- Email: [email protected]
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Nuclear Physics B27 (1971) 605-614. North-Holland Publishing Company
STRANGE-PARTICLE PRODUCTION IN 7 GeV/c :rr-p INTERACTIONS* A. PEEKNA*, W . D . W A L K E R , B.Y. OH** and M. A. THOMPSON University of Wisconsin D. R. CLEAR***, D. N. HOA and J. P R E N T I C E University of Toronto Received 10 August 1970 (Revised manuscript received 15 December 1970) Abstract: Various cross sections are presented. Data on quasi-two-body reactions are found to be generally consistent with the Regge-pole model. There are some indications that the highest-lying trajectory does not always exclusively dominate at this energy. i. C R O S S S E C T I O N S
The c r o s s s e c t i o n s r e p o r t e d h e r e a r e b a s e d on 160 000 e x p o s u r e s of the MURA - ANL 30 inch hydrogen bubble c h a m b e r . The c h a m b e r had two g a m m a - r a y - c o n v e r t e r plates, of 0.76 and 1.09 radiation lengths, positioned v e r t i c a l l y in the d o w n s t r e a m q u a r t e r of the c h a m b e r . The c o n v e r t e r plates p r o v e d v e r y useful in r e s o l v i n g a m b i g u i t i e s involving ~o and unseen K o. E x cluding A / ~ o ambiguities, only 6% of those events for which the final state should be fully r e s o l v a b l e (--< 1 m i s s i n g neutral) r e m a i n e d in the " a m b i g u ous" c a t e g o r y . The c o n v e r t e r plates w e r e not v e r y helpful in r e s o l v i n g A / ~ o ambiguities; b r e m s s t r a h l u n g and collision l o s s e s of the c o n v e r s i o n e l e c t r o n s in the plates s e r i o u s l y d e t r a c t f r o m the detection efficiency if the g a m m a m o m e n t u m is l e s s than 200 M e V / c , as is typical of g a m m a s f r o m ~ o decay. Event topologies m e a s u r e d include all 2V ° events and t w o - p r o n g +V° events; f o r m o s t of the e x p o s u r e the t w o - p r o n g +Vo events w e r e r e q u i r e d to have a proton t r a c k slow enough to be identifiable by bubble density, either at the main v e r t e x or at the VO. This was taken into account in computing total c r o s s section f r o m t w o - p r o n g +V° events; the c o r r e c t i o n b a s i c a l l y c o n s i s t e d of n o r m a l i z i n g to the n u m b e r of events with f o u r - m o m e n t u m t r a n s f e r to the b a r y o n below a cutoff value of I t I = 0.8 GeV 2. C o r r e c t i o n s $
Work supported in part by the US Atomic Energy commission, and National Research Council of Canada. * Now at Wisconsin State University, Oshkosh, Wisconsin. ** Now at Michigan State University, East Lansing, Michigan. *** Deceased.
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w e r e a l s o m a d e f o r n e u t r a l d e c a y m o d e s of V ° a n d f o r t h o s e V ° t h a t d e c a y e i t h e r o u t s i d e t h e c h a m b e r o r t o o c l o s e t o t h e p r o d u c t i o n v e r t e x to b e spotted by the scanners. Each event was weighted by the inverse probabilit y of t h e a s s o c i a t e d VO d e c a y i n g in t h e d e c a y f i d u c i a l r e g i o n , a n d t h e e v e n t w a s g i v e n z e r o w e i g h t if a s e e n V ° d e c a y w a s o u t s i d e t h i s r e g i o n . S y s t e m a tic errors due to ambiguous events and events whose identification was not a b s o l u t e l y c e r t a i n w e r e i n c o r p o r a t e d i n t o t h e s t a t e d e r r o r s in t h e c r o s s s e c t i o n s ; t h e s y s t e m a t i c e r r o r s w e r e a s s u m e d i n d e p e n d e n t of p u r e l y s t a t i s tical errors. T h e c r o s s s e c t i o n s f o r v a r i o u s f i n a l s t a t e s a r e d i s p l a y e d in t a b l e 1. W i t h t h e e x c e p t i o n of f o u r - p r o n g +2VO e v e n t s , t h e A c o u l d n o t b e s e p a r a t e d f r o m t h e ~o w i t h a d e g r e e of r e l i a b i l i t y s u f f i c i e n t to p e r m i t c o m p u t a t i o n of s e p a rate cross sections with reasonable errors. There is also large r.o contam i n a t i o n in f i n a l s t a t e s w h o s e k i n e m a t i c f i t h y p o t h e s i s i n v o l v e d a A a n d an u n s e e n K ° o r ~o; a s t u d y of t w o - p r o n g +2V o e v e n t s s h o w e d t h a t m o s t ~-~+L'OK 1 e v e n t s f i t ~-~+AKO if t h e m e a s u r e d i n f o r m a t i o n on t h e K 1 i s d i s carded. If t h e K - d e c a y s in KOK-~ f i n a l s t a t e s w e r e c o m p l e t e l y u n c o r r e l a t e d t h e n t h e c r o s s s e c t i o n f o r KO~-~ w o u l d b e f o u r t i m e s t h e c r o s s s e c t i o n f o r K1K 1 b u t p r o d u c t i o n of K - p a i r r e s o n a n c e s i n v a l i d a t e s t h i s a s s u m p t i o n . T h u s KOKO c r o s s s e c t i o n s w e r e n o t c o m p u t e d f o r i n d i v i d u a l f i n a l s t a t e s . T h e c r o s s s e c t i o n f o r ~ - p K 1 K 2 w a s c o m p u t e d by m e a n s of s u b t r a c t i n g t h e n u m b e r of p r e d i c t e d ~ - P K 1 K 1 e v e n t s w i t h o n l y one of t h e K1 d e c a y i n g v i a t h e c h a r g e d m o d e f r o m t h e n u m b e r of ~ - p K 1 u n s e e n K ° e v e n t s . Cross sections for two-body and quasi-two-body states observed are l i s t e d in t a b l e 2~ L i s t e d c r o s s s e c t i o n s in t h e f o r w a r d d i r e c t i o n a r e i n t e g r a t e d o v e r two i n t e r v a l s in t h e s q u a r e of t h e f o u r - m o m e n t u m t r a n s f e r t, (to-t) < 0 . 4 GeV 2 a n d (to-t) < 0.8 GeV2; t o d e n o t e s t a t z e r o s c a t t e r i n g a n g l e . T h e c r o s s s e c t i o n s a p p l y to t h e d e c a y m o d e s i n d i c a t e d in t h e t a b l e . T h e K+~ - a n d K ° ~ ° d e c a y s of t h e K+O(890) a n d KNO(1420) w e r e a s s u m e d to b e in t h e r a t i o two to one in a c c o r d a n c e w i t h i s o p i n c o n s e r v a t i o n . P o s s i b l e Table 2 C r o s s sections for two-body states Two-body s t a t e , decay mode (h/~°)K °
Cross sections [~b] over momentum t r a n s f e r interval (to-t) < 0.4 (to-t) < 0.8 total 28.8~8.6
31.0±9.0
33.0±
9.2
(A/~°)K*°(890), K*(890) ~ KTr
14.4~2.9
22.3±3.6
26.2 + 1 5 . 9 - 5.6
(A/~°)KN°(1420), KN(1420) --* KTr
11.9~2.6
14.4±2.9
~o(1385)K °, ~°(1385) - , A~ o
15.0±5.1
15.0~5.1
17.5 +10"8 - 4.2 1 5 . 0 ± 5.1
5.3~2.2
5.7~2.3
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Fig. 1. C r o s s s e c t i o n o v e r the m o m e n t u m t r a n s f e r (to-t) < 0.4 GeV 2 v e r s u s s q u a r e of c . m . e n e r g y s , f o r (a)/T-p --* ( A / ~ ° ) K ° , (b) /T-p -* (A/~o)K*o (890), K* (890) --*K/T.
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F i g . 2. T o t a l c r o s s s e c t i o n v e r s u s s q u a r e of c . m . e n e r g y s. f o r (a) /T-p -* ( A / ~ ° ) K *° (890), K* (890) -*K/T, (b)/T-p--* S o (1385)K ° , S ° (1385) - , A ~ , (c)/T-p --* S ° (1385)K *° (890), S ° (1385) --* A/To, K*O (890) --*K/T.
STRANGE-PARTICLE PRODUCTION
609
c o n t a m i n a t i o n of f i n a l s t a t e s i n v o l v i n g a ~ ° ( 1 3 8 5 ) f r o m A(1405) - ~ ° l r ° w a s not corrected for.
2. E N E R G Y D E i ~ E N D E N C E O F T W O - B O D Y CROSS S E C T I O N S P l o t s of c r o s s s e c t i o n o v e r (to-t) < 0.4 v e r s u s t h e s q u a r e of t h e c. m . e n e r g y s f o r ( A / r . ° ) K ° a n d (A/~O)K*O(890) a r e d i s p l a y e d in f i g . 1, a n d p l o t s of t o t a l c r o s s s e c t i o n v e r s u s s f o r (A/~O)K*O(890), ~ ° ( 1 3 8 5 ) K ° a n d ~o(1385)K*O(890) in f i g . 2. The Regge-pole model predicts that at sufficiently high energies the s c a t t e r i n g a m p l i t u d e i s d o m i n a t e d b y t h e p o l e in t h e c r o s s e d c h a n n e l w h o s e t r a j e c t o r y l i e s h i g h e s t on t h e C h e w - F r a u t s c h i p l o t ; when t h i s i s t h e c a s e t h e d e p e n d e n c e of t h e d i f f e r e n t i a l c r o s s s e c t i o n on e n e r g y b e c o m e s s 2 ~ ( t ) - 2 . In o u r c a s e t h e h i g h e s t - l y i n g c r o s s e d - c h a n n e l t r a j e c t o r i e s a r e t h e K* a n d K**, b o t h w i t h R e ~ ( t ) ~ 0.35 + 0 . S t . T h e a v e r a g e v a l u e of ~(t) in t h e i n t e r v a l (to-t) < 0.4 i s a p p r o x i m a t e l y 0.2, r e s u l t i n g in a n a p p r o x i m a t e s - d e p e n d e n c e of s - 1 . 6 f o r t h e c r o s s s e c t i o n o v e r (to-t) < 0.4. T o t h e e x t e n t t h a t t h e f o r w a r d p e a k c o n t a i n s m o s t of t h e c r o s s s e c t i o n o v e r t h e e n e r g y r a n g e b e i n g c o n s i d e r e d , one c a n e x p e c t s i m i l a r s - d e p e n d e n c e a l s o f o r t h e t o t a l c r o s s s e c t i o n $. T h e s t r a i g h t l i n e s s h o w n on t h e p l o t s r e p r e s e n t b e s t f i t s to s -n w i t h n u n d e t e r m i n e d b e f o r e t h e f i t . T h e v a l u e s of n o b t a i n e d in t h e f i t s a r e d i s p l a y e d in t a b l e 3. A g r e e m e n t w i t h s - 1 . 6 i s v e r y g o o d f o r ~ - p - ~ ( A / ~ ° ) K ° in t h e e n e r g y r a n g e a b o v e 2.3 G e V / c p i o n l a b m o m e n t u m ; d a t a f r o m l o w e r e n e r g i e s a r e n o t i n c l u d e d in t h e f i t . On t h e o t h e r h a n d , c o n f i n i n g t h e f i t t o t h e p i o n l a b m o m e n t u m r a n g e 1.6 t o 4.0 G e V / c r e s u l t s in a c o n s i d e r a b l y l o w e r v a l u e f o r n ; v a l u e s r e p o r t e d b y D a h l et a l . a r e 1.0 ± 0.2 f o r AK o a n d 0.75 * 0.3 f o r ~OK o [2]. T h e c r o s s s e c t i o n v e r s u s e n e r g y d a t a on t h e o t h e r r e a c t i o n s c a n a l s o b e c o n s i d e r e d c o n s i s t e n t w i t h d o m i n a n c e of t h e K * - K * * trajectories but they are not precise enough for this to be a really good test.
Table 3 F i t s of the energy dependence of the c r o s s section to s -n Two-body state ( A / ~ ° ) K ° , ( t o - t ) < 0.4 (A/~°)K *°, (to-t) < 0.4 (A/~°)K *° ~°(1385)K°
~°(1385)K*O
n 1.58 1.75 0.98 1.64 1.05
* 0.09 * 0.30 ± 0.47 ~- 0.46 ~- 0.65
Ref. [1] is a general review of the Regge-pole model.
Chi square confidence level 0.55 0.35 0.22 0.04 0.65
610
A. P E E K N A
et al.
45
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Fig. 3. The K+# -
mass f r o m #-K+A andTr-E+~ o.
3. PRODUCTION AND DECAY OF K*O(890) and KN°(1420) Decay a n g u l a r d i s t r i b u t i o n s f o r K*(890) in ~ - p -~ (h/~ °)K*°(890) and for
KN(1420) --* K+~ - in ~ - p -~ ( h / ~ O)KNO(1420) a r e d i s p l a y e d in fig. 4. As is evident f r o m the K+~ - m a s s plot (fig. 3) the s a m p l e s of K*(890) and KN(1420) a r e v e r y clean, a l m o s t b a c k g r o u n d f r e e . Data f r o m the U n i v e r sity of Toronto, b a s e d on 210 000 e x p o s u r e s of the s a m e bubble c h a m b e r , a r e included. As p e r usual convention, the J a c k s o n angle 0 is the angle b e tween the d e c a y - p r o d u c t ~- and the d i r e c t i o n of the incident y - , in the r e s t f r a m e of the decaying r e s o n a n c e , and ¢ is the angle between the r e s p e c t i v e n o r m a l s to the production and decay planes, a l s o called the T r e i m a n - Y a n g angle. T h e decay a n g u l a r distributions can be e x p r e s s e d in t e r m s of the spin density m a t r i x ; for the d e c a y K*(890)-~ K~(1- -~ 0- 0-) the distribution, folded in ¢, is
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Fig. 4. Decay angular distribution for (a) K* (890) produced in/r-p --. (A/~O)K*O(890), (b) KN(1420 ) produced in #-p --* (A/~°)KN° (1420), where O and ~ are the Jackson angle s. W(cosO, qS) = ~
3[
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w h e r e the p a r e e l e m e n t s of the spin density m a t r i x [8]. The e l e m e n t P l l h a s been e x p r e s s e d h e r e a s
½(1-Poo), a r i s i n g out of the
requirement
T r p = 1. When this is i n t e g r a t e d o v e r ~b and cos O s e p a r a t e l y , the d i s t r i b u tions in e a c h a n g l e a r e
612
A. PEEKNA et al.
3 EPooCOS2 0 + ~(11 - Poo) sin2 e
W(cosO) = ~
1
W(~o)=l [1-2Pl_l COS2~ ] . V a l u e s of the K*(890) s p i n - d e n s i t y m a t r i x e l e m e n t s a s d e t e r m i n e d by a m a x i m u m - l i k e l i h o o d fit a r e p r e s e n t e d in t a b l e 4. F o r the d e c a y KN(14~0 ) --* K~ (2 + --* 0 - 0-) the a n g u l a r d i s t r i b u t i o n folded in q~, is 15
W(cos 0, ~) = ~ -
-
I3poo(COS2 0 - ~)2 + 2(1
Poo - 2P22) sin2 8 c o s 2 0 + P22 sin4 ~
2cos qbsin20 [ ReP21 sin20 + q-6Rep 10 (cos20 - ½)] 2 c o s 2 q~sin 20 [ 2p 1-1 c ° s 2 0 - ~/6ReP20 (cos 2 0 - -~)]
+ 2ReP2-1 c°s3~sin20sin20
+ P 2 - 2 c°s4q~sin40 I "
H e r e P l l has been e x p r e s s e d in t e r m s of P00 and P22. T h e s e p a r a t e d i s t r i b u t i o n s in 0 and ~b a r e W(cos O) = -~- 3Ooo (cos20 _½)2 + 2(1 - P o p - 2022) s in20 cos20 + 022 sin40
W(~) = ~
[ 3 + 602_2 cos4q~ - 6 P l _ l cos2~b - 2 v~ReP20 c o s 2 ~b I •
When all eight p - p a r a m e t e r s w e r e left f r e e to v a r y in the m a x i m u m - l i k e l i hood fit without a p p l y i n g additional c o n s t r a i n t s , the r e s u l t i n g v a l u e f o r P22 t u r n e d out to be s l i g h t l y l e s s than z e r o . T h e r e f o r e the fit w a s r e d o n e with all Pi" f o r which i o r j = 2 s e t to z e r o . R e s u l t s of this fit a r e p r e s e n t e d in table35. Table 4 K* (890) spin-density matrix elements. Poo = 0.182 + 0.071 Pl-1 = 0.227 ± 0.068 Repl 0 = -0.066 ~- 0.039 Table 5 KN°(1420) spin-density matrix elements. Poo = 0.357 =e 0.096 P l - 1 = 0.036 ~- 0.089 Repl 0 = 0.005 :L 0.066 The
Pij for which i
or j = 2 can be considered consistent with zero and were set to zero in the fit.
,
STRANGE-PARTICLE PRODUCTION
613
T h e s e decay a n g u l a r d i s t r i b u t i o n s and fitted s p i n - d e n s i t y m a t r i x e l e m e n t s can e a s i l y be r e l a t e d to p r e d i c t i o n s by the R e g g e - p o l e model. The K* and K** t r a j e c t o r i e s h a v e " n o r m a l " p a r i t y ; they contain only s t a t e s such that f o r spin J the p a r i t y is (-1)J. If a f t e r the m a n n e r of G o t t f r i e d and J a c k s o n [8], the production r e a c t i o n is e x a m i n e d f r o m the viewpoint of a p a r t i a l - w a v e a n a l y s i s in the t - c h a n n e l , it is s e e n that the a s s u m p t i o n of the K* a n d / o r K** t r a j e c t o r i e s , whether they a r e d e g e n e r a t e o r not, r e s u l t s in a r e s t r i c t i o n on the t - c h a n n e l p a r t i a l w a v e s , n a m e l y the r e l a t i o n P = (-1) J between t h e i r total a n g u l a r m o m e n t a J and p a r i t i e s P. The effect of the p a r i t y o p e r a t i o n ) on a t w o - p a r t i c l e s t a t e of total a n g u l a r m o m e n t u m J, M, and h e l i c i t i e s ~ 1 and 2 is given by [9]
I JM; ~i~2 > = 7/I~2(-I)J-SI-$2 1JM; -~I-~2 > , w h e r e 771 and 772 a r e the i n t r i n s i c p a r i t i e s of the individual p a r t i c l e s of spin S 1 and S 2. In our c a s e the p a r t i c l e s of i n t e r e s t a r e e i t h e r a ~(0-) and a K*(890) (1-), or a lr and a KN(1420) (2+); in both c a s e s the above e x p r e s s i o n becomes F)]JM;
k>
: (-1)J + I ] J M ;
- ~> ,
which i m p l i e s that f o r helicity z e r o the p a r i t y m u s t be (-I) J + l . T h e r e f o r e it is c l e a r that the r e q u i r e m e n t P = (-1) J i m p o s e d by the d o m i n a n c e of the K* a n d / o r K** t r a j e c t o r i e s r u l e s out helicity z e r o in the t - c h a n n e l c . m . f r a m e f o r the p r o d u c e d K*(890) and KN(1420). H e l i c i t i e s d i f f e r e n t f r o m z e r o a r e p e r m i t t e d ; the l i n e a r c o m b i n a t i o n
having p a r i t y ( - 1 ) J if ~ ¢ 0. A t r a n s f o r m a t i o n f r o m the t-channel c . m . f r a m e of the p r o d u c e d r e s o n a n c e does not change the helicity, which can be identified as the spin c o m p o n e n t along the d i r e c t i o n of the incident ~-. The e x c l u s i v e d o m i n a n c e of the K* - K * * t r a j e c t o r i e s would thus r e s u l t in v a n ishing of all P i j f o r which i or j = 0. The fitted v a l u e s of Poo and R e P l 0 f o r the K*(890) d i s p l a y e d in table 4 a r e sufficiently c l o s e to z e r o to indicate c o n s i s t e n c y with a high d e g r e e of d o m i n a n c e by the K* - K * * t r a j e c t o r i e s , though s o m e contribution f r o m t channel s t a t e s of P = (-1)J+l (as on the K - t r a j e c t o r y ) a l s o s e e m s to be p r e sent. The fitted v a l u e of Poo f o r the KN(1420) is l a r g e enough to indicate a m o r e definite contribution f r o m t - c h a n n e l s t a t e s of P = (-1)J+l; thus the r e a c t i o n Ir-p -* (A/Z'O)KNO(1420) cannot be c o n s i d e r e d e x c l u s i v e l y d o m i acted by the K* - K * * t r a j e c t o r i e s at this e n e r g y . A c h e c k of the a n g u l a r d i s t r i b u t i o n s of the A - d e c a y 7r- in AK*O(890) and AKNO(1420) (not shown) y i e l d e d no evidence of A p o l a r i z a t i o n though it is p o s s i b l e that s m a l l p o l a r i z a t i o n could have been m a s k e d by ~ o c o n t a m i n a tion. L a c k of p o l a r i z a t i o n is c o n s i s t e n t with d o m i n a n c e of a single t r a j e c t o r y since in the R e g g e - m o d e l p o l a r i z a t i o n can a r i s e only f r o m i n t e r f e r e n c e between different poles [1].
614
A. PEEKNA et al.
4. CONCLUSIONS In s u m m a r y , w e f i n d t h a t t h e e n e r g y d e p e n d e n c e of t h e c r o s s s e c t i o n in t h e f o r w a r d d i r e c t i o n (to- t < 0.4) f o r ~ - p -* ( A / ~ ° ) K ° i s in g o o d a g r e e m e n t w i t h d o m i n a n c e of t h e K* - K * * t r a j e c t o r i e s . F o r t h e r e a c t i o n y - p -~ (A/~.O)K*q(890) t h e e n e r g y d e p e n d e n c e of t h e c r o s s s e c t i o n a n d t h e d e c a y a n g u l a r d i s t r i b u t i o n s of t h e K* p o i n t to d o m i n a n c e by t h e K* - K * * t r a j e c t o r i e s ; t h e l a c k of A p o l a r i z a t i o n in ~ - p -~ AK*O(890) i s a l s o c o n s i s t e n t w i t h t h i s . Y e t t h e K* d e c a y a n g u l a r d i s t r i b u t i o n h i n t s a t a s l i g h t K e x c h a n g e c o n t r i b u t i o n . T h e KN°(1420) d e c a y a n g u l a r d i s t r i b u t i o n s s h o w a d e f i n i t e c o n t r i b u t i o n f r o m t - c h a n n e l s t a t e s of t h e " a b n o r m a l " s p i n - p a r i t y s e r i e s P = ( - 1 ) J +1, i n d i c a t i n g t h a t t h e r e a c t i o n y - p -~ ( A / ~ °)KN°(1420) i s n o t e x c l u s i v e l y d o m i n a t e d b y t h e K* - K** t r a j e c t o r i e s a t t h i s e n e r g y .
RE F E R E N C E S [1] G. E. Hite, Revs. Mod. Phys. 41 (1969) 669. [2] O. I. Dahl, L. M. Hardy, R. I, Hess, J. K i r z , D. H. Miller and J. A. Schwartz, Phys. Rev. 163 (1967) 1430. [3] O. I. Dahl, L.M. Hardy, J. Kirz and D. H. M i l l e r , Phys. Rev. 163 (1967) 1377. [4] J. Bartsch, L. Bondar, R. Speth, G. Hotop, G. Knies, F. Storm, J. M. Brownlee, N. N. Biswas, D. L u e r s , N. Schmitz, R. Seeliger and G. P. Wolf, Nuovo Cimento 33 (1966) A1010. [5] D.J. Grennel, G.R. Kalbfleish, K. W. Lai, J. M. S c a r r , T. G. Schumann, I.O. Skillieorn and M. S. Webster Phys. Rev. L e t t e r s 18 (1967) 86. [6] E. Bertolueci, I. Manelli, G. P i e r a z z i n i , A. Seribany, F. S e r g a m p i e t r i and M. L. Vincelli, CERN 68-7 Vol. 2 (1968) 190. [7] D. H. M i l l e r , A. Z. Kovaes, R. McIlwain, T.R. P a l f r e y and G. W. Tautfest, Phys. Rev. 140 (1965) B360. [8] K. Gottfried and J. D. Jackson, Nuovo Cimento 33 (1964) 309. [9] M. Jacob and G. C. Wick, Ann. of Phys. 7 (1959) 404.
Nuclear Physics B27 (1971) 605-614. North-Holland Publishing Company
STRANGE-PARTICLE PRODUCTION IN 7 GeV/c :rr-p INTERACTIONS* A. PEEKNA*, W . D . W A L K E R , B.Y. OH** and M. A. THOMPSON University of Wisconsin D. R. CLEAR***, D. N. HOA and J. P R E N T I C E University of Toronto Received 10 August 1970 (Revised manuscript received 15 December 1970) Abstract: Various cross sections are presented. Data on quasi-two-body reactions are found to be generally consistent with the Regge-pole model. There are some indications that the highest-lying trajectory does not always exclusively dominate at this energy. i. C R O S S S E C T I O N S
The c r o s s s e c t i o n s r e p o r t e d h e r e a r e b a s e d on 160 000 e x p o s u r e s of the MURA - ANL 30 inch hydrogen bubble c h a m b e r . The c h a m b e r had two g a m m a - r a y - c o n v e r t e r plates, of 0.76 and 1.09 radiation lengths, positioned v e r t i c a l l y in the d o w n s t r e a m q u a r t e r of the c h a m b e r . The c o n v e r t e r plates p r o v e d v e r y useful in r e s o l v i n g a m b i g u i t i e s involving ~o and unseen K o. E x cluding A / ~ o ambiguities, only 6% of those events for which the final state should be fully r e s o l v a b l e (--< 1 m i s s i n g neutral) r e m a i n e d in the " a m b i g u ous" c a t e g o r y . The c o n v e r t e r plates w e r e not v e r y helpful in r e s o l v i n g A / ~ o ambiguities; b r e m s s t r a h l u n g and collision l o s s e s of the c o n v e r s i o n e l e c t r o n s in the plates s e r i o u s l y d e t r a c t f r o m the detection efficiency if the g a m m a m o m e n t u m is l e s s than 200 M e V / c , as is typical of g a m m a s f r o m ~ o decay. Event topologies m e a s u r e d include all 2V ° events and t w o - p r o n g +V° events; f o r m o s t of the e x p o s u r e the t w o - p r o n g +Vo events w e r e r e q u i r e d to have a proton t r a c k slow enough to be identifiable by bubble density, either at the main v e r t e x or at the VO. This was taken into account in computing total c r o s s section f r o m t w o - p r o n g +V° events; the c o r r e c t i o n b a s i c a l l y c o n s i s t e d of n o r m a l i z i n g to the n u m b e r of events with f o u r - m o m e n t u m t r a n s f e r to the b a r y o n below a cutoff value of I t I = 0.8 GeV 2. C o r r e c t i o n s $
Work supported in part by the US Atomic Energy commission, and National Research Council of Canada. * Now at Wisconsin State University, Oshkosh, Wisconsin. ** Now at Michigan State University, East Lansing, Michigan. *** Deceased.
606
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w e r e a l s o m a d e f o r n e u t r a l d e c a y m o d e s of V ° a n d f o r t h o s e V ° t h a t d e c a y e i t h e r o u t s i d e t h e c h a m b e r o r t o o c l o s e t o t h e p r o d u c t i o n v e r t e x to b e spotted by the scanners. Each event was weighted by the inverse probabilit y of t h e a s s o c i a t e d VO d e c a y i n g in t h e d e c a y f i d u c i a l r e g i o n , a n d t h e e v e n t w a s g i v e n z e r o w e i g h t if a s e e n V ° d e c a y w a s o u t s i d e t h i s r e g i o n . S y s t e m a tic errors due to ambiguous events and events whose identification was not a b s o l u t e l y c e r t a i n w e r e i n c o r p o r a t e d i n t o t h e s t a t e d e r r o r s in t h e c r o s s s e c t i o n s ; t h e s y s t e m a t i c e r r o r s w e r e a s s u m e d i n d e p e n d e n t of p u r e l y s t a t i s tical errors. T h e c r o s s s e c t i o n s f o r v a r i o u s f i n a l s t a t e s a r e d i s p l a y e d in t a b l e 1. W i t h t h e e x c e p t i o n of f o u r - p r o n g +2VO e v e n t s , t h e A c o u l d n o t b e s e p a r a t e d f r o m t h e ~o w i t h a d e g r e e of r e l i a b i l i t y s u f f i c i e n t to p e r m i t c o m p u t a t i o n of s e p a rate cross sections with reasonable errors. There is also large r.o contam i n a t i o n in f i n a l s t a t e s w h o s e k i n e m a t i c f i t h y p o t h e s i s i n v o l v e d a A a n d an u n s e e n K ° o r ~o; a s t u d y of t w o - p r o n g +2V o e v e n t s s h o w e d t h a t m o s t ~-~+L'OK 1 e v e n t s f i t ~-~+AKO if t h e m e a s u r e d i n f o r m a t i o n on t h e K 1 i s d i s carded. If t h e K - d e c a y s in KOK-~ f i n a l s t a t e s w e r e c o m p l e t e l y u n c o r r e l a t e d t h e n t h e c r o s s s e c t i o n f o r KO~-~ w o u l d b e f o u r t i m e s t h e c r o s s s e c t i o n f o r K1K 1 b u t p r o d u c t i o n of K - p a i r r e s o n a n c e s i n v a l i d a t e s t h i s a s s u m p t i o n . T h u s KOKO c r o s s s e c t i o n s w e r e n o t c o m p u t e d f o r i n d i v i d u a l f i n a l s t a t e s . T h e c r o s s s e c t i o n f o r ~ - p K 1 K 2 w a s c o m p u t e d by m e a n s of s u b t r a c t i n g t h e n u m b e r of p r e d i c t e d ~ - P K 1 K 1 e v e n t s w i t h o n l y one of t h e K1 d e c a y i n g v i a t h e c h a r g e d m o d e f r o m t h e n u m b e r of ~ - p K 1 u n s e e n K ° e v e n t s . Cross sections for two-body and quasi-two-body states observed are l i s t e d in t a b l e 2~ L i s t e d c r o s s s e c t i o n s in t h e f o r w a r d d i r e c t i o n a r e i n t e g r a t e d o v e r two i n t e r v a l s in t h e s q u a r e of t h e f o u r - m o m e n t u m t r a n s f e r t, (to-t) < 0 . 4 GeV 2 a n d (to-t) < 0.8 GeV2; t o d e n o t e s t a t z e r o s c a t t e r i n g a n g l e . T h e c r o s s s e c t i o n s a p p l y to t h e d e c a y m o d e s i n d i c a t e d in t h e t a b l e . T h e K+~ - a n d K ° ~ ° d e c a y s of t h e K+O(890) a n d KNO(1420) w e r e a s s u m e d to b e in t h e r a t i o two to one in a c c o r d a n c e w i t h i s o p i n c o n s e r v a t i o n . P o s s i b l e Table 2 C r o s s sections for two-body states Two-body s t a t e , decay mode (h/~°)K °
Cross sections [~b] over momentum t r a n s f e r interval (to-t) < 0.4 (to-t) < 0.8 total 28.8~8.6
31.0±9.0
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9.2
(A/~°)K*°(890), K*(890) ~ KTr
14.4~2.9
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11.9~2.6
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F i g . 2. T o t a l c r o s s s e c t i o n v e r s u s s q u a r e of c . m . e n e r g y s. f o r (a) /T-p -* ( A / ~ ° ) K *° (890), K* (890) -*K/T, (b)/T-p--* S o (1385)K ° , S ° (1385) - , A ~ , (c)/T-p --* S ° (1385)K *° (890), S ° (1385) --* A/To, K*O (890) --*K/T.
STRANGE-PARTICLE PRODUCTION
609
c o n t a m i n a t i o n of f i n a l s t a t e s i n v o l v i n g a ~ ° ( 1 3 8 5 ) f r o m A(1405) - ~ ° l r ° w a s not corrected for.
2. E N E R G Y D E i ~ E N D E N C E O F T W O - B O D Y CROSS S E C T I O N S P l o t s of c r o s s s e c t i o n o v e r (to-t) < 0.4 v e r s u s t h e s q u a r e of t h e c. m . e n e r g y s f o r ( A / r . ° ) K ° a n d (A/~O)K*O(890) a r e d i s p l a y e d in f i g . 1, a n d p l o t s of t o t a l c r o s s s e c t i o n v e r s u s s f o r (A/~O)K*O(890), ~ ° ( 1 3 8 5 ) K ° a n d ~o(1385)K*O(890) in f i g . 2. The Regge-pole model predicts that at sufficiently high energies the s c a t t e r i n g a m p l i t u d e i s d o m i n a t e d b y t h e p o l e in t h e c r o s s e d c h a n n e l w h o s e t r a j e c t o r y l i e s h i g h e s t on t h e C h e w - F r a u t s c h i p l o t ; when t h i s i s t h e c a s e t h e d e p e n d e n c e of t h e d i f f e r e n t i a l c r o s s s e c t i o n on e n e r g y b e c o m e s s 2 ~ ( t ) - 2 . In o u r c a s e t h e h i g h e s t - l y i n g c r o s s e d - c h a n n e l t r a j e c t o r i e s a r e t h e K* a n d K**, b o t h w i t h R e ~ ( t ) ~ 0.35 + 0 . S t . T h e a v e r a g e v a l u e of ~(t) in t h e i n t e r v a l (to-t) < 0.4 i s a p p r o x i m a t e l y 0.2, r e s u l t i n g in a n a p p r o x i m a t e s - d e p e n d e n c e of s - 1 . 6 f o r t h e c r o s s s e c t i o n o v e r (to-t) < 0.4. T o t h e e x t e n t t h a t t h e f o r w a r d p e a k c o n t a i n s m o s t of t h e c r o s s s e c t i o n o v e r t h e e n e r g y r a n g e b e i n g c o n s i d e r e d , one c a n e x p e c t s i m i l a r s - d e p e n d e n c e a l s o f o r t h e t o t a l c r o s s s e c t i o n $. T h e s t r a i g h t l i n e s s h o w n on t h e p l o t s r e p r e s e n t b e s t f i t s to s -n w i t h n u n d e t e r m i n e d b e f o r e t h e f i t . T h e v a l u e s of n o b t a i n e d in t h e f i t s a r e d i s p l a y e d in t a b l e 3. A g r e e m e n t w i t h s - 1 . 6 i s v e r y g o o d f o r ~ - p - ~ ( A / ~ ° ) K ° in t h e e n e r g y r a n g e a b o v e 2.3 G e V / c p i o n l a b m o m e n t u m ; d a t a f r o m l o w e r e n e r g i e s a r e n o t i n c l u d e d in t h e f i t . On t h e o t h e r h a n d , c o n f i n i n g t h e f i t t o t h e p i o n l a b m o m e n t u m r a n g e 1.6 t o 4.0 G e V / c r e s u l t s in a c o n s i d e r a b l y l o w e r v a l u e f o r n ; v a l u e s r e p o r t e d b y D a h l et a l . a r e 1.0 ± 0.2 f o r AK o a n d 0.75 * 0.3 f o r ~OK o [2]. T h e c r o s s s e c t i o n v e r s u s e n e r g y d a t a on t h e o t h e r r e a c t i o n s c a n a l s o b e c o n s i d e r e d c o n s i s t e n t w i t h d o m i n a n c e of t h e K * - K * * trajectories but they are not precise enough for this to be a really good test.
Table 3 F i t s of the energy dependence of the c r o s s section to s -n Two-body state ( A / ~ ° ) K ° , ( t o - t ) < 0.4 (A/~°)K *°, (to-t) < 0.4 (A/~°)K *° ~°(1385)K°
~°(1385)K*O
n 1.58 1.75 0.98 1.64 1.05
* 0.09 * 0.30 ± 0.47 ~- 0.46 ~- 0.65
Ref. [1] is a general review of the Regge-pole model.
Chi square confidence level 0.55 0.35 0.22 0.04 0.65
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3. PRODUCTION AND DECAY OF K*O(890) and KN°(1420) Decay a n g u l a r d i s t r i b u t i o n s f o r K*(890) in ~ - p -~ (h/~ °)K*°(890) and for
KN(1420) --* K+~ - in ~ - p -~ ( h / ~ O)KNO(1420) a r e d i s p l a y e d in fig. 4. As is evident f r o m the K+~ - m a s s plot (fig. 3) the s a m p l e s of K*(890) and KN(1420) a r e v e r y clean, a l m o s t b a c k g r o u n d f r e e . Data f r o m the U n i v e r sity of Toronto, b a s e d on 210 000 e x p o s u r e s of the s a m e bubble c h a m b e r , a r e included. As p e r usual convention, the J a c k s o n angle 0 is the angle b e tween the d e c a y - p r o d u c t ~- and the d i r e c t i o n of the incident y - , in the r e s t f r a m e of the decaying r e s o n a n c e , and ¢ is the angle between the r e s p e c t i v e n o r m a l s to the production and decay planes, a l s o called the T r e i m a n - Y a n g angle. T h e decay a n g u l a r distributions can be e x p r e s s e d in t e r m s of the spin density m a t r i x ; for the d e c a y K*(890)-~ K~(1- -~ 0- 0-) the distribution, folded in ¢, is
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x
x
.
x
o
r~ o
-.,$ ~o
~
o,o
x
-o
x° x
o
--x
°o I
I
I
Xl
cos O
L
o
, -I.0
i -0.5
K.{1420) from Tr K
, ~ ,[-1 RI 0.0 0.5
(~,°)
-*h
1.15< M ( 7r- K*)< 1.6.5
B o WlSCONSIN,29EVENTS r"l x T O R O N T O , 2 7 E V E N T S 1.0
Fig. 4. Decay angular distribution for (a) K* (890) produced in/r-p --. (A/~O)K*O(890), (b) KN(1420 ) produced in #-p --* (A/~°)KN° (1420), where O and ~ are the Jackson angle s. W(cosO, qS) = ~
3[
PooCOS20 + ~i ( 1- P o o ) sin2O
"3 - P l - 1 sin20 cos2~b - V~Repl0 sin20 c o s ~ J ,
w h e r e the p a r e e l e m e n t s of the spin density m a t r i x [8]. The e l e m e n t P l l h a s been e x p r e s s e d h e r e a s
½(1-Poo), a r i s i n g out of the
requirement
T r p = 1. When this is i n t e g r a t e d o v e r ~b and cos O s e p a r a t e l y , the d i s t r i b u tions in e a c h a n g l e a r e
612
A. PEEKNA et al.
3 EPooCOS2 0 + ~(11 - Poo) sin2 e
W(cosO) = ~
1
W(~o)=l [1-2Pl_l COS2~ ] . V a l u e s of the K*(890) s p i n - d e n s i t y m a t r i x e l e m e n t s a s d e t e r m i n e d by a m a x i m u m - l i k e l i h o o d fit a r e p r e s e n t e d in t a b l e 4. F o r the d e c a y KN(14~0 ) --* K~ (2 + --* 0 - 0-) the a n g u l a r d i s t r i b u t i o n folded in q~, is 15
W(cos 0, ~) = ~ -
-
I3poo(COS2 0 - ~)2 + 2(1
Poo - 2P22) sin2 8 c o s 2 0 + P22 sin4 ~
2cos qbsin20 [ ReP21 sin20 + q-6Rep 10 (cos20 - ½)] 2 c o s 2 q~sin 20 [ 2p 1-1 c ° s 2 0 - ~/6ReP20 (cos 2 0 - -~)]
+ 2ReP2-1 c°s3~sin20sin20
+ P 2 - 2 c°s4q~sin40 I "
H e r e P l l has been e x p r e s s e d in t e r m s of P00 and P22. T h e s e p a r a t e d i s t r i b u t i o n s in 0 and ~b a r e W(cos O) = -~- 3Ooo (cos20 _½)2 + 2(1 - P o p - 2022) s in20 cos20 + 022 sin40
W(~) = ~
[ 3 + 602_2 cos4q~ - 6 P l _ l cos2~b - 2 v~ReP20 c o s 2 ~b I •
When all eight p - p a r a m e t e r s w e r e left f r e e to v a r y in the m a x i m u m - l i k e l i hood fit without a p p l y i n g additional c o n s t r a i n t s , the r e s u l t i n g v a l u e f o r P22 t u r n e d out to be s l i g h t l y l e s s than z e r o . T h e r e f o r e the fit w a s r e d o n e with all Pi" f o r which i o r j = 2 s e t to z e r o . R e s u l t s of this fit a r e p r e s e n t e d in table35. Table 4 K* (890) spin-density matrix elements. Poo = 0.182 + 0.071 Pl-1 = 0.227 ± 0.068 Repl 0 = -0.066 ~- 0.039 Table 5 KN°(1420) spin-density matrix elements. Poo = 0.357 =e 0.096 P l - 1 = 0.036 ~- 0.089 Repl 0 = 0.005 :L 0.066 The
Pij for which i
or j = 2 can be considered consistent with zero and were set to zero in the fit.
,
STRANGE-PARTICLE PRODUCTION
613
T h e s e decay a n g u l a r d i s t r i b u t i o n s and fitted s p i n - d e n s i t y m a t r i x e l e m e n t s can e a s i l y be r e l a t e d to p r e d i c t i o n s by the R e g g e - p o l e model. The K* and K** t r a j e c t o r i e s h a v e " n o r m a l " p a r i t y ; they contain only s t a t e s such that f o r spin J the p a r i t y is (-1)J. If a f t e r the m a n n e r of G o t t f r i e d and J a c k s o n [8], the production r e a c t i o n is e x a m i n e d f r o m the viewpoint of a p a r t i a l - w a v e a n a l y s i s in the t - c h a n n e l , it is s e e n that the a s s u m p t i o n of the K* a n d / o r K** t r a j e c t o r i e s , whether they a r e d e g e n e r a t e o r not, r e s u l t s in a r e s t r i c t i o n on the t - c h a n n e l p a r t i a l w a v e s , n a m e l y the r e l a t i o n P = (-1) J between t h e i r total a n g u l a r m o m e n t a J and p a r i t i e s P. The effect of the p a r i t y o p e r a t i o n ) on a t w o - p a r t i c l e s t a t e of total a n g u l a r m o m e n t u m J, M, and h e l i c i t i e s ~ 1 and 2 is given by [9]
I JM; ~i~2 > = 7/I~2(-I)J-SI-$2 1JM; -~I-~2 > , w h e r e 771 and 772 a r e the i n t r i n s i c p a r i t i e s of the individual p a r t i c l e s of spin S 1 and S 2. In our c a s e the p a r t i c l e s of i n t e r e s t a r e e i t h e r a ~(0-) and a K*(890) (1-), or a lr and a KN(1420) (2+); in both c a s e s the above e x p r e s s i o n becomes F)]JM;
k>
: (-1)J + I ] J M ;
- ~> ,
which i m p l i e s that f o r helicity z e r o the p a r i t y m u s t be (-I) J + l . T h e r e f o r e it is c l e a r that the r e q u i r e m e n t P = (-1) J i m p o s e d by the d o m i n a n c e of the K* a n d / o r K** t r a j e c t o r i e s r u l e s out helicity z e r o in the t - c h a n n e l c . m . f r a m e f o r the p r o d u c e d K*(890) and KN(1420). H e l i c i t i e s d i f f e r e n t f r o m z e r o a r e p e r m i t t e d ; the l i n e a r c o m b i n a t i o n
having p a r i t y ( - 1 ) J if ~ ¢ 0. A t r a n s f o r m a t i o n f r o m the t-channel c . m . f r a m e of the p r o d u c e d r e s o n a n c e does not change the helicity, which can be identified as the spin c o m p o n e n t along the d i r e c t i o n of the incident ~-. The e x c l u s i v e d o m i n a n c e of the K* - K * * t r a j e c t o r i e s would thus r e s u l t in v a n ishing of all P i j f o r which i or j = 0. The fitted v a l u e s of Poo and R e P l 0 f o r the K*(890) d i s p l a y e d in table 4 a r e sufficiently c l o s e to z e r o to indicate c o n s i s t e n c y with a high d e g r e e of d o m i n a n c e by the K* - K * * t r a j e c t o r i e s , though s o m e contribution f r o m t channel s t a t e s of P = (-1)J+l (as on the K - t r a j e c t o r y ) a l s o s e e m s to be p r e sent. The fitted v a l u e of Poo f o r the KN(1420) is l a r g e enough to indicate a m o r e definite contribution f r o m t - c h a n n e l s t a t e s of P = (-1)J+l; thus the r e a c t i o n Ir-p -* (A/Z'O)KNO(1420) cannot be c o n s i d e r e d e x c l u s i v e l y d o m i acted by the K* - K * * t r a j e c t o r i e s at this e n e r g y . A c h e c k of the a n g u l a r d i s t r i b u t i o n s of the A - d e c a y 7r- in AK*O(890) and AKNO(1420) (not shown) y i e l d e d no evidence of A p o l a r i z a t i o n though it is p o s s i b l e that s m a l l p o l a r i z a t i o n could have been m a s k e d by ~ o c o n t a m i n a tion. L a c k of p o l a r i z a t i o n is c o n s i s t e n t with d o m i n a n c e of a single t r a j e c t o r y since in the R e g g e - m o d e l p o l a r i z a t i o n can a r i s e only f r o m i n t e r f e r e n c e between different poles [1].
614
A. PEEKNA et al.
4. CONCLUSIONS In s u m m a r y , w e f i n d t h a t t h e e n e r g y d e p e n d e n c e of t h e c r o s s s e c t i o n in t h e f o r w a r d d i r e c t i o n (to- t < 0.4) f o r ~ - p -* ( A / ~ ° ) K ° i s in g o o d a g r e e m e n t w i t h d o m i n a n c e of t h e K* - K * * t r a j e c t o r i e s . F o r t h e r e a c t i o n y - p -~ (A/~.O)K*q(890) t h e e n e r g y d e p e n d e n c e of t h e c r o s s s e c t i o n a n d t h e d e c a y a n g u l a r d i s t r i b u t i o n s of t h e K* p o i n t to d o m i n a n c e by t h e K* - K * * t r a j e c t o r i e s ; t h e l a c k of A p o l a r i z a t i o n in ~ - p -~ AK*O(890) i s a l s o c o n s i s t e n t w i t h t h i s . Y e t t h e K* d e c a y a n g u l a r d i s t r i b u t i o n h i n t s a t a s l i g h t K e x c h a n g e c o n t r i b u t i o n . T h e KN°(1420) d e c a y a n g u l a r d i s t r i b u t i o n s s h o w a d e f i n i t e c o n t r i b u t i o n f r o m t - c h a n n e l s t a t e s of t h e " a b n o r m a l " s p i n - p a r i t y s e r i e s P = ( - 1 ) J +1, i n d i c a t i n g t h a t t h e r e a c t i o n y - p -~ ( A / ~ °)KN°(1420) i s n o t e x c l u s i v e l y d o m i n a t e d b y t h e K* - K** t r a j e c t o r i e s a t t h i s e n e r g y .
RE F E R E N C E S [1] G. E. Hite, Revs. Mod. Phys. 41 (1969) 669. [2] O. I. Dahl, L. M. Hardy, R. I, Hess, J. K i r z , D. H. Miller and J. A. Schwartz, Phys. Rev. 163 (1967) 1430. [3] O. I. Dahl, L.M. Hardy, J. Kirz and D. H. M i l l e r , Phys. Rev. 163 (1967) 1377. [4] J. Bartsch, L. Bondar, R. Speth, G. Hotop, G. Knies, F. Storm, J. M. Brownlee, N. N. Biswas, D. L u e r s , N. Schmitz, R. Seeliger and G. P. Wolf, Nuovo Cimento 33 (1966) A1010. [5] D.J. Grennel, G.R. Kalbfleish, K. W. Lai, J. M. S c a r r , T. G. Schumann, I.O. Skillieorn and M. S. Webster Phys. Rev. L e t t e r s 18 (1967) 86. [6] E. Bertolueci, I. Manelli, G. P i e r a z z i n i , A. Seribany, F. S e r g a m p i e t r i and M. L. Vincelli, CERN 68-7 Vol. 2 (1968) 190. [7] D. H. M i l l e r , A. Z. Kovaes, R. McIlwain, T.R. P a l f r e y and G. W. Tautfest, Phys. Rev. 140 (1965) B360. [8] K. Gottfried and J. D. Jackson, Nuovo Cimento 33 (1964) 309. [9] M. Jacob and G. C. Wick, Ann. of Phys. 7 (1959) 404.