Volume 36B. number 6 P H Y S I C S L E T T E R S 18 October 1971

M U L T I P A R T I C L E P R O D U C T I O N F R O M e + - e I N T E R A C T I O N S A T H I G H

B. BARTOLI , F. F E L I C E T T I , H. OGREN and V. SILVESTRINI

Laboratori Nazionali di Frascat i del CNEN, Frascat i , Italy

G. MARINI, A. NIGRO and N. S P I N E L L I Ist i tuto di Fis ica del l 'Univers i th , Sezione di Roma dell ' INFN, Rome, Italy

and

F. VANOLI Ist i tuto di Fisica Superiore del l 'Universi th ,

Sezione di Napoli dell INFN, Naples, Italy

Received 20 August 1971

E N E R G Y

Measurements of multiple part icle production at ADONE, the Frascat i e t e - s torage ring, have been carr ied out at C. M. energies 1.4 GeV to 2.4 GeV. The hadronic nature of the observed par t ic les is d iscussed and a lower limit of 30 nbarn set for the total multiparticle c ross section.

We p r e s e n t the r e s u l t s of an e x p e r i m e n t c a r - r i e d out at ADONE, the F r a s c a t i 2 × 1.5 GeV e+e - s t o r a g e r ing . Th i s e x p e r i m e n t was de - s i g n e d to p e r f o r m an in i t ia l e x p l o r a t i o n of the f e a t u r e s of e+e - i n t e r a c t i o n s . E n e r g i e s b e t w e e n 1.4 and 2.4 GeV in the c e n t e r of m a s s s y s t e m w e r e e x p l o r e d in t h i s e x p e r i m e n t .

A d e t a i l e d d e s c r i p t i o n of the e x p e r i m e n t a l a p p a r a t u s ( see fig. 1) has b e e n g iven p r e v i o u s l y

4

¢ ~ B , a m ax is ! ~"~ "'; sco , l

T E L E $ C ~ . 3 ~ " ~ r ' P ~ TELE$COP~ 4

Fig. 1. Section of ~,',~ experimental apparatus orthogonal to beam axis. The 0 . 'ceptance is between 60 ° and 120 °

(z-axis beinl, a!ong the beam direction).

598

[I] . The m e t h o d u s e d fo r a n a l y s i s , and s o m e p r e l i m i n a r y r e s u l t s have a l r e a d y b e e n p r e s e n t e d e l s e w h e r e [2].

Le t us r e c a l l h e r e tha t the a p p a r a t u s c o n s i s t s of four i den t i ca l t e l e s c o p e s s u r r o u n d i n g one ex - p e r i m e n t a l s e c t i o n of ADONE and c o v e r i n g ~0 .35 of the to ta l so l id ang le as s e e n f r o m the c e n t e r of the a p p a r a t u s * . Each t e l e s c o p e c o n s i s t s of a b s o r b e r s , s c i n t i l l a t i o n c o u n t e r s , and m a g n e t o - s t r i c t i v e s p a r k c h a m b e r s , which a l low us to e x t r a c t the fo l lowing i n f o r m a t i o n c o n c e r n i n g the d e t e c t e d p a r t i c l e s :

a) p u l s e he igh t a n a l y s i s in a l e a d - s c i n t i l l a t o r s a n d w i c h to iden t i fy e l e c t r o n s by t h e i r e l e c t r o - m a g n e t i c s h o w e r s ;

b) a z i m u t h a l d i r e c t i o n , (p, of the d e t e c t e d p a r t i c l e ( z - a x i s a long the b e a m d i r e c t i o n ) . When m o r e than two p a r t i c l e s e n t e r the s a m e t e l e s c o p e only that c l o s e s t to the m a g n e t o s t r i c t i v e p i c k - u p is r e c o r d e d .

We a l so r e c o r d the t i m e of e a c h even t with r e s p e c t to the b e a m - b e a m i m p a c t (At). 22 cm of Fe a b s o r b e r c o v e r the top two t e l e s c o p e s and above the a b s o r b e r two l a r g e s c i n t i l l a t i o n coun- t e r s (CR1, CR2), in a n t i c o i n c i d e n c e with our t r i g g e r , d r a s t i c a l l y r e d u c e the flux of d e t e c t e d

* Actually the source has a finite longitudinal length [1] which is comparable with the linear dimension of the counters. This reduces the effective solid angle of the apparatus.

Volume 36B, number 6 PHYSICS LETTERS 18 October 1971

cosmic rays. In a second stage of the experiment,

a second absorber (1.5 cm of iron, 5 cm lead) and two additional counters CR 3 and CR 4 were placed above CR I and CR 2. CR 3 and CR 4 were then put in anticoincidence with our tr igger, while CR I and CR 2 were simply recorded in as- sociation with each event. These marked events then give us information on the penetration of the detected par t ic les *

The reaction we wish to d iscuss here is

+ a + b + e + e- ~ + + a n y t h i n g (1)

w h e r e a + and b ± a r e c h a r g e d p a r t i c l e s . The m a s t e r c o i n c i d e n c e w h i c h t r i g g e r s the

a p p a r a t u s r e q u i r e s the p r e s e n c e of at l e a s t two c h a r g e d p a r t i c l e s (a + and b ±) d e t e c t e d in two d i f - f e r e n t t e l e s c o p e s * * . If, in a d d i t i o n to a + and b ±, o t h e r p a r t i c l e s e n t e r o t h e r t e l e s c o p e s , they a r e a l s o r e c o r d e d . If t he a d d i t i o n a l p a r t i c l e s a r e n e u t r a l s they wi l l g ive a p u l s e in the s c i n t i l l a t i o n s a n d w i c h (C+D) but not in the i n i t i a l c o u n t e r A.

The s e l e c t i o n of e v e n s f r o m r e a c t i o n (1) (non- c o p l a n a r e v e n t s ) i s m a d e wi th the fo l lowing c r i t e r i a :

a) m o r e t han two c h a r g e d p a r t i c l e s a r e d e t e c t e d ;

b) two c h a r g e d p a r t i c l e s a r e o b s e r v e d and t hey h a v e a n o n - c o p l a n a r i t y a n g l e , I A ~ I , l a r g e r t h e n 13 ° .

+ - a±b ± D e m o n s t r a t i o n o f the e x i s t e n c e o f e e -~ + any th ing . In fig. 2(a) we show t he d i s t r i b u t i o n of e v e n t s f u l f i l l i n g the a b o v e c r i t e r i a , a s a func - t i on of AL F r o m t h i s d i s t r i b u t i o n we can d e f i n e an i n t e r v a l i n - t i m e wi th the b e a m - b e a m i m p a c t . In fig. 2(b) we show the d i s t r i b u t i o n of non - c o p l a n a r i n - t i m e e v e n t s a s a f u n c t i o n of the d i s - t a n c e , L, b e t w e e n t he p a r t i c l e t r a j e c t o r y and t he e+e - b e a m ax i s . We s e e t h a t the i n - t i m e , n o n - e o p l a n a r e v e n t s , e s s e n t i a l l y c o m e f r o m b e a m i n t e r a c t i o n s . If we s e l e c t on ly t h o s e e v e n t s fo r w h i c h ILI ~< 30 m m we o b t a i n a t o t a l of 1033 e v e n t s .

The c o s m i c r a y b a c k g r o u n d , CR, v a r i e s fo r t he d i f f e r e n t e n e r g i e s and t he d i f f e r e n t d e t e c t e d c o n f i g u r a t i o n s (2 p a r t i c l e s d e t e c t e d , 3 p a r t i c l e s d e t e c t e d , t e c . ) f r o m 0% to 30%, the a v e r a g e c o n - t a m i n a t i o n being 16%.

• The minimum kinetic energy of a peon to be marked was ~ 350 MeV, while peons with more than ~ 500 MeV were vetoed by CR 3 and CR4, unless they

were absorbed by nuclear interaction (actually the fraction of particles absorbed is quite large: e.g. ~5~o of 400 MeV peons). In order to have a homo- geneous set of data the marked events have not been included in the total of events given in table i.

• * If a ~ and b i are peons their minimum energy to bc detected is ~ 75 MeV.

150

~ i n n i 40 50 60 70

~. d t ~channe ls~

t O 0

i i - 5 0 0 +50

C (m m) Cosmic

I r a y s Bhabha

50

" / y t,m 1 . . . .

e v e n t s 5 0

J UTL t a i l - ,~%

50 fO0 Pu lse h e i g h t f~channe ls )

2

g

e ÷ e ~ e + e-

e" e ~ a * + D*+ a n y t h i n g

%

! T

- 2 0

- f O ~ ' ~ ~ . .

. O "

I I U I n ~ I " ~ r 6 8 fO " 2

P r i m a r y e l e c t r o n e n e r g y ~ G e V j E i r

~. 30 _ ~] c 2 r r ' , 2 r~ ° •

'~ ', MC~,IT"

-,8o ~, -doo t ~ " ' doo' ' ,~o o @ C d e g r e e s )

Fig. 2. Analysis of non-coplanar evens (see text). (a) At distribution of events from the beam region. (b) L distribution of in-time events compared with the out-of-time (C. R.) normalized distribution (arrows indicate source definition. (c) pulse height distribution compared with C.R. and Bhabha elec- tron spectra. (d) the fraction of "marked" events compared to "marked" Bhabha events. (e) h(P dis- tribution compared with a phase space Montecarlo calculation for two possible peon final states.

To determine the amount of e -gas background, we have collected data with one beam and with two separated beams stored in the ring***. The average contamination over the full sample was 26~'~, although it var ies considerably with each detected configuration and increases with C. M. energy. A final correction of 18cJ~ was applied to the two charged tracks events due to the non- coplanarity cut [Atp[ ~< 13 ° . This correction was determined by a smooth interpolation of the experimental A(p distribution between -13 ° and +13 ° which, as will be seen, is consistent with a statist ical distribution determined by a Monte- carlo program.

After subtraction of CR and e-gas contamina- tion and after the A(p cut correction, a total of

*** The normalization of these e-gas background runs was obtained by monitoring single bremsstrahlung production on the residua| gas [2].

599

Volume 36B, n u m b e r 6 P H Y S I C S L E T T E R S 18 Oc tobe r 1971

Tab le 1 L i s t of n o n - c o p l a n a r e v e n t s a c c o r d i n g to the i r de tec ted con f igu ra t i ons , a f t e r all the c o r r e c t i o n s were appl ied .

The c rude n u m b e r of e v e n t s de t ec t ed a r e g iven in p a r e n O ' e s i s (no. 4 c h a r g e d e v e n t s were de tec ted) .

C . M .

energy" E +E_ (~ev)

(I)

1.4

1.5

1.6

1.65

1.7

1.75

1.8

1.85

1.9

2.0

2.4

t o t a l s

Integrated Corrected luminosity Bhabha

(cm -2) events

(2)

l 1 9 x l O 32

231 720 ~ 34

67 166 = 17

76 170 ~: 17

130 261 + 21

83 152 • 16

115 189 ~ 18

514 770 :e 36

122 166 ~= 17

257 293 = 25

751 453 ± 23

!2465 * 1032 3812 :~ 83

N o n

Even t s with 2 cha rged p a r t i c l e s de tec ted

(3) (4)

(55) 472 ¢ 33 40.6 ± 9.4

(99) 90.7 ± 12.1

(32) 26.5 : 7.0

(44) 28.2 i 8.6

(59) 42.9 t 9.7

(46) 33.1 ± 8.5

(68) 50.1 ± 10.5

(109) 84.9 + 16.4

(45) 24.5 ~ 8.8

(145) 90.4 ± 17.9

(140) 22,6 -- 24,6

(842) 534.5 ± 43.7

c o p 1 a n a r e v e n t s

Even t s with Even t s with Even t s with Even t s with 2 cha rged 2 cha rged 3 cha rged 3 cha rged +1 neu t r a l +2 n e u t r a l s p a r t i c l e s +1 neu t r a l

de t ec t ed d e ~ c t e d de t ec t ed de t ec t ed (5) (6) (6) (7)

(8) (0) (6) (1) 6 . 4 ± 3 . 5 0 . 1 = 1 . 1 5 . 4 ± 2 . 5 0 , 6 ± 1 . 1

(15) (1) (12) (1) 11.1 ± 4 . 8 1.0 ~ 1 . 2 1 1 . 1 ± 3 . 8 0 . 6 ± 1 , 5

(4) (0) (6) (0) 2 . 8 ± 2 . 4 0.0 • 1.1 5.3 ¢ 2 . 5 0,0 ±1 .1

(7) (2) (2) (2) 6 . 4 ± 3 . 1 2.0 ± 1.5 1.7 • 1.5 2 . 0 ± 1 . 5

(7) (1) (1) (0) 4 . 1 ± 3 . 3 0 . 3 ± 1 . 1 0 . 0 ± 1 . 2 0 . 0 ± 1 . 3

(4) (0) (4) (0) 1,8 i 2.8 0.0 ± 1.1 3 , 4 ± 2 . 1 0.0 ~ 1 . 2

(4) (0) (2) (0) 1.0 ± 2,6 -0 .3 ± 1.1 2,0 ± 1.5 -0 .3 t 1,3

(23) (2) (10) (2) 25.9 ~6 .5 -2 .0 ± 1.7 1 0 , 6 ± 4 , 2 2 . 7 ± 2 . 3

(3) (2) (3) (0) 2.1 ~ 2 . 3 2 . 0 = 1 . 5 3 . 3 ± 2 . 0 0.0 ~ 1 . 2

(7) (0) (5) (0) 5.8 = 3 . 7 0.0 ± 1.1 5 , 8 ± 2 . 7 -0 .7 ~ 1 . 5

(26) (3) (13) (2) 2 1 . 9 ± 6 . 3 3 . 9 ± 2 . 5 12.7 =4 .1 1 . 7 ± 2 . 0

(108) (ii) (64) 89.3 • 13.6 6.9 ± 4.0 61.3 ± 9.1

Tota l n o n - c o p l a n a r

e v e n t s

(8)

(70) 53.0 ± 10.4

(128) 114.5 + 13.7

(42) 34.6 + 7.9

(57) 40.3 ¢ 9.5

(65) 47.3 + 10.5

(54) 38.3 + 9.3

(74) 52.5 + 11.0

(146) 122.1 + 18.6

(53) 31.9 ~ 9.5

(157) 101.3 ± 18.5

(184) 62.8 :L 25.9

(8) (1033) 6.6 ± 5.0 698,6 ± 47.1

698 e v e n t s r e m a i n . T h e s e e v e n t s a r e l i s t e d in t a b l e 1 f o r e a c h C . M . e n e r g y a c c o r d i n g to t h e i r d i f f e r e n t d e t e c t e d c o n f i g u r a t i o n s . In t h e s a m e t a b l e we g i v e t h e c o r r e c t e d n u m b e r of B h a b h a e v e n t s * c o l l e c t e d a t t h e s a m e t i m e u n d e r t h e s a m e c o n d i t i o n s . T h e i n t e g r a t e d l u m i n o s i t i e s in c o l u m n (2) w e r e d e d u c e d f r o m t h e s e B h a b h a e v e n t s in o r d e r to m i n i m i z e p r o b l e m s d u e to u n c e r t a i n t i e s in t h e s p a r k c h a m b e r s e f f i c i e n c i e s ( the c h a m b e r e f f i c i e n c i e s w e r e m e a s u r e d to be b e t w e e n 0 .85 a n d 0 .95 ) .

Nature of lhe observed particles. F i g . 2(c) s h o w s t h e p u l s e h e i g h t s p e c t r u m of p a r t i c l e s in t h e s h o w e r c o u n t e r s (C+D). T h e d i s t r i b u t i o n of t h e d e t e c t e d n o n - c o p l a n a r e v e n t s i s c o m p a r e d w i t h t h e s p e c t r u m of m i n i m u m i o n i z i n g p a r t i c l e s (C. R. ) a n d h i g h e n e r g y e l e c t r o n s f r o m B h a b h a

* See ref . [lJ for the c o r r e c t i o n s appl ied to the Bhabha even t s .

s c a t t e r i n g . T h e s p e c t r u m of n o n - c o p l a n a r e v e n t s i s s i m i l a r to t h e C. R. s p e c t r u m , a l t h o u g h i t s h o w s n o n n e g l i g i b l e t a i l t o w a r d s t h e l a r g e r p u l s e h e i g h t s . H o w e v e r t h e r e i s no c o r r e l a t i o n b e t w e e n l a r g e p u l s e h e i g h t s in t h e d i f f e r e n t telescopes f o r e a c h e v e n t . If t h e d e t e c t e d p a r t i c l e s w e r e p i o n s , t h i s t a i l i s w h a t o n e w o u l d e x p e c t d u e to t h e f o l - l o w i n g effects: t h e p r o b a b i l i t y to h a v e m o r e t h a n o n e p a r t i c l e in t h e s a m e t e l e s c o p e , e s t i m a t e d to b e 12% f r o m t h e f r a c t i o n o f e v e n t s w i t h m o r e t h a n two d e t e c t e d p a r t i c l e s ; n u c l e a r i n t e r a c t i o n s in t h e s a n d w i c h c o u n t e r s ; t h e p o s s i b i l i t y t h a t t h e d e t e c t e d p a r t i c l e i s a s l o w p i o n . W e c o n c l u d e t h a t t h e b u l k o f t h e d e t e c t e d p a r t i c l e s a r e no t h i g h e n e r g y e l e c - t r o n s , a n d t h a t t h e p u l s e h e i g h t s p e c t r u m i s c o m - p a t i b l e w i t h a l l o f t h e m b e i n g p i o n s .

In f ig . 2(d) we h a v e p l o t t e d a s a f u n c t i o n of t h e i n c i d e n t e l e c t r o n e n e r g y (E~:) t h e f r a c t i o n o f e v e n t s c o n t a i n i n g a p a r t i c l e w h i c h c r o s s e s t h e 22 c m of F e a b s o r b e r a n d s t o p s b e t w e e n C R 1 , C R 2

600

Volume 36B, number 6 PHYSICS LETTERS 18 October 1971

and CR3, CR 4 (marked events). While the num- ber of marked Bhabha events decreases to zero at low energies, the number of marked non- coplanar events remains constant (within the large errors) at 16%. We can therefore exclude the possibility that these non-coplanar events are due to low energy (~< 500 MeV) electrons. Further, the fraction of marked non-coplanar events is consistent with a major part of the detected particles being pions. (We have calcu- lated that 16% of ~ 400 MeV pions would be marked).

Additional information on the nature of the non-coplanar events can be obtained from the A(p (non-coplanarity) distribution*. This distr i- bution is shown in fig. 2(e). For reference it is compared with the statitical distribution expected for e+e - - r,+~-r,+~ - and e+e - ~ ~+~;-~o~o (phase space Montecarlo calculation). We can conclude that the detected non-coplanar events have a A(p distribution compatible with some mixture of final states with a statistical angular distribution. They do not contain, for ]A(p I >I 13 °, a significant contribution from the reaction e+e - -- e+e-e+e - (the only plausible reaction which could give low energy non-coplanar electrons) since the distribu- tion for this reaction would be peaked around

~,~ : 0 [31. Energy dependence of the yield. In fig. 3 we

show the e n e r g y d e p e n d e n c e of t he r a t i o of n o n - c o p l a n a r e v e n t s to t he i n t e g r a t e d l u m i n o s i t y .~ = f . ~ (t)dt a t e a c h C. M. e n e r g y . T he d a t a p o i n t s of fig. 3 d i v i d e d by the e f f i c i e n c y of d e t e c - t ion , ¢ , of the a p p a r a t u s d i r e c t l y p r o v i d e t he c r o s s - s e c t i o n s .

Absolute z,alues of the cross-sections. T h e e v a l u a t i o n of c r o s s - s e c t i o n s i n v o l v e s a d e t a i l e d c a l c u l a t i o n of the e f f i c i e n c y of d e t e c t i o n of o u r a p p a r a t u s wh ich , of c o u r s e , d e p e n d s on the s t a t e s a c t u a l l y p r o d u c e d . T h e y i e l d (n D) of e v e n t s in a g i v e n d e t e c t e d c o n f i g u r a t i o n D (D cou ld be , fo r e x a m p l e , t h r e e c h a r g e d t r a c k s (3c) + a n e u t r a l ( In) d e t e c t e d in o u r a p p a r a t u s ) i s g i v e n by

n D =-[2"~¢A(xA

.t2 i s t he i n t e g r a t e d l u m i n o s i t y ; ~A is t he c r o s s - s e c t i o n to p r o d u c e a g i v e n c h a n n e l A ( for e x a m p l e ,

* ~ p is the dif ference of the angles between the az i - muthal project ion of the t racks and is zero when the two par t ic les go in opposite d i rec t ions . The sign of Acp is specular ly defined for left and right te lescopes . If one par t ic le goes in a top telescope the event will have a posit ive Aq9 if the other par t ic le l ies in the half plane {defined by the f i r s t track) containing the other top telescope. Consistently, if both par t ic les go in the bottom telescope A~p is posi t ive.

I033CNON COPLANAR E V E N T S ) / ~ p .

Ccm ~)

~ x t t ~e

2 x t • ~o

• ,~ , , z ~ , ----Y'---.---':'--? "~ '_- .~_-r_~.~ . . . . ~ " - " ~ ~"-~ ----'----:---_

714 ! t i ! i i l ,6 ,,s ~'o 212 2 C M EN~RSY E, + E. ( ' ~ e V )

Fig. 3. Energy dependence of the ratio of the number of non-coplanar events to the integrated luminosity .C. The curves are the result of a phase space M.C. cal- culation of this ratio for several possible channels using a constant cross-section for each channel of

30 nbarn.

7 A =(~(e+e - - - ,-r ~ ~ n ) ) ; ~ " - + - and EA is the efficiency of the apparatus to detect the configuration D from reaction A.

Since we have six different detected configura- tions of evens (2c, 2c+In, 2c+2n, 3c, 3c+n. 4c) in principle, apart from the statistical signifi- cance of some of our experimental numbers, it would be possible to extract from the data the cross-sect ions for six different channels once the efficiencies have been calculated. However. ap r io r i , there is no reason to res t r ic t the choice of final states to 6 or less channels and moreover the actual dynamics of the processes a r e unknown. A,

As an e x a m p l e , we h a v e c a l c u l a t e d the CD s u s i n g a s t a t i s t i c a l m o d e l of p ion p r o d u c t i o n ( i n v a r i a n t p h a s e s p a c e M o n t e c a r l o c a l c u l a t i o n ) . We o b t a i n e f f i c i e n c i e s ( see t a b l e 2) r a n g i n g f r o m -~: 1% to ~10% d e p e n d i n g on the C. M. e n e r g y , the

p r o d u c e d c h a n n e l , and the d e t e c t e d c o n f i g u r a t i o n . T h i s m e a n s , c l e a r l y , t h a t to o b t a i n c r o s s - s e c t i o n s we m u s t m u l t i p l y the o b s e r v e d n u m b e r s of e v e n t s by a c a l c u l a t e d , m o d e l d e p e n d e n t , n u m b e r r a n g i n g f r o m 10 to m o r e t h a n 100 in the d i f f e r e n t c a s e s . The s m a l l v a l u e s of t h e s e e f f i c i e n c i e s r e s u l t m a i n l y f r o m the s m a l l s o l i d a n g l e s e e n by the a p p a r a t u s and the e n e r g y c u t s on the d e t e c t e d p a r t i c l e s . To i n c r e a s e the u n c e r t a i n t y , c o r r e c - t i o n s fo r n u c l e a r a b s o r b t i o n ( a l r e a d y i n c l u d e d in t he ~ ' s of t a b l e 2, a s s u m i n g the p a r t i c l e s a r e p ions ) , t u r n out to be of the o r d e r of 20% - 5 0 ~ d e p e n d i n g on the e n e r g y and c h a n n e l . F o r a l l of

601

Table 2 Values of the efficiencies to detect a particular configu- ration from several possible produced states of pions,

assuming a statistical model. (Invariant phase space Montecarlo calculation)

Produced Efficiency for detect ion of

state E++E. 2c 2c+ln 2c+2n 3c 3c+ln 4c GeV % % % % % %

1.4 2.2 0.7 0.0 Ir+s- no 1.8 1.4 0.5 0.0

2.4 0.6 0.2 0.0

I?*-2.ir” 1.4 1.1 0.7 0.2 1.8 1.0 0.7 0.1 2.4 0.7 0.4 0.1

7r+s-3a” 1.4 0.5 0.4 0.2 1.8 0.6 0.5 0.2 2.4 0.6 0.3 0.2

1.4 0.1 0.2 0.1 ?l+71-4s” 1.8 0.2 0.4 0.2

2.4 0.2 0.3 0.2

1.4 8.5 0.9 0.0 +-+- R7T7Tll 1.8 7.0 0.7 0.0

2.4 4.0 0.4 0.0

1.4 ?i’n-lit-no 1.8

4.0 1.5 0.0 0..4 0.1 0.0 4.1 1.4 0.0 0.4 0.1 0.0

2.4 3.5 1.0 0.0 0.2 0.1 0.0

1.4 lr+7r-7r+71-27r” 1.8

1.6 1.0 0.1 0.1 0.1 0.0 2.4 1.7 0.4 0.3 0.1 0.0

2.4 2.0 1.4 0.3 0.2 0.2 0.0

6.5 0.6 0.0 3n+ + 371

1.4 1.8 8.8 1.3 0.1 2.4 7.4 1.1 0.1

1.4 0.1 0.0 0.0 4i++ + 4r- 1.8

2.4 i

6.3 0.7 0.0 8.3 1.6 0.1

Volume 36B, number 6 PHYSICS LETTERS 18 October 1971

to safely extract a reasonably model independent cross section for multiparticle production.

Keeping in mind the above considerations, we have plotted in fig. 3 for several possible chan- nels (A) the value of NA/.&? (=EATA) calculated using the efficiencies obtained by the phase space MC program, and a constant cross-section (IJA) Of 30 nbarn.

Using these same efficiencies (eA), i.e. with the hypothesis that we are dealing with statistical production of pions, we can put a conservative lower limit on the value of the cross-section o(e+e- - a* + b* + anything) by assuming that only the channel with the largest efficiency con- tributes. This yields *

o(e+e- - a + b + anything) 2 30 nbarn

averaged over the energy range explored (1.4 - 2.4 GeV). This is in agreement with our prelimi- nary evaluation in the energy range 1.6 to 2.0 GeV.

* A slightly larger value for this limit could be set if one takes into consideration the separate configura- tions containing charged+neutrals.

References [l] B. Bartoli, F. Felicetti, G. Marini, A. Nigro,

H. Ogren, V. Silvestrini, N. Spinelli, F. Vanoli, Phys. Letters 36B (1971) 593.

]2] B. Bartoli, B. Coluzzi, F. Felicetti, G. Goggi, G. Marini, F. Massa, D. Scannicchio, V. STGestrini, F. Vanoli, Nuovo Cimento 70A (1970) 615.

[3] S. J. Brodsky, T. Kinoshita and H. Terazawa, Phys. Rev. Letters 25 (1970) 9’72: and Cornell report

these reasons we feel that with the existing CLNS-152 (1971).

small solid angle apparatus it is very difficult

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