i, ¢ t+~+

65-

120 90

60 3e

'°

o

BJA°x102 1

-3o

lo

-6o

t~/I

A3/A°x103I

-~oo.

-¢so •

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-rso.

B2/AoX10 2

-900. IOSOI 1ZOO. ] .

. . . . . . . . . . . . . .

'°' A,./Aox 102

-25 ~

t Ti

.

-15

:!t i

-4S -10S~

-35

I I~

~Z~

I 500

I 70a

"800 *00

t, 100

IncidentK-momentum(GeVlc)--~ Fzg.6a.

~oo

50O

t

' I ?nO

Centre of moss energy(GeV) I 800

1 soo

45-

z ooo

z ~oo

D'/A°xl0~ 4

31. o

15-

-5o

15•

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5.

°1so

-5. .15 .

50,

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E1/A ° x 102

{ )0.

10 II? -10 6Z

$? 12

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-30

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F2/Ao x 102

-37 4.

-62

-4.

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02/A°x 103

,01 6,1

G1/AoX 102

SO

30

10

-t0

201

'ill

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°zS !

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Fig. 6b.

{~~~,~

"400 ~eO

H3/A°x 103

I 1~

1 sao

1 soo

I 7w

Incident K-momentum (GeVlc) --~ Fig. 6 The most slgmflcant Legendre polynomial expansion coefficients for K - p - * n-1~+(1385). The curve Is the result of the pamal-wave analysis. The data from the present experiment are shown as n, while the CRSS data are shown as x

212

R u t h e r f o r d Laboratory - Imperial College Collaboratton/ K - p

Ir~ ~ -+( 1 3 8 5 )

Centre of m a s s energy(GeV) ,,oi

Aox

10 3

35oj

11o i 300 J zso |

,oi

200 J Iso j

3oi

1oo 4 1o

AlIA ox 102

1oo [

! /

.oi ,oi ~o

oi

40

-zo i

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.i A2/Ao x 101 ÷

:o

,oo

,i

-1o

.zo

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'[[ B,/Aox 10z

A4/Ao x 101

t

~

"t Fig. 7a. *oo

~ 1oo

i

~oo

1

500

I 70O

Incident K- momentum (GeVlc) ---~

Rutherford Laboratory - Imperial College Collaboratton / K - p ~ ~r~~+-(1385)

i ~

I ~o

2o

2 ooo

2 1oo

1 BOO

+

1 900

2 000

°° EjAo x 102 40 ZO

o

-lo

-so C~/A°x 102

t

-~0

-4n

-30

lZ

-80

'° F3/A ox 102

ZS

6

-Z

+

ol

I

Gl/AoXl02

-251

oi -12SI

37~

H 3/A o x

103

6~

ii,i

'AoX1°

Fig. 7b.

-31Z o ~oo

i 1oo

I 300

~ 500

I 700

Incident K- momentum (GeV/c) --~ Fig 7 As for fig 6, but for K - p --, *r+~-(1385)

213

2 100

214

Rutherford Laboratory - Imperial College Collaboration / K - p --* ~r~~±(1385)

Table 5 The data used m this analysis and the X2 contribution of each set given as ×2 per data point Momentum range (GeV/c)

cm Energy range (MeV)

Experiment

No of momenta

0.960-1 355

1775-1957

This expt

11

1 462-1 843

2005-2170

CRSS (1)

9

Type of data

No (N) of data points

×2/N

*r-X+ n+~ - Ir-Z + n+X-

Ao, AI/A o BI/A o Ct/A o DI/A o EllA o Ft/Ao Gl/A o HI/A o A o, AlIA o B1/A o Ct/A o DI/A o

88 88 77 66 77 66 77 55 72 72 63 54

88 88 77 66 77 66 77 55 72 72 63 54

0 93 0.84 1.18 1 06 0 63 0 34 0 53 0 49 0 87 1 00 090 0 95

Total no of parameters = 62, no. of data points = 1710, x2/N = 0.78.

used data from the present hlgher-stamtlcs experiment m the region o f overlap. The data employed in the present partial wave a n a l y m are listed m table 5.

4.1. The parametrisation A partial-wave amphtude TLL'I2J, where L and L ' are the incoming and outgoing orbital angular momenta, I is the isotopic spm and J is the total angular m o m e n t u m , is parametnsed as a sum o f a background term and, if required, Brelt-Wigner terms" T : TB + TR ,

(1 1)

where 7"8 is the background term and TR is a sum of non-relativistic Brelt-Wlgner resonances o f the form t

e,~,

(12)

e-i where t is the resonance amphtude and e = 2(ER -- E)/F(E). The energy-dependent width P is o f the form. I'(E) : P(ER)

kot(kr) ER , kRot(kR r) E

(13)

where vl is the Blatt and Welsskopf angular m o m e n t u m barrier [16] for the incoming orbital angular m o m e n t u m l. The radius of interaction, r, is taken to be 1 fm In these formulae E and k are the c.m. energy and m o m e n t u m and ER and kR are their

0.81 0.89 0 84 0 59 040 0.36 0 70 0 47 0 78 0 95 0 88 1 13

Rutherford Laboratory -Impertal College Collaboration / K - p ~ ~r~r~±(1385)

215

values at the resonance energy and t = xV~x' = x / r e r , / r '

,

F e and P~ being the partial widths of the elastic and the IrI~(1385) channel The energy dependence of the elastic partial width was assumed to be the same as that of the total width. For P~, k and kR m the formula correspond to the c.m. momenta of the outgoing pamcles and l refers to the outgoing orbital angular momentum It should be pointed out that the specific form assumed for the energy dependence of the widths does not affect the results significantly. The background term has the form

TB = Bx/-BtB%' R(E) e'°(E) ,

(14)

where M R(E) =

N

~ m=O

amPm(E'),

0(E) = ~ n=O

bnPn(E'),

E' = 2 E - Ema x - Eml n Ema x - E m m

such that E' equals +1 and - 1 at energies Emax and Emm JUSt above the upper end and below the lower end of the energy range fitted, and Pro, Pn are Legendre polynomials. The parameters am and bn are determined by fitting. The angular momentum barrier factor Bl has the form

k Bt = - kma x

Emax vl(kr) E Vl(kmaxr)

(15)

The various expansion coefficients of eqs. (9) and (10) may be related to the partialwave amplitudes by

~l

=

~ ~ L2LII2J2 * XLILIIIJ1 PART(TZILII1JITL2L'212J2) , L1L'II1J 1 L2L'212J2

(16)

where r/l is any of the coefficients A t - tit, x's are the quasi two-body equivalent of the Trlpp coefficients [17], and PART stands for Re (ABCD coefficients) or Im (EFGH coefficients).

4.2 The partial-wave solution Several partial-wave solutions were developed starting from different assumptions about the presence of backgrounds and the less well estabhshed resonant states. How. ever, the significant partial-wave amphtudes obtained were found to be essentially similar in all solutions [18] and so only the solution obtained with the mimmum number of free parameters is described here.

216

Rutherford Laboratory - Imperial College Collaboration/K-p ~ lr~~+ (1385)

Within the energy range 1775-2170 MeV there are three established I = 1 states, D15(1775), F15(1920), F17(2040) and four 1= 0 states, P03(1900), D05(1830), F05(1820) and G07(2110) An mltlal basic solution was developed with these resonances and no background amplitudes in any of the partial waves. The masses and widths were fixed to the values found m the partial-wave analysis of two-body channels, ref. [15]. The resonant amphtudes were constrained to be purely imaginary at the resonant mass This solution gave a X2 of 5362 for 1696 degrees of freedom At this stage the less well estabhshed resonances S11(1775), S11(1955), P01(1853) and S01(1825), D13(1920), F05(2100), G09(1808) reported in ref. [15] were added. Again the masses and widths were fixed and the amplitudes constrained to be purely Imaginary at the resonant masses. After refitting, this solution gave a X2 of 3358 for 1687 degrees of freedom. In order to improve the fit, background amplitudes were then introduced. This was done lteratively. In the first iteration two-parameter backgrounds (N = M = 0) see eq. (14)) were tried in each wave In turn and retained for that wave wtuch gave the largest improvement m X2. The second iteration permitted either a second wave to carry N = M = 0 background or an increase m order of the background already found. This process of iteration was continued until there was no further significant improvement in X2 Background amplitudes were found necessary for waves with J ~< 25-with the exception of SDO1, FP05, FF05 and none were necessary for the higher waves This solution gave a Xz of 1289 for 1636 degrees of freedom In order to investigate the significance of the 'less well established' resonances, this solution was re-mlnimlsed with each resonant amphtude removed in turn. Only those resonant amphtudes which lead to a change in ×2 of more than 10 units were retained in the final solution These were the SD01(1825), FP05(2100), FF05(2100) and the DS13(1920) amphtudes Using the same criterion for the established resonances, the amphtudes FP15(1920), FF15(1920), FH17(2040), GD07(2110) and the GG07(2110) were removed. However, the F15 wave was then dominated by a highly structured four-parameter background amplitude exhibiting a slgmficant loop in the argand diagram suggesting a resonance of mass around 1900 MeV It was possible, qmte satisfactorily, to replace this background by a two-parameter background and an F15 resonance, presumably the F15(1920), but the mass and width had to be changed to the values gwen m table 6. It should be noted however, that these values are in fact within the range pernutted by the errors quoted in ref. [15] This solution has a X2 of 1326 for 1660 degrees of freedom It should be noted that the value of the ×2 per degree of freedom is unusually small. This IS probably because the partial-wave analysis programme does not take into account the correlation terms among the coefficients The coefficients for which the X2 per data point is particularly small are those associated with the polansatlon, presumably because of the severe mathematical bounds on these values. The overall features of the data are well described by this solution as can be seen

Rutherford Laboratory - Imperial College Collaboration/K-p -~ ~ ± (1385)

217

Table 6 Resonant ampbtudes consadered for K.N ~ 7r~(1385), note that our conventaon as meson first, baryon second m both the m m a l and the final states Resonance

Status

Elastacaty a) (x)

Outgoing wave

tTrZ(1385)

Predactlons [26] of tTrl~(1385) b) from SU(6) w @0(3) fits

Branching fraction into 7r~(1385)

S01(1825)

Possible

0 37 + 0 05

D

- 0 056 -+0 028

- 0 128

0 008

P03(1900)

Estabhshed

0 18 -+002

P F

<0 030 +0126 -+0 055

+0 05 -0100

0088

< 0 04

S

- 0 066 -+0 025

- 0 177

>0 109

D13(1920)

Possable

D D05(1830)

Estabhshed

0 04 -+ 0 03

D15(1775)

Estabhshed

041 +-003

D G D G

F05(1820)

Estabhshed

0 57 +-0 02

P F

+0 018 - 0 141 -+0 014 <0 030

0

0 497

0

+ 0 184 -+0011 <0 030

+0 115

0 083

+ 0 167 -+0 054 - 0 065 ±0.029

+0 215

0 049

- 0 091

0 007

F05(2100)

Possible

0 07 -+0 03

P

F15(1906) Wadth 135 MeV

Estabhshed

0 05 -+003

P F

<0 01 -0039 +-0 009

- 0 035 +0021

0030

F17(2040)

Estabhshed

0.24 -+0 02

F

- 0 153 -+0 026

- 0 127

0.098

F

- 0 071 -+0 025 <0 03

0 072

H a) From ref [15] b) The values hsted are with the exceptaon of the D13 amphtudes the predictions of fit 1 of ref [26] in which only the estabhshed resonances were used The values for the D13 amphtudes are the predictions of fit 2 of ref [26] The overall sign is arbitrary and we have chosen it to obtain maximum agreement with the measured amphtudes f r o m figs. 6 a n d 7. H o w e v e r , t h e c m . e n e r g y r e g i o n 1 7 7 0 - 1 8 1 0

M e V is c o m p a r -

atively p o o r l y f i t t e d E f f o r t s t o i m p r o v e t h e fit to t h e d a t a m t t u s r e g i o n w i t h o n e or

0 063

0 012 0 009 0 005 0 001

0 025

0 099 -0 156' -0 027

-0 028

-0 011

-0 034

-0 038

-0 045

-0 055

-0 064

-0 071

-0 076

-0 080

-0 082

-0 085

-0 087

-0 090

-0 092

-0 095

-0 097

-0 099

-0 102

-0 104

-0

-0

-0 112

-0 114

-0 116

-0 118

-0 120

-0 126

0 101 -0 152

0 I02 -0 147

0 102 -0 143

133

0 103

0 102 -0 127

0 102 -0 122

0 I01 -0 117

0 100 -0 Iii

0 098 -0 I05

0 096 -0 I00

0 094 -0 094

0 091 -0 088

0 088 -0 082

0 085 -0 076

0 082 -0 071

0 078 -0 065

0 074 -0 059

0 069 -0 054

0 064 -0 048

0 059 -0 042

0 054 -0 037

0 048 -0 032

0 042 -0 027

0 036 -0 022

0 029 -0 017

0 022

0 015 -0 008 ! -0 122

-0 124

0 098 -0 16C

0 007 -0 004

0 002 -0 053

0 007 -0 054

0 019

0 025 -0 047

0 027 -0 045

0 029 -0 042

0 031

0 032 -0 038

O 032 -0 035

0 033 -0 033

0 033 -0 031

0 034 -0 030

0 034 -0 028

0 026

0 015

0 022 -0 0491

0 040

0 011

0 034

0 033 -0 025

0 033 -0 024

0 033 -0 022

0 033 -0 021

0 032

0 032 -0 019

0 032

0 031

0 031 -0 016

0 031 -0 n16

0 030 -0 015 0 030 -0 014

0 029

0 029 -0 013

0 029 -0 013

1 8U

1 8,~

1 85i

1 861

i 87:

1 88

1 89

1 90

1 91

I 92

1 93

I 94

1 95

1 96

I 97

1 98

1 99

2 O0

2 Ol

2 02

2 03

2 04

2 05

2 06

2 07

2 08

20q

2 i0 2 II

2 12

2 13

2 14

2 15

0 004

0 007

00zl

-0 008

-0 016

-0 025

0 028 -0 012

0 028 -0 012

0 028 -0 011

2 16

2 17

0 012

0 000

0 103 -0

-0 000

0 01~

0 017

0 018

0 020

0 051lI

0 052 i

-0 053

0 021 0 022 0 022 0 023! 0 023 0 024 0 024 0 025 0 026 0 026 0 027 0 028 0 029 0 030 0 031 0 031

-0 024 -0 024 -0 024 -0 025 -0 025 -0 025 - 0 026 -0 026 -0 027 -0 027 -0 027 - 0 028 -0 028 -0 029 - 0 029 -0 029 -0 030

0 003 -0 024 -0 000 -0 021 -0 003 -0 019 -0 007 -0 016 -O 010 -0 015 -0 012 -0 013 0 015 -0 012 -0 018 -0 010 -0 020 - 0 0 0 S -0 023 -0 008 -0 025 -0 007 -0 027 -0 006 -0 029 -0 006 -0 031 - 0 0 0 S -0 033 -0 004 -0 035 -0 004 -0 037 -0 003

0 006

-0 081

0 034 0 034

120 122

-0 -0 -0 123 -0 124

0 094 0 082 0 071 0 061 0 052 0 044 0 036 0 029 0 023 0 018 0 013 0 010 0 009

-0 070 -0 071 -0 071 -0 071 -0 069 -0 067 -0 063 -0 059 -0 054 -0 048 -0 041 -0 034 -0 027

0 023 0 019 0 016

0 026

0 029

0 032

0 035

0 03~

0 040

0 043

0 046

0 048

0 051

0 130 -0 012

-0 129 -0 007

0 006 0 007 0 007 0 007 0 007

-0 084 -0 086 - 0 088 -0 090 -0 091

0 031 0 032 0 032

112

-0 -0 114

0 033

i18 119

-0 -0

00ll

0 042 -0 001 0 042 -0 00~ 0 042 -0 00. 0 042 -0 00; 0 042 -0 001

0 014 0 010 0 005 0 001

-0 083 -0 083

-0 082 -0 004 -0 082 -0 009 -0 081 -0 014 -0 080 -0 020

00l

0 01Z

00l 0 01~

0 018 -0 000

-0 004 -0 038 -0 0 4 8

0 038 0 038

0 009

-0 033 138

-0 0 071

0 013

-0 116

0 01; 0 019 0 009

-0 007 -0 041 0 038

-0 I15

0 037 137

-0 00SS

0 014

0 Of: 0 020

-0 010 0 036 0 009

-0 114

-0 045 -0 001: -0 032 -0 047 -0 000 -0 032 0 038 136

-0 0 048

0 013

0 01, 0 021 0 035 -0 031 -0 043 -0 001 0 009 0 038

135

-0

0 038

0 010

0 Of,

-0 113

0 037

-0 134

0 030

0 023 -0 019 -0 051 -0 014 -0 048 0 034 -0 031 -0 042 -0 002 0 008

-0 III

0 006

0 Of, 0 025 0 033

-0 0 3 ] -0 040 -0 002 O 008 -0 110

0 037 0 037

-0 132 -0 133

0 028 -0 031 -0 054 -0 024 -0 053

0 032

-0 030 -0 039 -0 003 0 008

-0 109

0 023

0 001

0 036

-0 131

0 01~ 00D 0 008

-0 107

0 012 0 017

-0 012 -0 005

0 01; 0 033 0 030 -0 046 -0 054 0 008 I06

-0 0 036

-0 130

O 010

-0 019

00l 0 035 0 053 -0 051 0 008

-0 104

0 036

-0 129

0 037

0 008

0 00'

0 039 -0 060 -0 048 0 008

-0 103

0 03E

128

-0

-0 066 -0 043 0 008

101

-0

0 035

-0 126

0 00, 000i 0 008

-0 100

0 035

-0 125

0 00~ 0 041 0 040 0 007

-0 098

0 034

0 044

-0 038 -0 055

-0 071 -0 038

-0 077 -0 026

0 042 0 007

-0 096

-0 075 -0 032

0 007 0 007

0 033 -0 095

0 042 - 0 0 l l

0 042

0 041

0 041 -0 01! -0 084

0 041 -0 01(

0 041

0 041 -0 02{

0 041 -0 02Z

0 041 -0 02(

0 039 -0 03z 0 040 -0 03(

0 038 -0 04(

0 027 -0 05~ 0 034 -0 04E

-0 084

0 I03

-0 085

0 017 - 0 0 S ~

0 023 0 018

0 125

-0 073

0 002 ~0 061

-0 086 -0 085

0 145

-0 048

-0 012 -0 05~

-0 025 -0 031 -0 022 -0 043

-0 024 -0 0 2 !

-0 021 -0 014

FFO5

-0 093

0 033

0 032

-0 116

-0 I15

0 006

-0 083

0 031

-0 111

0 030

0 02~

0 021

-0 023

0 006

-0 079

-0 I09

-0 068

0 053

0 028 0 021

-0 023

0 011 -0 032 0 007 0 028

0 006

0 109

0 056

0 034

0 088 -0 087

0 022

-0 023

0 014 -0 037

0 006

0 077

0 030

-0 075

108

0 030

-0

-0 063

0 059

0 040

-0 090

0 022

-0 022

0 018 -0 044

0 006

-0 073

0 029

0 126

0 063

0 048

-0 091

0 023

-0 021

0 021 -0 052

0 00~

-0 071

0 029

103

0 054

0 068

0 058

-0 092

0 024

-0

0 145

0 072

0 070

-0 093

0 026

-0 019

0 024 -0 074

0 1631 -0 105 0 160' - 0 106

0 14~

0 027 -0 010

0 062

0 085

-0 091

0 028

-0 017

0 021 -0 089 -0 021

000S

0 013 -0 105

0 031 0 030

-0 010 -0 014

-0 002 -0 120

0 024 -0 062

-0 098

0 00S

-0 062

0 005

0 031

0 15S

-0 004

0 012

-0 026 -0 129

0 005

0 027

-0 097

-0 060

0 004

-0 058

0 146

0 027

0 028

0 001

0 024

0 006

0 077 -0 112:

0 121

0 090

0 064

0 044

O 057

0 070

0 071

0 065

FP05

-0 054 -0 127

-0 069

0 121

0 085

0 026

-0 095

0 OO4

-0 055

0 028

0 oga

0 094

0 026

-0 093

0 004

-0 053

-0 102

0 072

0 095

0 025

-0 091

0 019

0 008

-0 091 -0 0911

0 014

0 008

-0 095 -0 06~

0 005

0 054

0 093

0 025

-0 089

0 004

-0 051

0 004

0 011

0 008

0 008

0 007

0 051

0 086 -0 037 -0 092

-0 066

0 03S

0 089

0 024

-0 088

-0 048

0 046

DGO5

-0 064

0 028

0 085

0 024

-0 086

0 003 0 003

-0 044

DDO5

0 028

0 017

0 080

0 023

-0 084

DD03

0 027

0 009

0 075

0 023

-0 082

DS03

-0 i00

0 001

0 069

0 058 -0 011 0 064 0 006

0 052 -0 016

PF03

-0 038

0 077

0 079

0 078

0 074

0 069

0 066

0 057

0 056

-0 127 -0 003

109

107

0 060

-0 023

0 096 -0 16]

0 138

0 059

-0 021

0 094 -0 167

-0 002 -0 052

1 82

00~O

-0 007

1 81

0 054

0 019

0 092 -0 170

-0 010 -0 047

0 053

0 052

0 050

1 80

-0 015

-0 014

-0 017

175

0 087 -0

172

177

0 083 -0

PP03

0 089 -0

0 040

PPOI

-0 014 -0 044

0 016

-0 018 -0 036

SDOI

I 79

1 78

1 77

:CM

Table 7 K - p ~ rrZ(1385) partial-wave amplitudes, given as real and tmagmary parts at l 0 MeV centre-of-mass energy intervals for Z ( 1 3 8 5 ) decaying into A~"

$

0

i

E

i

~o

0 082

-0 094

-0 104

0 i12

0 120

1 8S

l 90

I 91

I 92

1 93

0 008

-0 059

-0 071

0 083

-0 079 -0 080

-0 081 -0 081

-0 082

0 023

-0 118

-0 l|l

-0 102

-0 093

-0 083 -0 009

-0 073

-0 062 -0 016

-0 018

2 04

2 05

2 06

2 07

2 08

2 I0 -0 040 -0 017

-0 029 -0 014

2 03

2 11

2 12

0 018

0 024

2 16

2 17

0 03¢

0 01~

0 010

2 15

-0 005

-0 084 -0 084

0 OlC

0 002

2 14

-0 079

-0 077 -0 078

-0 077

-0 083 0 001, -0 083

2 13 -0 008 -0 006

0 011

2 09 -0 051 -0 017

0 013

0 003

0 005

0 013

-0 075 -0 076

0 033

-0 124

2 02

-0 021

0 01;

0 012

0 012

0 012

0 011

0 011

0 Oil

00I!

0 Oil

0 Oil

0 Oil

0 Oil

0 Oil -0 030

-0 029

-0 028

-0 027

-0 027

-0 026

-0 025

-0 024

-0 024

-0 023

• 0 075 -0 039

• 0 081 -0 042

• 0 086 -0 045

-0 091 -0 047

-0 096 -0 050

-0 lOl -0 053

-0 106 -0 055

-0 Ill -0 058

-0 ll~ -0 060

-0 121 -0 063

-0 037

-0 036

-0 035

-0 035

-0 034

-0 034

-0 033

-0 032

-0 032

-0 031

-0 125 -0 065 -0 030

-0 130 -0 067

-0 134 -0 070

-0 138 -0 072

-0 142 -0 074

0 011

-0 150 -0 078

-0 154 -0 080

-0 157 -0 082

-0 161 -0 083

-0 164 -0 085

-0 167 -0 087 -0 022

-0 020

088

170 - 0

-0 172 -0 089

-0

-0 020

-0 019

-0 018

-0 017

-0 016

-0 016

-0 015

-0 014

-0 013

-0 013

-0 175 -0 09I

-0 177 -0 092

-0 180 -0 093

-0 182 -0 094

-0 183 -0 095

-0 185 -0 096

-0 186 -0 097

0 188 -0 097

-0 189 -0 0=~

-0 189 -0 09~

-0 146 -0 076

0 011

-00lO

-0 009

-0 008

0 008

0 009

0 009

0 008

0 007

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Rutherford Laboratory - Imperial College Collaboration / K - p ~ ~r,+ (1385) Fsgure S(o)

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Ftg 8 Argand diagrams for the active parUal waves. The arrows are 12 5 MeV long, spaced at 50 MeV intervals more resonances having widths greater than 30 MeV were unsuccessful. It would require higher statistics to allow for finer binning m this energy region to resolve any narrow structures. The resonant amplitudes obtained m the f'mal fit are given in table 6. The partial-wave amplitudes are presented at every 10 MeV c.m. energy interval in table 7, and the Argand diagrams for the active partial waves are shown in fig.8.

5. Comparison with SU(3) Having assigned resonances into SU(3) multiplets, it is then possible in certain cases to predict the relative signs of resonance amphtudes. The D05(1830) and D15(1755) are both members of the s - octet and using the accepted value for the F- and D-admixture parameter (o0 for their couphng to the mmal K - p state the relative sign of their D-wave decay amphtudes to n~(1385) is predicted to be negative We find this to be the case m contrast to the results obtained by Prevost et al. [19].

228

Rutherford Laboratory - Imperial College Collaboratton / K - p ~ 1r~~+-(1385}

Table 8 Comparison of the signs of resonant amphtudes with those predicted by SU(3) from lrN ~ N*/ A ~ 7rA,note that the overall sign is arbitrary SU(3) multlplet

Resonant amphtude

Observed sign

Predicted sign

S-

octet

DD05(1830) DD15(1775)

(-) +

(-) +

S÷

octet

FP05(1820) FF05(1820) FF15(1906)

+ -

+ -

7+

decuplet

FF17(2040)

The 7r~(1385) amphtudes can also be related by SU(3) to the 7rA decay of nonstrange N* and A resonances, the amphtude signs of many of wtuch have been determined [20]. The signs of amphtudes obtained m the present analysis for members of the 3 - octet, 3 ÷ octet and 7+ decuplet are compared with those deraved from ira amphtudes m table 8. The five relatwe signs wluch may be determmed are all as expected. For the F15 amphtude the sign is very sensitive to the value of the admixture parameter a and was obtained using the most recent value reported by Samaos et al. [21] and this value is therefore supported. (The analysis of Cashmore et al. [20] uses an earher value ofct and predicts the wrong F15 sign.) It should be noted that the convention used by Cashmore et al [20] (baryon first, meson second m both inmal and final states) is related to the convention used m this analysis by an overall sxgn change, which is not measurable.

6. Classification of Y* 's in SU(6)w The reaction channel K - p -+ lrN(1385) discussed in ttus paper is an example of SU(3) inelastic scattenng, 1.e., the mmal and final state baryons come from different SU(3) multiplets. Moreover, the initial and final orbital angular momenta may be different. Resonant amplitudes coupled to this channel can therefore in pnnciple put strong constraints on symmetries higher than SU(3), such as SU(6)w ® O(3), wtuch seek to embrace the spins of resonances. Using an approach based on the Melosh transformation [23], Cashmore, Hey and Iatchfield [24-26] have fitted rates of decays of baryons in the (70, 1 - ) and (56, 2 +) multlplets into the ground state (56, 0 ÷) by pseudoscalar meson emission These fits predict couphngs m the ~ ~ 7rN(1385) channel and comparison with the present results (table 6) permits the following observations to be made (a) Four resonances assigned to the (70, 1 - ) namely S01(1825), D13(1920),

Rutherford Laboratory - Imperial College Collaboration/K-p ~ lr~~± (1385)

229

D15(1775) and D05(1830) are found to have significant rr~(1385) couplings. The measured signs and rough magmtudes of the first three agree with the predictions. However the D05(1830) as an unmixed member of the quark-spin ~ SU(3) octet is predicted to decouple from K.N, yet, as In the 2-body ~Tr channel [15] it is found to have a large.resonant amplitude. (b) There IS no evidence for the predicted large amphtudes for the D03(1815) and S1 i(1930) members of the (70, 1 - ) (c) F05(1820), F15(1906) and F17(2040) states assigned to the (56, 2 +) are observed to have significant 7rZ(1385) couplings The F05 and F17 signs are as predicted, and in particular the sign of the P-wave decay amphtude of the F05 confirms the "SU(6)w hke" P/F sign ratio reported In the An analysis [28]. (d) In agreement with pre&ction, the F15(1906) amplitudes are found to be small in magnitude In view of this the apparent sign dasagreement of the F-wave decay amphtude is probably not significant. (e) A major disagreement occurs in the sign of the large amplitude for the F-wave decay of the P03(1900) when assigned to the (56, 2+), suggesting that such an assignment is Incorrect. It could be a candidate for the (70, 2 +) multlplet pre&cted by Horgan and Dalitz [22] to be mass degenerate with the (56, 2 ÷) multiplet. The observation of the F05(2100) In the present analysis and In the ZTr channel [27,15] provides supporting evidence for that multiplet.

6. Conclusions New data are presented on the reaction K - p ~ A°~r÷rr- at eleven energies between 1775 and 1957 MeV in the c.m. These high-statistics data allow the best measurement to date of the masses and widths of the E(1385) resonance. The real parts of the density matrix elements for the reactions K - p ~ lr±E~(1385) have been extracted in terms of Legendre polynomial expansion coefficients using an incoherent quasi two-body model. The information available from the A decay has also been exploited to obtam the polarisatlon coefficients corresponding to the imaginary parts of the density matrices. Using these coefficients together with those from the CRSS experiment, an energy dependent partial-wave analysis has been carried out and the couphngs of resonances to the ~ q ~ nZ(1385) channel have been determined. The well established resonances D15(1775), D05(1830), F05(1820), P03(1900) and F17(2040) were found to have significant couphngs to this channel. An Interesting feature of the solution is that, with the exception of the P03(1900), the partial wave with the lower outgoing orbital angular momentum dommates Of the less well estabhshed resonances only the S01(1825), F05(2100) and the D13(1920) are required. It should be noted that as In the K,N -~ two-body channels and the K - p ~ 1rA(1520) channel [29], there IS no evidence for any P13 resonances. Using SU(3) symmetry, the relative signs of the resonance couphngs are found to

230

Rutherford Laboratory - lmpertal College Collaboration / K - p --* 7r~;~± (1385)

be m c o m p l e t e agreement with those p r e & c t e d f r o m m e a s u r e m e n t s o f the rrN ~ ~rA reaction. The results have also been c o m p a r e d with predictions of S U ( 6 ) w ® 0 ( 3 ) m o d e l fits.

References [1] A de Bellefon, A. Berthon, L K Rangan, J. Vrana, T C Bacon, A. Brandstetter, I Butterworth, S M Deen, C M. Fisher, P J Lltchfleld, R J Mdler, J R SmRh, G Burgun, J Meyer, E Pauh, G Poulard, B Talhnl, W WoJclk, J Zatz and R Strub, Nuovo Clm 7A (1972) 567 [2] RL-IC Collaboration, B Conforto, G P. Gopal, G E Kalmus, P J Lltchfleld, R T Ross, A J. Van Horn, T C Bacon, I Butterworth, E F Clayton and R M Waters, Nucl Phys BI05 (1976) 189 [3] RL-IC Collaboration, E.F. Clayton, T C Bacon, I. Butterworth, R M Waters, B Conforto, G P Gopal, G.E. Kalmus, R T Ross and A J. Van Horn, Nucl Phys B95 (1975) 130 [4] M. Jones, R Levl-Settl, D Merrdl and R D. Tnpp, Nucl Phys B90 (1975) 349 [5] J Gnsehn, A Glvernaud, R Barloutaud, J Prevost, F Grandlm, C Kleshng, D E Plane, W. Wlttek, P. Balllon, C. Brlcman, M Ferro-Luzzl, J O. Petersen, E Burkhardt, H. Oberlack, A Putzer and H. Schlelch, Nucl. Phys. B93 (1975) 189 [6] R Armenteros, M Ferro-Luzzl, D.W G.S Leith, R Leva-Settl, A Mmten, R D Tnpp, H Ftlthuth, V Hepp, E Kluge, H Schneider, R Barloutaud, P Granet, J Meyer and J P. Porte, Nucl Phys B8 (1968) 233 [7] J.D Jackson, Nuovo Clm 34 (1964) 1 [8] S O. Holmgren, M. Agudar-Bemtez, F Barrelro, R J. Hemmgway, M J Losty, R P. Worden, J. Zatz, J.C. Kluyver, G.G.G. Massaro, E.W. Klttel and R.T. Van de Walle, Nucl. Phys. B119 (1977) 261. [9] S.R. Borenstem, G R Kalbflelsch, R.C Strand, V. Vanderburg and J W Chapman, Phys Rev. D9 (1974) 3006. [10] Particle Data Group, Rev Mod. Phys 48 (1976) 1 [ 11 ] B. Franek, The extraction of quasi-two body processes from 3-body final states, programme EXTRA, Rutherford Laboratory Report RL-77-069/A [12] S.M Deen, Generahsed partial-wave analysis, Rutherford Laboratory Report RPP/H/68 [13] P J Lltchfleld, private commumcatlon [14] A Berthon, G. Tristram, J Vrana, T C Bacon, A Brandstetter, I Butterworth, G P Gopal, P S Jones, P J Lltchfleld, M Mandelkern, J Meyer, G Poulard, B Tallml, W Wojchk, J Zatz and R Strub, Nuovo Clm 21A (1974) 146 [15] RL-IC Collaboration, G P Gopal, R T Ross, A J Van Horn, A C McPherson, E F Clayton, T.C Bacon and I Butterworth, Nucl Phys Bl19 (1977) 362. [ 16] J M Blatt and V F Welsskopf, Theoretical nuclear physics, (Wiley, New York, 1952) p. 361 [17] B Franek, Coefficients for partml-wave analysis of two-body reactions with general spins, Rutherford Laboratory Bubble Chamber Research Group Phystcs Note 110, Rutherford Laboratory Report, to be pubhshed [18] R Stern, Ph D thesis, Unwerslty of London, unpubhshed [19] J Prevost, R. Barloutaud, J Gnsehn, F Plerre, C Bncman, J O Peterson, J Meyer, H Fllthuth and E Kluge, Nucl Phys. B69 (1974) 246 [20] R.J. Cashmore, D W G S. Leith, R S Longacre and A H Rosenfeld, Nucl. Phys B92 (1975) 37 [21] N P Samlos, M Goldberg and B T Meadows, Rev Mod Phys. 46 (1974) 49 [22] R Horgan and R H Dahtz, Nucl Phys B66 (1973) 135, R Horgan, Nucl Phys B71 (1974)514.

Rutherford Laboratory - Imperial College Collaboration / K - p -~ rr~r~+-(1385) [23] [24] [25] [26] [27]

231

H.J Melosh, Plays Rev. D9 (1974) 1095 A J O Hey, P.J Lltchfield and R J Cashmore, Nucl. Phys B95 (1975) 516 R J Cashmore, A J.G Hey and P J Lltchfield, Nucl Phys. B98 (1975) 237 P J. Lltchfleld, R.J Cashmore and A J G. Hey, Rutherford Laboratory Report RL-76-111 A de Bellefon, A Berthon, P Btllotr, J M Brunet, G Tristram, J Vrana, B Baccarl, G Poulard, D Revel ahd B Tallml, Nuovo Clm 37A (1977) 175 [28] Review talk by K W J Barnham at the Baryon Resonances c o n f , Oxford, 1976 and references therein [29] W. Cameron, B Franek, G.P Gopal, G E Kalmus, A C McPherson, R T Ross, D.H Saxon, T C Bacon, I Butterworth, R W M Hughes, P Newham and R A Stern, Nucl Phys B131 (1977) 399