- Email: [email protected]
Search for the decay μ+ → e+e+e−
Nuclear Physics B299 (1988) 1-6 North-Holland, Amsterdam
S E A R C H F O R T H E D E C A Y p.+-~ e +e +e -
SINDR UM Collaboration
U. BELLGARDT and G. OTTER IlL Phys. Institut B der R WTH Aachen, D-5100 Aachen, FRG
R. EICHLER, L. FELAWKA1, C. NIEBUHR and H.K. WALTER IMP der ETH Z~rieh, CH-5234 Villigen, Switzerland
W. BERTL and N. LORDONG SIN, CH-5234 Villigen, Switzerland
J. MARTINO CEN Saclay, F-91191 Gif sur Yvette, France
S. EGLI, R. ENGFER, Ch. GRAB2, M. GROSSMANN-HANDSCHIN, E.A. HERMES, N. KRAUS, F. MUHEIM, H. PRUYS, A. VAN DER SCHAAF and D. VERMEULEN Physik-Institut der Universitiit Z~rich, CH-8001 Zfirich, Switzerland
Received 1 October 1987
The search for the decay/x + ~ e +e+e with the SINDRUM spectrometer has been continued. The result is a new upper limit for the branching ratio B, ~ 3e = F(/~ --* 3e)/F(/x ~ e2v) < 1.0× 10 12 (90% CL).
T h e m i n i m a l s t a n d a r d model of electroweak interactions with massless n e u t r i n o s p o s t u l a t e s l e p t o n flavour conservation, i.e. the separate conservation of electron, m u o n a n d tau n u m b e r . Processes like/z + ~ e + e + e -, /~+ --* e + 7 ( 7 ) or ~t-A ~ e-+A c o n v e r s i o n have indeed n o t b e e n observed [1]. M a n y extensions of the s t a n d a r d model, however, like supersymmetry, technicolour, compositeness, horizontal symmetry, left-right symmetry, can break this conservation law [2]. The predicted 1Present address: Univ. of Victoria, c/o TRIUMF, Vancouver, BC, Canada, V6T 2A3. 2 Present address: SLAC, PO Box 4349, Bin 65, Stanford, CA 94305, USA. 0550-3213/88/$03.50©Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
2
U. B e l l g a r d t
e t al. /
~ + ~
e +e +e -
branching ratios for the reactions with lepton flavour violation depend strongly on the model considered and could be as large as the present experimental limits. The search for the decay g + ~ e+e+e - with the S I N D R U M magnetic spectrometer started in 1983. The result of the previous period of data taking, B , ~ 3e = F(/~ 3 e ) / F ( ~ ~ e21,) < 2.4 X 10 -12 (90% CL), was published in 1985 [3]. In this letter we describe the acquisition and analysis of the data taken in 1986 and present the result of the combined experiment. Detailed descriptions can be found in refs. [3, 4]. A/~+ beam of 28 M e V / c from the ~rE3 channel at SIN was stopped at a rate of - 5 x 106/~+/s. The hollow double-cone target made of Rohacell has diameter 58 mm, length 220 mm and thickness 11 m g / c m 2 (the effective thickness in the beam direction is 90 mg/cm2). The decay electrons and positrons were detected in the S I N D R U M spectrometer, which consists of five concentric multiwire proportional chambers (MWPC) and a cylindrical array of 64 scintillation counters arranged in a homogeneous magnetic field of 0.33 T parallel to the beam axis. The coordinate of the MWPC hits along the anode wires is determined from the signals induced on +45 ° helical cathode strips. For a field of 0.33 T the momentum resolution is Ap/p = (12.0 _+ 0.4)% (FWHM) at p = 50 MeV/c. The spectrometer covers a solid angle of ~2/4~r = 73%. To improve the off-line reconstruction efficiency in this run four instead of three wire chambers were equipped with cathode strip readout. The first three stages of the trigger for data readout, the hodoscope majority coincidence (MC), the charge preselector (CPS) and the track preselector (TPS) were left unchanged. These trigger processors selected events with at least one negatively and two positively charged tracks within a time interval of 7 ns using the information of the hodoscope and the anode wires of the chambers, logically OR'ed into 64 or 128 sectors per MWPC. The fourth trigger stage, the track correlator (TCR), searches for e+e+e - triples with a total transverse momentum below a certain maximum. The value of this maximum momentum was lowered from 25 to 17 M e V / c . As a consequence the trigger efficiency for the decay/~ ~ 3e2u was reduced by about 40%. The increase in trigger rate caused by the higher beam intensity was compensated by an LSI-11 processor which was used to select events with three hodoscope signals within 2.5 ns. The selected events were read out and filtered by the on-line computer and then written to tape. The filter program performs a track search and analysis in the r-ep projection as described in [5], using the full resolution of the detector. Typical rates were MC: 2 x 104/s, CPS: 5 x 103/s, TPS: 80/s, TCR: 6/s, LSI: 2 / s , tape: 0.3/s. About 106 events were recorded on magnetic tape for further analysis. In the off-line analysis a 3-dimensional reconstruction of the events was performed. All onqine requirements were repeated and a vertex fit was applied to each e +e + e - combination. Events for which no proper vertex was found or for which the vertex position was outside the target were rejected. In fig. 1 a fully reconstructed event is shown in both the r-ep and the r-z projection.
B e l l g a r d t e t a L / #+ ~ e + e + e -
SINDRUM 18
16
B
14 .
=
3292
RUN =
GAUSS
58
EVENT = 5467
NEVT = 414 TIME = 1 7 / 5 / 8 6 3 TRACKS
A
TR I
FOUND
5 / 8.1 PT=24.5 TR 2 5/ 8.4 PT=23.9 TR 3 5/ 8.4 PT=35.1
4/ 1.2 P=-24.6 4/ 8.8 P= 2 3 . 9 4/ 8 . 7 P= 3 8 . 3
NASS= 8 3 . 3 PT= 2 0 . 9 PZ= 1 2 . 8 2
3~
32
;2
3~
46
48
~
3
Fig. 1. A reconstructed event shown in the r-tp and r-z projections.
U.
Bellgardt
et
,
0 0
L
,
al.
/
f.t + ~
,
,
,
,
e + e + e -
i
,
,
,
,
,
,
,
1200 800
@
400 0
-2
0
2
At [ns] Fig. 2. Distribution of the time difference between the mean time of the e+e invariant mass and the time of the second positron.
pair with the lowest
The resulting sample contains about 16600 events, 45% of which are accidental coincidences between e+e - pairs having low invariant mass (mainly from Bhabha scattering) and uncorrelated decay positrons. For this reason the difference At between the mean time of the e+e - pair and the time of the second positron was chosen to distinguish prompt and accidental events. In fig. 2 the distribution of At is shown for events from the kinematically allowed region Y~Ei + lY~p~lc <~muc z. The distribution shows a prompt peak containing 9280 _+ 100 events on top of a flat background of accidental events. According to Monte Carlo simulations, (2.3 + 0.2)% of these events are/~ ~ e2p7 decays with subsequent e+e - pair production in the target. After correction for this background the number of reconstructed prompt events is 9070 +_ 100. These events are interpreted as ~t---, 3e2~, decays with a possible small contribution from the decay /~ ~ 3e. To distinguish /~ ~ 3e decays from other processes with a final state e+e+e - ( + a n y t h i n g ) the kinematical constraints EEi= m~,c2 and ])Zpi[ = 0 can be applied. Since the error of the observable IEP~[ differs considerably from one event to the other we use /32-(p±/Op±)2+ (Pll/aplL) 2 instead. The quantities Pll and p . are the components of Y~Pi in and perpendicular to the decay plane, respectively; Op~ = 0.7 M e V / c and op, = 1.8 M e V / ¢ are the corresponding errors. Fig. 3 shows the distributions of EE~ v e r s u s /32 for prompt events (At < 0.8 ns), accidental events (At > 1.0 ns) and M o n t e Carlo generated/~ ~ 3e events. N o p r o m p t events are seen in a region containing 95% of the simulated /t ~ 3e events. The upper limit for the branching ratio of the decay was calculated using 2.3
% ~ 3e2~, . B~ ~ 3e2,, ( 9 0 % C L ) .
Here the factor 2.3 is the number of predicted events which lead with 90% probability to the observation of at least one event. B . o 3e2~= 3.6 × 10 -5 [6] is the branching ratio for the decay ~t ~ 3e2u. The efficiency e includes the geometrical
U. Bellgardt et aL / iz + --* e + e + e -
p2
60 ,'. 50 _ o 4O 30 ! 'i
". •
0
p2
60' 5O
60
~,
95
'
105
115 (bi"
95
105
li5
.............................
•
50
40
(~)
•
. . . .•. ,. ,. . . . . . . . .• . . . . . ". . . . .*.
40- *g* 30. 80 I0, 0 lS2
, •
' .....
'
(e)
:
30
20 lO 95
105
115 ~E i [MeV]
Fig. 3. Distributions of )?E, versus ~2 = ( p _ L / % ~ ) 2 + (Pll/%)2 for prompt events (a), accidental events (b) and Monte Carlo generated /~---)3e decays (c). The prompt spectrum (a) contains a contribution of accidental events which amounts to 50% of the accidental distribution (b). The contour defines a region containing 95% of the/~ ~ 3e events.
a c c e p t a n c e o f S I N D R U M for the given m a g n e t i c field, the efficiency of the four trigger stages a n d the efficiencies of the on-line filter a n d the off-line r e c o n s t r u c t i o n p r o g r a m . T h e factor e~_ 3¢ includes the 95% cut shown in fig. 3. N o t e that b y taking the r a t i o % ~ 3¢2~/~ ~ 3e m a n y systematic errors are minimized. T h e efficiencies have b e e n d e t e r m i n e d b y M o n t e C a r l o simulations using a c o n s t a n t m a t r i x element for /~ ---) 3e a n d a V - A m a t r i x element for/~ ---) 3e2v [7]. T h e results were e ~ 3eZv (3.1 + 0.3) × 10 - s a n d e ~ 3 ¢ = (15.5 __+0.2)%, where c o m m o n systematic errors have been removed. =
G i v e n these values a n d c o m b i n i n g the result with the one of the first m e a s u r i n g p e r i o d , we o b t a i n a new u p p e r limit of B~ ~ 3e < 1.0 × 10-12 (90% C L ) . T h i s w o r k was s u p p o r t e d b y the Swiss I n s t i t u t e for N u c l e a r R e s e a r c h ( S I N ) a n d b y the Swiss N a t i o n a l Science F o u n d a t i o n . T h e A a c h e n group was s u p p o r t e d b y the
6
U. B e l l g a r d t e t a L
/ It + ~ e + e + e
-
Bundesministerium fiir Forschung und Technologie of the Federal Republic of Germany. References [1] Particle Data Group, Phys, Lett. 170B (1986) 1 [2] J.D. Vergados, Phys. Reports 133 (1986); W. Buchmiiller and D. Wyler, Nucl, Phys. B286 (1986) 621 [3] W. Bertl et al., Nucl. Phys. B260 (1985) 1 [4] U. Bellgardt, thesis, to be submitted to the RWTH Aachen [5] A. van der Schaaf et al., Nucl. Instr. Meth. A240 (1985) 370 [6] N. Kraus, thesis, submitted to the Philosophical Faculty II of the University of ZiJrich (1985); P.M. Fishbane and K,J.F. Gaemers, Phys. Rev. D33 (1986) 159 [7] J. Sapirstein, LAMPF program library CPIZ (1982)
S E A R C H F O R T H E D E C A Y p.+-~ e +e +e -
SINDR UM Collaboration
U. BELLGARDT and G. OTTER IlL Phys. Institut B der R WTH Aachen, D-5100 Aachen, FRG
R. EICHLER, L. FELAWKA1, C. NIEBUHR and H.K. WALTER IMP der ETH Z~rieh, CH-5234 Villigen, Switzerland
W. BERTL and N. LORDONG SIN, CH-5234 Villigen, Switzerland
J. MARTINO CEN Saclay, F-91191 Gif sur Yvette, France
S. EGLI, R. ENGFER, Ch. GRAB2, M. GROSSMANN-HANDSCHIN, E.A. HERMES, N. KRAUS, F. MUHEIM, H. PRUYS, A. VAN DER SCHAAF and D. VERMEULEN Physik-Institut der Universitiit Z~rich, CH-8001 Zfirich, Switzerland
Received 1 October 1987
The search for the decay/x + ~ e +e+e with the SINDRUM spectrometer has been continued. The result is a new upper limit for the branching ratio B, ~ 3e = F(/~ --* 3e)/F(/x ~ e2v) < 1.0× 10 12 (90% CL).
T h e m i n i m a l s t a n d a r d model of electroweak interactions with massless n e u t r i n o s p o s t u l a t e s l e p t o n flavour conservation, i.e. the separate conservation of electron, m u o n a n d tau n u m b e r . Processes like/z + ~ e + e + e -, /~+ --* e + 7 ( 7 ) or ~t-A ~ e-+A c o n v e r s i o n have indeed n o t b e e n observed [1]. M a n y extensions of the s t a n d a r d model, however, like supersymmetry, technicolour, compositeness, horizontal symmetry, left-right symmetry, can break this conservation law [2]. The predicted 1Present address: Univ. of Victoria, c/o TRIUMF, Vancouver, BC, Canada, V6T 2A3. 2 Present address: SLAC, PO Box 4349, Bin 65, Stanford, CA 94305, USA. 0550-3213/88/$03.50©Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
2
U. B e l l g a r d t
e t al. /
~ + ~
e +e +e -
branching ratios for the reactions with lepton flavour violation depend strongly on the model considered and could be as large as the present experimental limits. The search for the decay g + ~ e+e+e - with the S I N D R U M magnetic spectrometer started in 1983. The result of the previous period of data taking, B , ~ 3e = F(/~ 3 e ) / F ( ~ ~ e21,) < 2.4 X 10 -12 (90% CL), was published in 1985 [3]. In this letter we describe the acquisition and analysis of the data taken in 1986 and present the result of the combined experiment. Detailed descriptions can be found in refs. [3, 4]. A/~+ beam of 28 M e V / c from the ~rE3 channel at SIN was stopped at a rate of - 5 x 106/~+/s. The hollow double-cone target made of Rohacell has diameter 58 mm, length 220 mm and thickness 11 m g / c m 2 (the effective thickness in the beam direction is 90 mg/cm2). The decay electrons and positrons were detected in the S I N D R U M spectrometer, which consists of five concentric multiwire proportional chambers (MWPC) and a cylindrical array of 64 scintillation counters arranged in a homogeneous magnetic field of 0.33 T parallel to the beam axis. The coordinate of the MWPC hits along the anode wires is determined from the signals induced on +45 ° helical cathode strips. For a field of 0.33 T the momentum resolution is Ap/p = (12.0 _+ 0.4)% (FWHM) at p = 50 MeV/c. The spectrometer covers a solid angle of ~2/4~r = 73%. To improve the off-line reconstruction efficiency in this run four instead of three wire chambers were equipped with cathode strip readout. The first three stages of the trigger for data readout, the hodoscope majority coincidence (MC), the charge preselector (CPS) and the track preselector (TPS) were left unchanged. These trigger processors selected events with at least one negatively and two positively charged tracks within a time interval of 7 ns using the information of the hodoscope and the anode wires of the chambers, logically OR'ed into 64 or 128 sectors per MWPC. The fourth trigger stage, the track correlator (TCR), searches for e+e+e - triples with a total transverse momentum below a certain maximum. The value of this maximum momentum was lowered from 25 to 17 M e V / c . As a consequence the trigger efficiency for the decay/~ ~ 3e2u was reduced by about 40%. The increase in trigger rate caused by the higher beam intensity was compensated by an LSI-11 processor which was used to select events with three hodoscope signals within 2.5 ns. The selected events were read out and filtered by the on-line computer and then written to tape. The filter program performs a track search and analysis in the r-ep projection as described in [5], using the full resolution of the detector. Typical rates were MC: 2 x 104/s, CPS: 5 x 103/s, TPS: 80/s, TCR: 6/s, LSI: 2 / s , tape: 0.3/s. About 106 events were recorded on magnetic tape for further analysis. In the off-line analysis a 3-dimensional reconstruction of the events was performed. All onqine requirements were repeated and a vertex fit was applied to each e +e + e - combination. Events for which no proper vertex was found or for which the vertex position was outside the target were rejected. In fig. 1 a fully reconstructed event is shown in both the r-ep and the r-z projection.
B e l l g a r d t e t a L / #+ ~ e + e + e -
SINDRUM 18
16
B
14 .
=
3292
RUN =
GAUSS
58
EVENT = 5467
NEVT = 414 TIME = 1 7 / 5 / 8 6 3 TRACKS
A
TR I
FOUND
5 / 8.1 PT=24.5 TR 2 5/ 8.4 PT=23.9 TR 3 5/ 8.4 PT=35.1
4/ 1.2 P=-24.6 4/ 8.8 P= 2 3 . 9 4/ 8 . 7 P= 3 8 . 3
NASS= 8 3 . 3 PT= 2 0 . 9 PZ= 1 2 . 8 2
3~
32
;2
3~
46
48
~
3
Fig. 1. A reconstructed event shown in the r-tp and r-z projections.
U.
Bellgardt
et
,
0 0
L
,
al.
/
f.t + ~
,
,
,
,
e + e + e -
i
,
,
,
,
,
,
,
1200 800
@
400 0
-2
0
2
At [ns] Fig. 2. Distribution of the time difference between the mean time of the e+e invariant mass and the time of the second positron.
pair with the lowest
The resulting sample contains about 16600 events, 45% of which are accidental coincidences between e+e - pairs having low invariant mass (mainly from Bhabha scattering) and uncorrelated decay positrons. For this reason the difference At between the mean time of the e+e - pair and the time of the second positron was chosen to distinguish prompt and accidental events. In fig. 2 the distribution of At is shown for events from the kinematically allowed region Y~Ei + lY~p~lc <~muc z. The distribution shows a prompt peak containing 9280 _+ 100 events on top of a flat background of accidental events. According to Monte Carlo simulations, (2.3 + 0.2)% of these events are/~ ~ e2p7 decays with subsequent e+e - pair production in the target. After correction for this background the number of reconstructed prompt events is 9070 +_ 100. These events are interpreted as ~t---, 3e2~, decays with a possible small contribution from the decay /~ ~ 3e. To distinguish /~ ~ 3e decays from other processes with a final state e+e+e - ( + a n y t h i n g ) the kinematical constraints EEi= m~,c2 and ])Zpi[ = 0 can be applied. Since the error of the observable IEP~[ differs considerably from one event to the other we use /32-(p±/Op±)2+ (Pll/aplL) 2 instead. The quantities Pll and p . are the components of Y~Pi in and perpendicular to the decay plane, respectively; Op~ = 0.7 M e V / c and op, = 1.8 M e V / ¢ are the corresponding errors. Fig. 3 shows the distributions of EE~ v e r s u s /32 for prompt events (At < 0.8 ns), accidental events (At > 1.0 ns) and M o n t e Carlo generated/~ ~ 3e events. N o p r o m p t events are seen in a region containing 95% of the simulated /t ~ 3e events. The upper limit for the branching ratio of the decay was calculated using 2.3
% ~ 3e2~, . B~ ~ 3e2,, ( 9 0 % C L ) .
Here the factor 2.3 is the number of predicted events which lead with 90% probability to the observation of at least one event. B . o 3e2~= 3.6 × 10 -5 [6] is the branching ratio for the decay ~t ~ 3e2u. The efficiency e includes the geometrical
U. Bellgardt et aL / iz + --* e + e + e -
p2
60 ,'. 50 _ o 4O 30 ! 'i
". •
0
p2
60' 5O
60
~,
95
'
105
115 (bi"
95
105
li5
.............................
•
50
40
(~)
•
. . . .•. ,. ,. . . . . . . . .• . . . . . ". . . . .*.
40- *g* 30. 80 I0, 0 lS2
, •
' .....
'
(e)
:
30
20 lO 95
105
115 ~E i [MeV]
Fig. 3. Distributions of )?E, versus ~2 = ( p _ L / % ~ ) 2 + (Pll/%)2 for prompt events (a), accidental events (b) and Monte Carlo generated /~---)3e decays (c). The prompt spectrum (a) contains a contribution of accidental events which amounts to 50% of the accidental distribution (b). The contour defines a region containing 95% of the/~ ~ 3e events.
a c c e p t a n c e o f S I N D R U M for the given m a g n e t i c field, the efficiency of the four trigger stages a n d the efficiencies of the on-line filter a n d the off-line r e c o n s t r u c t i o n p r o g r a m . T h e factor e~_ 3¢ includes the 95% cut shown in fig. 3. N o t e that b y taking the r a t i o % ~ 3¢2~/~ ~ 3e m a n y systematic errors are minimized. T h e efficiencies have b e e n d e t e r m i n e d b y M o n t e C a r l o simulations using a c o n s t a n t m a t r i x element for /~ ---) 3e a n d a V - A m a t r i x element for/~ ---) 3e2v [7]. T h e results were e ~ 3eZv (3.1 + 0.3) × 10 - s a n d e ~ 3 ¢ = (15.5 __+0.2)%, where c o m m o n systematic errors have been removed. =
G i v e n these values a n d c o m b i n i n g the result with the one of the first m e a s u r i n g p e r i o d , we o b t a i n a new u p p e r limit of B~ ~ 3e < 1.0 × 10-12 (90% C L ) . T h i s w o r k was s u p p o r t e d b y the Swiss I n s t i t u t e for N u c l e a r R e s e a r c h ( S I N ) a n d b y the Swiss N a t i o n a l Science F o u n d a t i o n . T h e A a c h e n group was s u p p o r t e d b y the
6
U. B e l l g a r d t e t a L
/ It + ~ e + e + e
-
Bundesministerium fiir Forschung und Technologie of the Federal Republic of Germany. References [1] Particle Data Group, Phys, Lett. 170B (1986) 1 [2] J.D. Vergados, Phys. Reports 133 (1986); W. Buchmiiller and D. Wyler, Nucl, Phys. B286 (1986) 621 [3] W. Bertl et al., Nucl. Phys. B260 (1985) 1 [4] U. Bellgardt, thesis, to be submitted to the RWTH Aachen [5] A. van der Schaaf et al., Nucl. Instr. Meth. A240 (1985) 370 [6] N. Kraus, thesis, submitted to the Philosophical Faculty II of the University of ZiJrich (1985); P.M. Fishbane and K,J.F. Gaemers, Phys. Rev. D33 (1986) 159 [7] J. Sapirstein, LAMPF program library CPIZ (1982)