- Email: [email protected]
A search for a keV pseudoscalar in the two-body decay of orthopositronium
Volume 237, number 2
PHYSICS LETTERS B
15 March 1990
A SEARCH FOR A keV PSEUDOSCALAR IN T H E T W O - B O D Y DECAY O F O R T H O P O S I T R O N I U M S.N. G N I N E N K O , Yu.M. K L U B A K O V , A.A. P O B L A G U E V and V.E. POSTOEV Institutefor Nuclear Research of the Academy of Sciences of the USSR, SU- I 17 312 Moscow, USSR Received 11January1990
We have searched for the exotic annihilation of orthopositronium: e +e- (3St) -*7+ a, where a is a light neutral pseudoscalar. The upper limit on the ratio of this decay rate to the 37 decay rate obtained is F(o-Ps--,'t+a)/F(o-Ps~37) <3.8× 10-4 (90% CL), if the mass m. < 30 keV. This result excludes the hypothesis of Samuel that this decay may resolve the discrepancy between the theoretical and experimental values of the orthopositronium lifetime in vacuum if the a mass is under 5.7 keV.
The precise d a t a o b t a i n e d by Westbrook et al. [ 1 ] indicate that the annihilation rate o f the o-Ps in vacuum, 2x, is greater than was predicted. The new experimental value, ;tx (exp.) = 7.0516 + 0.0013 ~ts- 1, exceeds the theoretical value 2 T ( t h e o r y ) = 7 . 0 3 8 3 + 0.00007 ~ts-t [2] by ten standard deviations and results in a relative contribution to the o-Ps decay rate of A R = A 2 - r / 2 x = 1.9× 10 -3, where ZXJ.T----J.T(exp.) - - 2 T ( t h e o r y ) = 0 . 0 1 3 3 + 0.0013 p.s-i. In order to explain this discrepancy, the authors o f ref. [3] have considered single-photon annihilation with production o f a light pseudoscalar: o-Ps~7+a.
( 1)
There are several experiments which searched for this decay o f o - P s [ 4 - 6 ]. The most precise measurement has been reported by A m a l d i et al. [6]. Their result excludes decay (1) at the level B R ( o - P s ~ ) , + a ) = F ( o - P s ~ 7 + a ) / F ( o - P s ~ 3 7 ) < 5 × 10 -6 -1 × 10 -6 if the mass o f the pseudoscalar is between 100 and 900 keV. None o f these experiments is sensitive to pseudoscalars with a mass rna < 100 keV. This is due to the presence o f single 511 keV's from the 27 annihilation and to detector inefficiency. Rccently, Samuel [7] has shown that a light neutral pseudoscalar with the coupling to electrons o ~ ' = g 2 / 4 n = 2 X 10 -8, mass m a < 5 . 7 keV, and lifetime r. > 0.14 s may resolve the o-PS lifetime discrepancy and be consistent with the ( g - 2 ) o f the elec-
iron and muon and, also, with the SLAC b e a m - d u m p experiment [8]. in a more recent work, Carlson and Salati [9] have noted that this would contradict the stellar models o f the sun and o f t h e horizontal branch stars. However, the authors o f ref. [ l0 ] have d e m onstrated that the result o f ref. [9] depends on the model one uses to describe the interaction between the a panicles. A n o t h e r possible exotic decay mode, o - P s - , n o t h ing, has been studied by Atoyan et al. [ 11 ]. Their result excludes this decay at the level F ( o - P s - - , n o t h i n g ) / F ( o - P s - - , 3)' ) < 5.8 × 10- 4 ( 90% CL). In this letter we report the result o f our search for the single-photon decay ( 1 ) for the pseudoscalar mass ma < 30 keV. The set-up we have used to search for decay ( 1 ) is shown in fig. 1. Positrons from the Na-22 source with activity ~ 3 ~tCi were detected by a 0.15 m m thick plastic scintillator. Two light guides brought the light to a pair o f photomultipliers FEU-85. The positrons that went through the scintillator were stopped in the target (silica aerogel with density p = 0 . 2 g/cm3), where about 12% o f t h e m formed the o-Ps. The 7 rays produced in positron annihilation were detected by a G e ( L i ) detector ( v o l u m e ---30 cm 3, resolution = 0 . 8 % F W H M at 511 keV) and a NaI calorimeter ( ~ 240 × 220 m m 3 ). The signal from the Ge ( L i ) detector ( G e ) was used in the pulse-height analysis and, also, for timing and lifetime measurements. The geometry of the set-up was selected in such a way that 287
Volume 237, number 2
PHYSICS LETTERS B
15 March 1990 ; 0o
oJ \ d) LIJ > LU
10 5
"0
4
n-
N
Fig. 1. Set-up ofthe experiment. ( 1) Nal calorimeter; (2) Ge( Li ) detector; (3) Na-22 source; (4) block of silica aerogel; (5) Nat counters: (6) plastic scintillator; (7) light guides; (8) photomultiplier tubes; (9) Ge(Li) detector housing.
1
® :C 2
o
40
80
120
150
, NS
when one o f the 7 quanta from a 2 7 annihilation event was detected by the Ge detector, the other 7 q u a n t u m necessarily entered the Nal calorimeter. The set-up also includes two NaI counters ( ~ 150 × 100 m m 3) for detecting the 1.27 MeV 7 ray emitted almost simultaneously with the positron. The coincidence between one o f the two Nal counters and the plastic scintillator was used as a positron-production tag and, also, to determine the time of posilronium formation and to open the time window ~ 200 ns. The trigger signal for data acquisition was taken to be a signal from Ge falling within this strobe. A C A M A C system interfaced to a P D P 11/40 computer and type drive was used for data acquisition, The Ge pulse height, the Nal-calorimeter pulse height, and the time interval between the positron tag and the Ge signal, all were recorded on a magnetic tape. In order to monitor the set-up, we used the 511 keV line. The datataking period was about a month. The basic idea o f this experiment was to observe decay ( 1 ) by comparing the inefficiencies of detection o f 2y annihilation events in the Nal calorimeter for different time intervals in the time spectrum of positron annihilation in aerogel. The interval A in the time spectrum shown in fig. 2 mainly corresponds to 23, events due to annihilation in flight and to singlet 3,-state decay of Ps. The long-lived component (interval B) is related to o-Ps annihilation and contains contributions from both 23, and 33, events. The contribution of 23, events is due to the quenching of the triplet Ps state owing to collisions which shorten the 288
Fig. 2. Time spectrum of positron annihilation obtained for aerogel; interval A: 0-30 ns, interval B: 40-160 ns. o-Ps life-time. The ratio of number of 2y and 3y events in the time "'tail" is
N2~/N3v = r!~/rl - 1 ,
(2)
where r~ = l/2-r (exp.) is the o-Ps life-time in vacuum and ZT is its life-time in the target. Let us now consider the energy release spectra in the NaI calorimeter corresponding to lime intervals A (fig. 3a) and B (fig. 3b ) and, also, to the signal in Ge from 511 keV 7 quanta. The low-energy part of the Nal spectrum shown in fig. 3a contains an admixture of events due to the inefficiency of 51 I keV ),-ray detection. The low-energy part of the NaI spectrum shown in fig. 3b, in addition to the events due to 27 inefficiency, contains an admixture of events due to the inefficiency of o - P s i 3 7 detection and, also, an excess of events from decay (1), zXN=N3v×BR(oPs-. 7 + a) X er~ (~,, is the efficiency ofT-quantum detection in Ge). The inefficiencies of 511 keV 7-quanta detection in the Nal calorimeter for time intervals A and B can be presented as
rlA =N2~,( I, A )/N2v( 2, A) ,
(3)
Y/B----N2~,(1, B)/N2~(2, B ) ,
(4)
where N2v( 1, A) and n2y(2, A) ( ~ v ( 1, B) and N2~(2, B) ) are the numbers of 51 1 keV events detected in Ge in the lime interval A ( B ) and within two energy
Volume 237, number 2
PHYSICS LETTERS B
xlO3
!t 102
®
L~
15 March 1990
We can assume that the 511 keV spectral line is almost identical to the 7 line from decay ( i ) in the Ge since their energy difference, AE= ~ ( m ] / m e ) , is negligible compared to the resolution of Ge for the m a < 3 0 keV. This gives us e2r/%a=2 and, using (2) we can write B R ( o - P s - , 7 + a ) = 2(r/B -- r/A) ( l ' o / I ' r -- 1 )
In order to obtain the number of 511 keV events, the spectra from the Ge(Li) detector for the energy release between 450 and 540 keV were fitted (we used the M I N U I T program [ 12] ) with a sum of two distributions for the time interval A:
103 7-
No(i, A)fo + N:~(i, A)f2~, 102
lO1
(7)
(8)
and with a sum of three distributions for the time interval B: _ _ _
450
.±
, [.
490 E KeY
.
530
.
i
0
200 400 E. KeY
6O0
Fig. 3. Energy spectra of the o-Ps decay measured in the Ge (Li) detector for energies between 450 and 540 keV and the corresponding spectra measured in the Nal calorimeter within time intervals 0-30 ns (a) and 40-160 ns (b). (b) shows the calculated contributions from 27 and 3y events and a constant background to the spectrum for the Ge( Li ) detector. The dashed curve for the Nal spectrum is the boundary line between two energy intervals: ( I ) E < 20 keV and ( 2 ) 20 < E < 600 keV.
intervals: (1) E < 2 0 keY and (2) 2 0 < E < 6 0 0 keV in the NaI calorimeter, respectively (see figs. 3a, 3b). For N2~( 1, B) and N2~(2, B) we can write N2y( 1, B) = N ~2~r/A + N 3 ~ B R ( o - P s ~ y + a ) ~ a ~ , (5) N2~, ( 2,
B ) = N2~¢/~2,t •
(6 )
Here N2~ and N3.f a r e the numbers of 27 and 37 events in the time "tail" and e2v is the efficiency of 7 detection for 27 annihilation in Ge. As concerns e ( = 0.93 ), this is the fraction of events from the spectrum of decay ( 1 ) with the energy release in the Nal calorimeter less than 20 keV (region 1 ). Actually, this energy release is due to the processes that may accompany decay ( 1 ) such as the superposition of pulses, PMtube noise, etc. The spectrum corresponding to decay ( 1 ) was found experimentally basing on the delay of the strobe for the Nal calorimeter.
No(i, B)f'o+N2r(i, B)f~vWN3v(i, B)f~v .
(9)
Here i = 1, 2, fo and f ~ represent the flat random background,.[2v is the experimental 511 keV spectral line in G e , f ~v=J2v, andf3r is the Monte Carlo 7 spectrum for 7 quanta with the energy close to maximum from o-Ps--,37, obtained by using the experimental form of the 511 keV linef2~. The ratio (2) was found by fitting the time "tail" with the function lexp(
--I/'CT)+C,
(10)
where the exponent describes the o-Ps decay and C represents the constant random background. This way we have found r/n--r/A= (0.56_+0.21 ) × 10 -4, rO/pT =2+0.05. Our final limit on the relative probability of the decay ( 1 ) is thus
F(o-Ps~7+a)/F(o-Ps--,37) (90% CL)
< 3.8 X 10 -4 ( 11 )
if the mass m a < 3 0 keV. The possible systematic effects, such as the dependence of the inefficiency on the point of annihilation inside the target, small broading of the line f2v compared to the f ~ line, dependence on the end-points of the energy interval used to select the events in Ge and others, were found to be negligible. In order to check the data handling, we added an admixture of experimental 511 keV events to the Ge spectrum in 289
Volume 237, number 2
PHYSICS LETTERS B
fig. 3b, that c o r r e s p o n d e d to B R ( o - P s ~ , + a ) = 1.9 X 10 -3, a s i m u l a t e d decay ( 1 ). T h i s resulted in that the B R ( o - P S ~ T + a ) was f o u n d to be ( 1 . 8 7 + 0 . 4 8 ) X 1 0 - 3 which agrees with the initial value w i t h i n the e s t i m a t e d error. Thus, o u r result ( 1 1 ) excludes the hypothesis o f S a m u e l [ 7 ] that decay ( 1 ) m a y resolve the discrepa n c y b e t w e e n the theoretical a n d e x p e r i m e n t a l values o f the o-Ps life-time in v a c u u m if the mass ma is u n d e r 5.7 keV. We are grateful to Professor V.A. M a t v e e v a n d Professor V.M. L o b a s h e v for their support. It is a pleasure to a c k n o w l e d g e the s t i m u l a t i n g interest o f M.I. D o b r o l i u b o v , A.Yu. Ignatiev a n d V.A. R u b a k o v , a n d the help o f G.S. A t o y a n , V.V. Isakov, E.S. K o n o b e y e v s k i i , V.D. Laptev, V.I. Stepanov, a n d Yu.V. Zacharov. O n e o f us ( S . N . G . ) wishes to t h a n k Professor M. S a m u e l for i n t e r e s t i n g discussions.
Note added. After this work was completed, we have f o u n d o u t that a n e w u p p e r limit for the rate o f the decay o - P s - - , T + a , B R ( o - P s - - , ) , + a ) < 6 . 4 X 10 - 5 -
290
15 March 1990
7 . 6 × 10 -6 for m a < 100 keY, has been o b t a i n e d ind e p e n d e n t l y by Orito et al. [ 13 ].
References [ 1 ] C.I. Westbrook, D.W. Gidley, R.S. Conti and A. Rich. Phys. Rev. Left. 58 (1987) 1328. [2] G.S. Adkins, Ann. Phys. (NY) 146 (1983) 78; W.E. Caswcll and G.P. Lepage, Phys. Rev. A 20 (1979) 36. [3] I. Cleymans and P.S. Ray, Left. Nuovo Cimento 37 ( 1983 ) 569. [4 ] G. Carboni and W. Dahmc, Phys. Lett. B 123 ( 1983 ) 349. [ 5 ] V. Metay et al., Nucl. Phys. A 409 ( 1983 ) 331. [6] U. Amaldi, G. Carboni, B. Jonson and J. Thun, Phys. Lett. B 153 (1985) 444. [7] M.A. Samuel, Mod. Phys. Lctt. A 3 (1988) 1117. [8] J.D. Bjorken et al., Phys. Rev. D 38 (1988) 3375. [9] E.D. Carlson and P. Salati, Phys. Lett. B 218 (1989) 79. [ 10] M. I. Dobroliubov and A.Yu. Ignatiev, Phys. Lelt. B 229 (1989) 418. [ 11 ] G.S. Atoyan, S.N. Gninenko, V.I. Razin and Yu.V. Ryabov, Phys. Lett. B 220 ( 1989 ) 317. [ 12 ] F. James and M. Roos, CERN computer library write-up, D506 (1977). [13] S. Orito, K. Yoshimura, T. Haga and M. Tsuchiak, Phys. Rev. Left. 63 (1989) 597.
PHYSICS LETTERS B
15 March 1990
A SEARCH FOR A keV PSEUDOSCALAR IN T H E T W O - B O D Y DECAY O F O R T H O P O S I T R O N I U M S.N. G N I N E N K O , Yu.M. K L U B A K O V , A.A. P O B L A G U E V and V.E. POSTOEV Institutefor Nuclear Research of the Academy of Sciences of the USSR, SU- I 17 312 Moscow, USSR Received 11January1990
We have searched for the exotic annihilation of orthopositronium: e +e- (3St) -*7+ a, where a is a light neutral pseudoscalar. The upper limit on the ratio of this decay rate to the 37 decay rate obtained is F(o-Ps--,'t+a)/F(o-Ps~37) <3.8× 10-4 (90% CL), if the mass m. < 30 keV. This result excludes the hypothesis of Samuel that this decay may resolve the discrepancy between the theoretical and experimental values of the orthopositronium lifetime in vacuum if the a mass is under 5.7 keV.
The precise d a t a o b t a i n e d by Westbrook et al. [ 1 ] indicate that the annihilation rate o f the o-Ps in vacuum, 2x, is greater than was predicted. The new experimental value, ;tx (exp.) = 7.0516 + 0.0013 ~ts- 1, exceeds the theoretical value 2 T ( t h e o r y ) = 7 . 0 3 8 3 + 0.00007 ~ts-t [2] by ten standard deviations and results in a relative contribution to the o-Ps decay rate of A R = A 2 - r / 2 x = 1.9× 10 -3, where ZXJ.T----J.T(exp.) - - 2 T ( t h e o r y ) = 0 . 0 1 3 3 + 0.0013 p.s-i. In order to explain this discrepancy, the authors o f ref. [3] have considered single-photon annihilation with production o f a light pseudoscalar: o-Ps~7+a.
( 1)
There are several experiments which searched for this decay o f o - P s [ 4 - 6 ]. The most precise measurement has been reported by A m a l d i et al. [6]. Their result excludes decay (1) at the level B R ( o - P s ~ ) , + a ) = F ( o - P s ~ 7 + a ) / F ( o - P s ~ 3 7 ) < 5 × 10 -6 -1 × 10 -6 if the mass o f the pseudoscalar is between 100 and 900 keV. None o f these experiments is sensitive to pseudoscalars with a mass rna < 100 keV. This is due to the presence o f single 511 keV's from the 27 annihilation and to detector inefficiency. Rccently, Samuel [7] has shown that a light neutral pseudoscalar with the coupling to electrons o ~ ' = g 2 / 4 n = 2 X 10 -8, mass m a < 5 . 7 keV, and lifetime r. > 0.14 s may resolve the o-PS lifetime discrepancy and be consistent with the ( g - 2 ) o f the elec-
iron and muon and, also, with the SLAC b e a m - d u m p experiment [8]. in a more recent work, Carlson and Salati [9] have noted that this would contradict the stellar models o f the sun and o f t h e horizontal branch stars. However, the authors o f ref. [ l0 ] have d e m onstrated that the result o f ref. [9] depends on the model one uses to describe the interaction between the a panicles. A n o t h e r possible exotic decay mode, o - P s - , n o t h ing, has been studied by Atoyan et al. [ 11 ]. Their result excludes this decay at the level F ( o - P s - - , n o t h i n g ) / F ( o - P s - - , 3)' ) < 5.8 × 10- 4 ( 90% CL). In this letter we report the result o f our search for the single-photon decay ( 1 ) for the pseudoscalar mass ma < 30 keV. The set-up we have used to search for decay ( 1 ) is shown in fig. 1. Positrons from the Na-22 source with activity ~ 3 ~tCi were detected by a 0.15 m m thick plastic scintillator. Two light guides brought the light to a pair o f photomultipliers FEU-85. The positrons that went through the scintillator were stopped in the target (silica aerogel with density p = 0 . 2 g/cm3), where about 12% o f t h e m formed the o-Ps. The 7 rays produced in positron annihilation were detected by a G e ( L i ) detector ( v o l u m e ---30 cm 3, resolution = 0 . 8 % F W H M at 511 keV) and a NaI calorimeter ( ~ 240 × 220 m m 3 ). The signal from the Ge ( L i ) detector ( G e ) was used in the pulse-height analysis and, also, for timing and lifetime measurements. The geometry of the set-up was selected in such a way that 287
Volume 237, number 2
PHYSICS LETTERS B
15 March 1990 ; 0o
oJ \ d) LIJ > LU
10 5
"0
4
n-
N
Fig. 1. Set-up ofthe experiment. ( 1) Nal calorimeter; (2) Ge( Li ) detector; (3) Na-22 source; (4) block of silica aerogel; (5) Nat counters: (6) plastic scintillator; (7) light guides; (8) photomultiplier tubes; (9) Ge(Li) detector housing.
1
® :C 2
o
40
80
120
150
, NS
when one o f the 7 quanta from a 2 7 annihilation event was detected by the Ge detector, the other 7 q u a n t u m necessarily entered the Nal calorimeter. The set-up also includes two NaI counters ( ~ 150 × 100 m m 3) for detecting the 1.27 MeV 7 ray emitted almost simultaneously with the positron. The coincidence between one o f the two Nal counters and the plastic scintillator was used as a positron-production tag and, also, to determine the time of posilronium formation and to open the time window ~ 200 ns. The trigger signal for data acquisition was taken to be a signal from Ge falling within this strobe. A C A M A C system interfaced to a P D P 11/40 computer and type drive was used for data acquisition, The Ge pulse height, the Nal-calorimeter pulse height, and the time interval between the positron tag and the Ge signal, all were recorded on a magnetic tape. In order to monitor the set-up, we used the 511 keV line. The datataking period was about a month. The basic idea o f this experiment was to observe decay ( 1 ) by comparing the inefficiencies of detection o f 2y annihilation events in the Nal calorimeter for different time intervals in the time spectrum of positron annihilation in aerogel. The interval A in the time spectrum shown in fig. 2 mainly corresponds to 23, events due to annihilation in flight and to singlet 3,-state decay of Ps. The long-lived component (interval B) is related to o-Ps annihilation and contains contributions from both 23, and 33, events. The contribution of 23, events is due to the quenching of the triplet Ps state owing to collisions which shorten the 288
Fig. 2. Time spectrum of positron annihilation obtained for aerogel; interval A: 0-30 ns, interval B: 40-160 ns. o-Ps life-time. The ratio of number of 2y and 3y events in the time "'tail" is
N2~/N3v = r!~/rl - 1 ,
(2)
where r~ = l/2-r (exp.) is the o-Ps life-time in vacuum and ZT is its life-time in the target. Let us now consider the energy release spectra in the NaI calorimeter corresponding to lime intervals A (fig. 3a) and B (fig. 3b ) and, also, to the signal in Ge from 511 keV 7 quanta. The low-energy part of the Nal spectrum shown in fig. 3a contains an admixture of events due to the inefficiency of 51 I keV ),-ray detection. The low-energy part of the NaI spectrum shown in fig. 3b, in addition to the events due to 27 inefficiency, contains an admixture of events due to the inefficiency of o - P s i 3 7 detection and, also, an excess of events from decay (1), zXN=N3v×BR(oPs-. 7 + a) X er~ (~,, is the efficiency ofT-quantum detection in Ge). The inefficiencies of 511 keV 7-quanta detection in the Nal calorimeter for time intervals A and B can be presented as
rlA =N2~,( I, A )/N2v( 2, A) ,
(3)
Y/B----N2~,(1, B)/N2~(2, B ) ,
(4)
where N2v( 1, A) and n2y(2, A) ( ~ v ( 1, B) and N2~(2, B) ) are the numbers of 51 1 keV events detected in Ge in the lime interval A ( B ) and within two energy
Volume 237, number 2
PHYSICS LETTERS B
xlO3
!t 102
®
L~
15 March 1990
We can assume that the 511 keV spectral line is almost identical to the 7 line from decay ( i ) in the Ge since their energy difference, AE= ~ ( m ] / m e ) , is negligible compared to the resolution of Ge for the m a < 3 0 keV. This gives us e2r/%a=2 and, using (2) we can write B R ( o - P s - , 7 + a ) = 2(r/B -- r/A) ( l ' o / I ' r -- 1 )
In order to obtain the number of 511 keV events, the spectra from the Ge(Li) detector for the energy release between 450 and 540 keV were fitted (we used the M I N U I T program [ 12] ) with a sum of two distributions for the time interval A:
103 7-
No(i, A)fo + N:~(i, A)f2~, 102
lO1
(7)
(8)
and with a sum of three distributions for the time interval B: _ _ _
450
.±
, [.
490 E KeY
.
530
.
i
0
200 400 E. KeY
6O0
Fig. 3. Energy spectra of the o-Ps decay measured in the Ge (Li) detector for energies between 450 and 540 keV and the corresponding spectra measured in the Nal calorimeter within time intervals 0-30 ns (a) and 40-160 ns (b). (b) shows the calculated contributions from 27 and 3y events and a constant background to the spectrum for the Ge( Li ) detector. The dashed curve for the Nal spectrum is the boundary line between two energy intervals: ( I ) E < 20 keV and ( 2 ) 20 < E < 600 keV.
intervals: (1) E < 2 0 keY and (2) 2 0 < E < 6 0 0 keV in the NaI calorimeter, respectively (see figs. 3a, 3b). For N2~( 1, B) and N2~(2, B) we can write N2y( 1, B) = N ~2~r/A + N 3 ~ B R ( o - P s ~ y + a ) ~ a ~ , (5) N2~, ( 2,
B ) = N2~¢/~2,t •
(6 )
Here N2~ and N3.f a r e the numbers of 27 and 37 events in the time "tail" and e2v is the efficiency of 7 detection for 27 annihilation in Ge. As concerns e ( = 0.93 ), this is the fraction of events from the spectrum of decay ( 1 ) with the energy release in the Nal calorimeter less than 20 keV (region 1 ). Actually, this energy release is due to the processes that may accompany decay ( 1 ) such as the superposition of pulses, PMtube noise, etc. The spectrum corresponding to decay ( 1 ) was found experimentally basing on the delay of the strobe for the Nal calorimeter.
No(i, B)f'o+N2r(i, B)f~vWN3v(i, B)f~v .
(9)
Here i = 1, 2, fo and f ~ represent the flat random background,.[2v is the experimental 511 keV spectral line in G e , f ~v=J2v, andf3r is the Monte Carlo 7 spectrum for 7 quanta with the energy close to maximum from o-Ps--,37, obtained by using the experimental form of the 511 keV linef2~. The ratio (2) was found by fitting the time "tail" with the function lexp(
--I/'CT)+C,
(10)
where the exponent describes the o-Ps decay and C represents the constant random background. This way we have found r/n--r/A= (0.56_+0.21 ) × 10 -4, rO/pT =2+0.05. Our final limit on the relative probability of the decay ( 1 ) is thus
F(o-Ps~7+a)/F(o-Ps--,37) (90% CL)
< 3.8 X 10 -4 ( 11 )
if the mass m a < 3 0 keV. The possible systematic effects, such as the dependence of the inefficiency on the point of annihilation inside the target, small broading of the line f2v compared to the f ~ line, dependence on the end-points of the energy interval used to select the events in Ge and others, were found to be negligible. In order to check the data handling, we added an admixture of experimental 511 keV events to the Ge spectrum in 289
Volume 237, number 2
PHYSICS LETTERS B
fig. 3b, that c o r r e s p o n d e d to B R ( o - P s ~ , + a ) = 1.9 X 10 -3, a s i m u l a t e d decay ( 1 ). T h i s resulted in that the B R ( o - P S ~ T + a ) was f o u n d to be ( 1 . 8 7 + 0 . 4 8 ) X 1 0 - 3 which agrees with the initial value w i t h i n the e s t i m a t e d error. Thus, o u r result ( 1 1 ) excludes the hypothesis o f S a m u e l [ 7 ] that decay ( 1 ) m a y resolve the discrepa n c y b e t w e e n the theoretical a n d e x p e r i m e n t a l values o f the o-Ps life-time in v a c u u m if the mass ma is u n d e r 5.7 keV. We are grateful to Professor V.A. M a t v e e v a n d Professor V.M. L o b a s h e v for their support. It is a pleasure to a c k n o w l e d g e the s t i m u l a t i n g interest o f M.I. D o b r o l i u b o v , A.Yu. Ignatiev a n d V.A. R u b a k o v , a n d the help o f G.S. A t o y a n , V.V. Isakov, E.S. K o n o b e y e v s k i i , V.D. Laptev, V.I. Stepanov, a n d Yu.V. Zacharov. O n e o f us ( S . N . G . ) wishes to t h a n k Professor M. S a m u e l for i n t e r e s t i n g discussions.
Note added. After this work was completed, we have f o u n d o u t that a n e w u p p e r limit for the rate o f the decay o - P s - - , T + a , B R ( o - P s - - , ) , + a ) < 6 . 4 X 10 - 5 -
290
15 March 1990
7 . 6 × 10 -6 for m a < 100 keY, has been o b t a i n e d ind e p e n d e n t l y by Orito et al. [ 13 ].
References [ 1 ] C.I. Westbrook, D.W. Gidley, R.S. Conti and A. Rich. Phys. Rev. Left. 58 (1987) 1328. [2] G.S. Adkins, Ann. Phys. (NY) 146 (1983) 78; W.E. Caswcll and G.P. Lepage, Phys. Rev. A 20 (1979) 36. [3] I. Cleymans and P.S. Ray, Left. Nuovo Cimento 37 ( 1983 ) 569. [4 ] G. Carboni and W. Dahmc, Phys. Lett. B 123 ( 1983 ) 349. [ 5 ] V. Metay et al., Nucl. Phys. A 409 ( 1983 ) 331. [6] U. Amaldi, G. Carboni, B. Jonson and J. Thun, Phys. Lett. B 153 (1985) 444. [7] M.A. Samuel, Mod. Phys. Lctt. A 3 (1988) 1117. [8] J.D. Bjorken et al., Phys. Rev. D 38 (1988) 3375. [9] E.D. Carlson and P. Salati, Phys. Lett. B 218 (1989) 79. [ 10] M. I. Dobroliubov and A.Yu. Ignatiev, Phys. Lelt. B 229 (1989) 418. [ 11 ] G.S. Atoyan, S.N. Gninenko, V.I. Razin and Yu.V. Ryabov, Phys. Lett. B 220 ( 1989 ) 317. [ 12 ] F. James and M. Roos, CERN computer library write-up, D506 (1977). [13] S. Orito, K. Yoshimura, T. Haga and M. Tsuchiak, Phys. Rev. Left. 63 (1989) 597.