- Email: [email protected]
Test of quantum electrodynamics by e+e− → μ+ μ−
Volume 37B, number 4
TEST
PHYSICS LETTERS
OF
QUANTUM
ELECTHODYNAMICS
13 December 1971
BY e + e - ~
~+t~-
V. E. BALAKIN, G.I. BUDKER~ L. M. KUHDADZE, A. P. ONUCHIN, E. V. PAKHTUSOVA, S.I. SEHEDNYAKOV, V . A . SIDOROV, A. N. SKHINSKY and A. G. KHABAKHPASHEV Institute of Nuclear Physics, Siberian Division of the USSR Academy of Sciences, Novosibirsk, USSR
Received 4 November 1971
At 4 values of energy from 102Oup to 1340 MeV the cross-section of electron-positron annihilation to a ~-meson pair has been measured, the limit of validity of quantum electrodynamics h > 3.1GeV has been obtained.
In 1969 the e x p e r i m e n t s on the • - m e s o n r e s onance [1] and 2 v - q u a n t u m annihilation [2] w e r e p e r f o r m e d with the e l e c t r o n - p o s i t r o n s t o r a g e r i n g V E P P - 2 at the e n e r g y 2 × 510 MeV. In 1970 the s a m e m a c h i n e was u s e d f o r the i n v e s t i g a t i o n of hadronic f o r m f a c t o r s at 3 e n e r g i e s : 2 × 590, 2 × 630 and 2 × 670 MeV [3]. In all t h e s e e x p e r i m e n t s e v e n t s of e l e c t r o n - p o s i t r o n annihilation into a t t - m e s o n p a i r w e r e d e t e c t e d as well so as to t e s t quantum e l e c t r o d y n a m i c s at high m o m e n t um t r a n s f e r s . The p r e l i m i n a r y r e s u l t s of this w o r k w e r e r e p o r t e d at the Kiev c o n f e r e n c e [4]. S i m i l a r e x p e r i m e n t s at p - m e s o n e n e r g y w e r e p e r f o r m e d in O r s a y [5]. At the Kiev c o n f e r e n c e the p r e l i m i n a r y r e s u l t s of s i m i l a r e x p e r i m e n t s in F r a s c a t i w e r e r e p o r t e d [6]. The p r o c e s s c o n s i d e r e d i s d e s c r i b e d by a single lowest o r d e r d i a g r a m
The i n v e s t i g a t i o n of this p r o c e s s e n a b l e s us to obtain i n f o r m a t i o n about the photon p r o p a g a t o r b e h a v i o u r at t i m e - l i k e m o m e n t u m t r a n s f e r s a s well as about the 7t~ i n t e r a c t i o n v e r t e x . The working conditions of the m a c h i n e during the e x p e r i m e n t s w e r e c h a r a c t e r i z e d by the f o l -
lowing p a r a m e t e r s : the i n i t i al c u r r e n t s w e r e 70 mA and 40 mA f o r e l e c t r o n s and p o s i t r o n s , r e s p e c t i v e l y , the m e a n l i f e t i m e was about 5 h o u r s , the l u m i n o s i t y aver_aged o v e r the m e a s u r e m e n t t i m e was 1028 c m -2 s e c - 1 . The l u m i n o s i t y m o n i t o r i n g has been c a r r i e d out by detecting the double b r e m s s t r a h l u n g events [7]. Th e d e t e c t i o n s y s t e m u s e d in the e x p e r i m e n t s at the e n e r g y of 2 × 510MeV was d e s c r i b e d in detail in [1,2]. It c o n s i s t e d of two i d e n t i c a l g r o u p s of sp ar k c h a m b e r s c o v e r i n g the solid angle of 2 ×0.9 s r n e a r the axis p e r p e n d i c u l a r to the plane of the orbit. E a c h group included the c o o r d i n a t e , ' s h o w e r ' and ' r a n g e ' c h a m b e r s , the total t h i c k n e s s of each g r o u p s m a t t e r being 1 7 0 g / c m 2 . F o r v et o i n g c o s m i c r a y s the d e t e c t i o n s y s t e m was c o v e r e d by a s c i n t i l l a t i o n c o u n t e r of d i m e n sions (160 × 160) c m 2. B e f o r e it lead (220 g / c m 2 thick) was p l a c e d to stop t~-mesons. The s w i t c h ing of this c o u n t e r into the a n t i c o i n c i d e n c e c h a n :~[ r e d u c e d the c o s m i c - r a y t r i g g e r i n g r a t e by a f a c t o r of 50. B e s i d e s that a slow c o i n c i d e n c e c i r cuit was u s e d with a t h r e s h o l d f o r the a n t i c o i n c i d e n c e c o u n t e r channel equal to 0.01 of the a v e r age p u l s e height. This i n f o r m a t i o n led to a r e duction of the c o s m i c background by a f a c t o r of 5. An additional r e d u c t i o n of the c o s m i c b a c k ground by a f a c t o r of 4 was a c h i e v e d by s y n c h r o nization of the d et ect i o n s y s t e m t r i g g e r i n g with the r.f. p h a s e of the s t o r a g e ring r e s o n a t o r . The g e o m e t r i c a l s c h e m e of the a p p a r a t u s u s e d in the e x p e r i m e n t on the h a d r o n i c f o r m f a c t o r i n v e s t i g a t i o n is shown in fig.1. It d i f f e r s f r o m the p r e v i o u s e x p e r i m e n t s by the s u b s t i t u tion of the w i r e s p a r k c h a m b e r s f o r the optical 435
Volume 37B, number 4
PHYSICS LETTERS
13 December 1971
~/07,,
e ÷÷
e-.z;p-
/2 \, IO
\ "-..
A.=j.IGeV
8 4 A, " J i Oel/
2 I
/.0
L________J ii
Fig.1. General experimental set-up: 1-anticoincidenee scintillation counter; 2-lead; 3-optical 'range' spark chamber; 4--optical 'shower' spark chamber; 5, 7scintillation counters; 6-water Cerenkov counter; 8coordinate wire spark chambers; 9-interaction region; 10 and l l - i n n e r and outer vacuum chambers, respectively; 12-storage ring magnet. c o o r d i n a t e s p ar k c h a m b e r s . B e s i d e s that the w a t e r C e r e n k o v c o u n t e r s w e r e p l a c e d between the s c i n t i l l a t i o n c o u n t e r s . F r o m each side of the i n t e r a c t i o n point t h r e e w i r e s p ar k c h a m b e r s with f e r r i t e - c o r e m e m o r y w e r e p l a c e d each c h a m b e r having two c o o r d i n a t e p l a n e s [8]. The w i r e c h a m b e r s o p e r a t e d o n - l i n e with the c o m p u t e r ' M i n s k - 2 2 ' [9], a ll the i n f o r mation was s i m u l t a n e o u s l y r e c o r d e d on the magnetic tape. The w i r e c h a m b e r s w e r e u s e d to d e t e r m i n e g e o m e t r i c a l c h a r a c t e r i s t i c s of the events. The p h o t o g r a p h s f r o m the optical s p a r k c h a m b e r s w e r e scanned f o r events having the uppe r and l o w e r t r a c k s i n t e r s e c t i n g in the m e d i an plan e of the s t o r a g e ring and the i n t e r s e c t i o n point in the b e a m region. The s e l e c t i o n of the p - m e s o n e v e n t s was made by the following c r i t e r i a : 1) The s p aci al n o n - c o l l i n e a r i t y angle between 436
/2
z~
2E, 0ev
Fig.2. Experimental values of the total ~-meson production cross-section against the energy. The solid and dashed curves give the calculated values of the total cross-sections for three parameters A . the h i g h e r and the l o w e r t r a c k s is AW < 5 o. F o r the events of the e x p e r i m e n t on 2 7 - q u a n t u m a n nihilation [2] w h e r e the l e a d p l a t e s i n s i d e the c o o r d i n a t e c h a m b e r c a u s e d notable multiple s c a t t e r i n g AW < 10 °. 2) The r a n g e of both p a r t i c l e s i s m o r e than the optical c h a m b e r thickness. Two kinds of the background m e a s u r e m e n t s w e r e p e r f o r m e d : with the b e a m s v e r t i c a l l y d i s p l a c e d f r o m each o t h e r by a d i s t a n c e of 2 m m and without the b e a m s . In the l a t t e r c a s e the s y s t e m of s y n c h r o n i z a t i o n with the r.f. p h a s e was switched off; that i n c r e a s e d the e f f e c t i v e m e a s u r e m e n t t i m e by a f a c t o r of 4. The m e a s u r e merit showed that the background was due to c o s m i c r a y s , t h e r e f o r e its n o r m a l i z a t i o n was made by the r a t i o of the t i m e spent on e f f e c t and background m e a s u r e m e n t s . To r e d u c e the background, r e s t r i c t i o n s on the solid angle of the s y s t e m w e r e introduced, the solid angle f o r the 2 × 510 MeV e x p e r i m e n t being r e d u c e d by 107o and that f o r t h r e e o t h e r e n e r g i e s - by 25%. The absolute v a l u e of the p - m e s o n - p a i r p r o duction c r o s s - s e c t i o n was c a l c u l a t e d with the help of the m o n i t o r i n g p r o c e s s of the e l a s t i c e l e c t r o n - p o s i t r o n s c a t t e r i n g . The e v e n t s of this p r o c e s s can be c h o s e n e a s i l y due to the c l e a r p i c t u r e of a s h o w e r in the h i g h e r and l o w e r s p a r k c h a m b e r s and they have no background. F o r m o n i t o r i n g , t h e s e e v e n t s w e r e s e l e c t e d by the s a m e g e o m e t r i c a l c r i t e r i a as the Ix - m e s o n p a i r s . The v a l i d i t y of quantum e l e c t r o d y n a m i c s f o r the e l a s t i c e l e c t r o n - p o s i t r o n s c a t t e r i n g in the
Volume 37B, n u m b e r 4
PHYSICS
LETTERS
13 D e c e m b e r 1971
Table 1 2E, GeV Effect
1.02 * 41
Background (normalized)
4. 5
1.02 ** 26 7.4
1.18
1.26
1.34
17
13
4
1.9
2.3
0.7
~+~t(background subtracted)
36.5 ± 6.5
18.6 :~ 5,4
15.1 =~4.2
10.7 :~ 4.2
3.3~2.0
e+e - --* e+e -
322
220
170
112
48
* Data obtained in the ~ - m e s o n r e s o n a n c e e x p e r i m e n t [1]. ** Data obtained in the 2 T-quantum annihilation e x p e r i m e n t [2]. r e g i o n of m o m e n t u m t r a n s f e r s c o n s i d e r e d w a s c h e c k e d e x p e r i m e n t a l l y [10, 11]. T h e s u m m a r y r e s u l t s of t h e e x p e r i m e n t s a r e g i v e n i n t a b l e 1. T h e r a d i a t i v e c o r r e c t i o n s [12, 13] f o r t h e c a l c u l a t i o n of t h e r a t i o of t h e n u m b e r of ~ - m e s o n e v e n t s to e l a s t i c s c a t t e r i n g a r e h i g h l y c o m p e n s a t e d if t h e g e o m e t r i c a l c r i t e r i a of t h e s e l e c t i o n a r e i d e n t i c a l . T h e e f f e c t of v a c u u m p o l a r i z a t i o n [12] i n t h e r e g i o n of t h e ~ - r e s o n a n c e i s n e g l i g i b l y small when averaging over energies is carried
out. T o r e p r e s e n t t h e p o s s i b l e d i s t o r t i o n of t h e reaction amplitude by a single parameter, we m a d e t h e u s u a l m o d i f i c a t i o n of t h e f o r m - f a c t o r
IFI2
= ( i ± 4 E 2 / A 2 ) -2
and using the maximum tained
, likelihood method we ob-
A > 3.1 GeV w i t h 95% c o n f i d e n c e l e v e l . I n f i g . 2 t h e e x p e r i m e n t a l v a l u e s of t h e ~ - m e s o n p r o d u c t i o n c r o s s s e c t i o n a r e p l o t t e d a s a f u n c t i o n of e n e r g y a s w e l l a s t h e t h e o r e t i c a l c r o s s - s e c t i o n s of t h i s p r o c e s s f o r t h r e e v a l u e s of A. All previous considerations assumed that initial particles were not polarized. Their polari z a t i o n [14, 15] l e a d s t o c h a n g i n g of t h e ~ - m e s o n a n g u l a r d i s t r i b u t i o n w h e r e a s t h a t of t h e e l e c t r o n positron pairs is practically unperturbed. The actual situation concerning the particles' polarization is not clear. There are reasons for b e l i e v i n g t h a t t h e p r e s e n c e of t h e c o u p l i n g r e s o n a n c e s a n d b e a m - b e a m i n t e r a c t i o n l e a d to d e p o larization. The experimental results in Orsay [16] a l s o c o n f i r m t h i s p o i n t of v i e w . T o c h e c k t h e s t a b i l i t y of t h e m a i n r e s u l t w e h a v e h a n d l e d t h e e x p e r i m e n t a l d a t a a s s u m i n g t h e p r e s e n c e of p o larization. Even for the limiting polarization, at a l l e n e r g i e s of t h e e x p e r i m e n t we f i n d A > 2 . 7 G e V w i t h 957o c o n f i d e n c e l e v e l .
In conclusion the authors express their gratit u d e to V.N. B a l e r f o r u s e f u l d i s c u s s i o n s of t h e r e s u l t s a n d to t h e l a r g e g r o u p of c o - w o r k e r s who took part in data recording and data processing.
Refe~'ences [1] V. E. Balakin et al., Phys. L e t t e r s 34B (1971) 328. [2] V. E. Balakin et al., Phys. L e t t e r s 34B (1971) 99. [3] V. E. Balakin et al., E x p e r i m e n t s on e l e c t r o n p o s i t r o n colliding b e a m s at 2 ×590, 2 ×630 and 2 ×670 MeV. Submitted to the XVth Intern. Conf., Kiev 1970; P r e p r i n t , Inst. of Nuel. Phys. 62-70, Novosibirsk. [4] V. E. BaLakin et al., E x p e r i m e n t s on muon p a i r s production on V E P P - 2 . Submitted to the XVth Intern. Conf., Kiev 1970; P r e p r i n t , Inst. of NueI. Phys. 6 1-70, Novosibirsk. [5] J. P e r e z - Y - J o r b a , P r o c . 4th Intern. Syrup. on E l e c t r o n and photon i n t e r a c t i o n s at high e n e r g i e s , Liverpool, 1969, p. 215. [6] B. Borgia et al., Contribution to Kiev conference 1970. [7] P. I. Golubnichy et al., P r o c . Intern. Symp. on E l e c t r o n and positron storage rings, Sac[ay, 1966; P. I. Golubnichy e t a [ . , Atomnaya Energiya 22 (1967) 167. [8] S. E. Baru et a[., P r o e . Syrup. on F i i m I e s s s p a r k and s t r e a m e r c h a m b e r s , Dubna 1969, p.164. [9] S. E. Baru et al., Proc. Syrup. on F i l m l e s s s p a r k and s t r e a m e r c h a m b e r s , Dubna 1969, p.168. [10] J. E. Augustin et al., Proc. Symp. on Electron and photon interactions, D a r s b u r y , 1969. [11] B. B o r g i a e t a[., Phys. L e t t e r s 35B (1971) 340. [12] G. Aitarelli et aL, Nuovo Cimente 47 (1967) 113. [13] S. M. Sukhanov, V. S. Fadin and V. A. Khoze, Doklady AN SSSR 178 (1968) 822. [14] A.A. Sokolov and I. M. Ternov, Soviet Phys. Dokiady 8 (1964) 1203. [15] V. N. B a l e r and V.N.Katkov, Phys. L e t t e r s 25A (1967) 492. [16] I. E. Augustin et al., P r e l i m i n a r y r e s u l t s of a m e a s u r e m e n t of the g + ~ - yield at the ~b° energy with the Orsay storage ring. Submitted to the Intern. Symp. on E l e c t r o n and photon i n t e r a c t i o n s at high e n e r g i e s , Ithaca, New York, 1971.
437
TEST
PHYSICS LETTERS
OF
QUANTUM
ELECTHODYNAMICS
13 December 1971
BY e + e - ~
~+t~-
V. E. BALAKIN, G.I. BUDKER~ L. M. KUHDADZE, A. P. ONUCHIN, E. V. PAKHTUSOVA, S.I. SEHEDNYAKOV, V . A . SIDOROV, A. N. SKHINSKY and A. G. KHABAKHPASHEV Institute of Nuclear Physics, Siberian Division of the USSR Academy of Sciences, Novosibirsk, USSR
Received 4 November 1971
At 4 values of energy from 102Oup to 1340 MeV the cross-section of electron-positron annihilation to a ~-meson pair has been measured, the limit of validity of quantum electrodynamics h > 3.1GeV has been obtained.
In 1969 the e x p e r i m e n t s on the • - m e s o n r e s onance [1] and 2 v - q u a n t u m annihilation [2] w e r e p e r f o r m e d with the e l e c t r o n - p o s i t r o n s t o r a g e r i n g V E P P - 2 at the e n e r g y 2 × 510 MeV. In 1970 the s a m e m a c h i n e was u s e d f o r the i n v e s t i g a t i o n of hadronic f o r m f a c t o r s at 3 e n e r g i e s : 2 × 590, 2 × 630 and 2 × 670 MeV [3]. In all t h e s e e x p e r i m e n t s e v e n t s of e l e c t r o n - p o s i t r o n annihilation into a t t - m e s o n p a i r w e r e d e t e c t e d as well so as to t e s t quantum e l e c t r o d y n a m i c s at high m o m e n t um t r a n s f e r s . The p r e l i m i n a r y r e s u l t s of this w o r k w e r e r e p o r t e d at the Kiev c o n f e r e n c e [4]. S i m i l a r e x p e r i m e n t s at p - m e s o n e n e r g y w e r e p e r f o r m e d in O r s a y [5]. At the Kiev c o n f e r e n c e the p r e l i m i n a r y r e s u l t s of s i m i l a r e x p e r i m e n t s in F r a s c a t i w e r e r e p o r t e d [6]. The p r o c e s s c o n s i d e r e d i s d e s c r i b e d by a single lowest o r d e r d i a g r a m
The i n v e s t i g a t i o n of this p r o c e s s e n a b l e s us to obtain i n f o r m a t i o n about the photon p r o p a g a t o r b e h a v i o u r at t i m e - l i k e m o m e n t u m t r a n s f e r s a s well as about the 7t~ i n t e r a c t i o n v e r t e x . The working conditions of the m a c h i n e during the e x p e r i m e n t s w e r e c h a r a c t e r i z e d by the f o l -
lowing p a r a m e t e r s : the i n i t i al c u r r e n t s w e r e 70 mA and 40 mA f o r e l e c t r o n s and p o s i t r o n s , r e s p e c t i v e l y , the m e a n l i f e t i m e was about 5 h o u r s , the l u m i n o s i t y aver_aged o v e r the m e a s u r e m e n t t i m e was 1028 c m -2 s e c - 1 . The l u m i n o s i t y m o n i t o r i n g has been c a r r i e d out by detecting the double b r e m s s t r a h l u n g events [7]. Th e d e t e c t i o n s y s t e m u s e d in the e x p e r i m e n t s at the e n e r g y of 2 × 510MeV was d e s c r i b e d in detail in [1,2]. It c o n s i s t e d of two i d e n t i c a l g r o u p s of sp ar k c h a m b e r s c o v e r i n g the solid angle of 2 ×0.9 s r n e a r the axis p e r p e n d i c u l a r to the plane of the orbit. E a c h group included the c o o r d i n a t e , ' s h o w e r ' and ' r a n g e ' c h a m b e r s , the total t h i c k n e s s of each g r o u p s m a t t e r being 1 7 0 g / c m 2 . F o r v et o i n g c o s m i c r a y s the d e t e c t i o n s y s t e m was c o v e r e d by a s c i n t i l l a t i o n c o u n t e r of d i m e n sions (160 × 160) c m 2. B e f o r e it lead (220 g / c m 2 thick) was p l a c e d to stop t~-mesons. The s w i t c h ing of this c o u n t e r into the a n t i c o i n c i d e n c e c h a n :~[ r e d u c e d the c o s m i c - r a y t r i g g e r i n g r a t e by a f a c t o r of 50. B e s i d e s that a slow c o i n c i d e n c e c i r cuit was u s e d with a t h r e s h o l d f o r the a n t i c o i n c i d e n c e c o u n t e r channel equal to 0.01 of the a v e r age p u l s e height. This i n f o r m a t i o n led to a r e duction of the c o s m i c background by a f a c t o r of 5. An additional r e d u c t i o n of the c o s m i c b a c k ground by a f a c t o r of 4 was a c h i e v e d by s y n c h r o nization of the d et ect i o n s y s t e m t r i g g e r i n g with the r.f. p h a s e of the s t o r a g e ring r e s o n a t o r . The g e o m e t r i c a l s c h e m e of the a p p a r a t u s u s e d in the e x p e r i m e n t on the h a d r o n i c f o r m f a c t o r i n v e s t i g a t i o n is shown in fig.1. It d i f f e r s f r o m the p r e v i o u s e x p e r i m e n t s by the s u b s t i t u tion of the w i r e s p a r k c h a m b e r s f o r the optical 435
Volume 37B, number 4
PHYSICS LETTERS
13 December 1971
~/07,,
e ÷÷
e-.z;p-
/2 \, IO
\ "-..
A.=j.IGeV
8 4 A, " J i Oel/
2 I
/.0
L________J ii
Fig.1. General experimental set-up: 1-anticoincidenee scintillation counter; 2-lead; 3-optical 'range' spark chamber; 4--optical 'shower' spark chamber; 5, 7scintillation counters; 6-water Cerenkov counter; 8coordinate wire spark chambers; 9-interaction region; 10 and l l - i n n e r and outer vacuum chambers, respectively; 12-storage ring magnet. c o o r d i n a t e s p ar k c h a m b e r s . B e s i d e s that the w a t e r C e r e n k o v c o u n t e r s w e r e p l a c e d between the s c i n t i l l a t i o n c o u n t e r s . F r o m each side of the i n t e r a c t i o n point t h r e e w i r e s p ar k c h a m b e r s with f e r r i t e - c o r e m e m o r y w e r e p l a c e d each c h a m b e r having two c o o r d i n a t e p l a n e s [8]. The w i r e c h a m b e r s o p e r a t e d o n - l i n e with the c o m p u t e r ' M i n s k - 2 2 ' [9], a ll the i n f o r mation was s i m u l t a n e o u s l y r e c o r d e d on the magnetic tape. The w i r e c h a m b e r s w e r e u s e d to d e t e r m i n e g e o m e t r i c a l c h a r a c t e r i s t i c s of the events. The p h o t o g r a p h s f r o m the optical s p a r k c h a m b e r s w e r e scanned f o r events having the uppe r and l o w e r t r a c k s i n t e r s e c t i n g in the m e d i an plan e of the s t o r a g e ring and the i n t e r s e c t i o n point in the b e a m region. The s e l e c t i o n of the p - m e s o n e v e n t s was made by the following c r i t e r i a : 1) The s p aci al n o n - c o l l i n e a r i t y angle between 436
/2
z~
2E, 0ev
Fig.2. Experimental values of the total ~-meson production cross-section against the energy. The solid and dashed curves give the calculated values of the total cross-sections for three parameters A . the h i g h e r and the l o w e r t r a c k s is AW < 5 o. F o r the events of the e x p e r i m e n t on 2 7 - q u a n t u m a n nihilation [2] w h e r e the l e a d p l a t e s i n s i d e the c o o r d i n a t e c h a m b e r c a u s e d notable multiple s c a t t e r i n g AW < 10 °. 2) The r a n g e of both p a r t i c l e s i s m o r e than the optical c h a m b e r thickness. Two kinds of the background m e a s u r e m e n t s w e r e p e r f o r m e d : with the b e a m s v e r t i c a l l y d i s p l a c e d f r o m each o t h e r by a d i s t a n c e of 2 m m and without the b e a m s . In the l a t t e r c a s e the s y s t e m of s y n c h r o n i z a t i o n with the r.f. p h a s e was switched off; that i n c r e a s e d the e f f e c t i v e m e a s u r e m e n t t i m e by a f a c t o r of 4. The m e a s u r e merit showed that the background was due to c o s m i c r a y s , t h e r e f o r e its n o r m a l i z a t i o n was made by the r a t i o of the t i m e spent on e f f e c t and background m e a s u r e m e n t s . To r e d u c e the background, r e s t r i c t i o n s on the solid angle of the s y s t e m w e r e introduced, the solid angle f o r the 2 × 510 MeV e x p e r i m e n t being r e d u c e d by 107o and that f o r t h r e e o t h e r e n e r g i e s - by 25%. The absolute v a l u e of the p - m e s o n - p a i r p r o duction c r o s s - s e c t i o n was c a l c u l a t e d with the help of the m o n i t o r i n g p r o c e s s of the e l a s t i c e l e c t r o n - p o s i t r o n s c a t t e r i n g . The e v e n t s of this p r o c e s s can be c h o s e n e a s i l y due to the c l e a r p i c t u r e of a s h o w e r in the h i g h e r and l o w e r s p a r k c h a m b e r s and they have no background. F o r m o n i t o r i n g , t h e s e e v e n t s w e r e s e l e c t e d by the s a m e g e o m e t r i c a l c r i t e r i a as the Ix - m e s o n p a i r s . The v a l i d i t y of quantum e l e c t r o d y n a m i c s f o r the e l a s t i c e l e c t r o n - p o s i t r o n s c a t t e r i n g in the
Volume 37B, n u m b e r 4
PHYSICS
LETTERS
13 D e c e m b e r 1971
Table 1 2E, GeV Effect
1.02 * 41
Background (normalized)
4. 5
1.02 ** 26 7.4
1.18
1.26
1.34
17
13
4
1.9
2.3
0.7
~+~t(background subtracted)
36.5 ± 6.5
18.6 :~ 5,4
15.1 =~4.2
10.7 :~ 4.2
3.3~2.0
e+e - --* e+e -
322
220
170
112
48
* Data obtained in the ~ - m e s o n r e s o n a n c e e x p e r i m e n t [1]. ** Data obtained in the 2 T-quantum annihilation e x p e r i m e n t [2]. r e g i o n of m o m e n t u m t r a n s f e r s c o n s i d e r e d w a s c h e c k e d e x p e r i m e n t a l l y [10, 11]. T h e s u m m a r y r e s u l t s of t h e e x p e r i m e n t s a r e g i v e n i n t a b l e 1. T h e r a d i a t i v e c o r r e c t i o n s [12, 13] f o r t h e c a l c u l a t i o n of t h e r a t i o of t h e n u m b e r of ~ - m e s o n e v e n t s to e l a s t i c s c a t t e r i n g a r e h i g h l y c o m p e n s a t e d if t h e g e o m e t r i c a l c r i t e r i a of t h e s e l e c t i o n a r e i d e n t i c a l . T h e e f f e c t of v a c u u m p o l a r i z a t i o n [12] i n t h e r e g i o n of t h e ~ - r e s o n a n c e i s n e g l i g i b l y small when averaging over energies is carried
out. T o r e p r e s e n t t h e p o s s i b l e d i s t o r t i o n of t h e reaction amplitude by a single parameter, we m a d e t h e u s u a l m o d i f i c a t i o n of t h e f o r m - f a c t o r
IFI2
= ( i ± 4 E 2 / A 2 ) -2
and using the maximum tained
, likelihood method we ob-
A > 3.1 GeV w i t h 95% c o n f i d e n c e l e v e l . I n f i g . 2 t h e e x p e r i m e n t a l v a l u e s of t h e ~ - m e s o n p r o d u c t i o n c r o s s s e c t i o n a r e p l o t t e d a s a f u n c t i o n of e n e r g y a s w e l l a s t h e t h e o r e t i c a l c r o s s - s e c t i o n s of t h i s p r o c e s s f o r t h r e e v a l u e s of A. All previous considerations assumed that initial particles were not polarized. Their polari z a t i o n [14, 15] l e a d s t o c h a n g i n g of t h e ~ - m e s o n a n g u l a r d i s t r i b u t i o n w h e r e a s t h a t of t h e e l e c t r o n positron pairs is practically unperturbed. The actual situation concerning the particles' polarization is not clear. There are reasons for b e l i e v i n g t h a t t h e p r e s e n c e of t h e c o u p l i n g r e s o n a n c e s a n d b e a m - b e a m i n t e r a c t i o n l e a d to d e p o larization. The experimental results in Orsay [16] a l s o c o n f i r m t h i s p o i n t of v i e w . T o c h e c k t h e s t a b i l i t y of t h e m a i n r e s u l t w e h a v e h a n d l e d t h e e x p e r i m e n t a l d a t a a s s u m i n g t h e p r e s e n c e of p o larization. Even for the limiting polarization, at a l l e n e r g i e s of t h e e x p e r i m e n t we f i n d A > 2 . 7 G e V w i t h 957o c o n f i d e n c e l e v e l .
In conclusion the authors express their gratit u d e to V.N. B a l e r f o r u s e f u l d i s c u s s i o n s of t h e r e s u l t s a n d to t h e l a r g e g r o u p of c o - w o r k e r s who took part in data recording and data processing.
Refe~'ences [1] V. E. Balakin et al., Phys. L e t t e r s 34B (1971) 328. [2] V. E. Balakin et al., Phys. L e t t e r s 34B (1971) 99. [3] V. E. Balakin et al., E x p e r i m e n t s on e l e c t r o n p o s i t r o n colliding b e a m s at 2 ×590, 2 ×630 and 2 ×670 MeV. Submitted to the XVth Intern. Conf., Kiev 1970; P r e p r i n t , Inst. of Nuel. Phys. 62-70, Novosibirsk. [4] V. E. BaLakin et al., E x p e r i m e n t s on muon p a i r s production on V E P P - 2 . Submitted to the XVth Intern. Conf., Kiev 1970; P r e p r i n t , Inst. of NueI. Phys. 6 1-70, Novosibirsk. [5] J. P e r e z - Y - J o r b a , P r o c . 4th Intern. Syrup. on E l e c t r o n and photon i n t e r a c t i o n s at high e n e r g i e s , Liverpool, 1969, p. 215. [6] B. Borgia et al., Contribution to Kiev conference 1970. [7] P. I. Golubnichy et al., P r o c . Intern. Symp. on E l e c t r o n and positron storage rings, Sac[ay, 1966; P. I. Golubnichy e t a [ . , Atomnaya Energiya 22 (1967) 167. [8] S. E. Baru et a[., P r o e . Syrup. on F i i m I e s s s p a r k and s t r e a m e r c h a m b e r s , Dubna 1969, p.164. [9] S. E. Baru et al., Proc. Syrup. on F i l m l e s s s p a r k and s t r e a m e r c h a m b e r s , Dubna 1969, p.168. [10] J. E. Augustin et al., Proc. Symp. on Electron and photon interactions, D a r s b u r y , 1969. [11] B. B o r g i a e t a[., Phys. L e t t e r s 35B (1971) 340. [12] G. Aitarelli et aL, Nuovo Cimente 47 (1967) 113. [13] S. M. Sukhanov, V. S. Fadin and V. A. Khoze, Doklady AN SSSR 178 (1968) 822. [14] A.A. Sokolov and I. M. Ternov, Soviet Phys. Dokiady 8 (1964) 1203. [15] V. N. B a l e r and V.N.Katkov, Phys. L e t t e r s 25A (1967) 492. [16] I. E. Augustin et al., P r e l i m i n a r y r e s u l t s of a m e a s u r e m e n t of the g + ~ - yield at the ~b° energy with the Orsay storage ring. Submitted to the Intern. Symp. on E l e c t r o n and photon i n t e r a c t i o n s at high e n e r g i e s , Ithaca, New York, 1971.
437