Nuclear Physics B138 (1978) 189-217
© North-Holland Publishing Company
ANOMALOUS e+e - AND p + p - EVENTS PRODUCED IN e+e - ANNIHILATIOI~
F.B. HEILE, M.L. PERL, G.S. ABRAMS, M.S. ALAM, A.M. BOYARSKI,
M. BREIDENBACH, J. D O R F A N , G.J. FELDMAN, G. GOLDHABER,
G. HANSON, J.A. JAROS, J.A. KADYK, D. LOKE **, R.J. MADARAS,
A.E. NELSON, J.M. PATERSON, I. PERUZZI *, M. PICCOLO *, T. PUN,
P. RAPIDIS and J.E. WlSS
Stanford Linear Accelerator Center, Stanford University, Stanford, California 94305, USA
and
Lawrence Berkeley Laboratory and Department of Physics, University of California,
Berkeley, California 94 720, USA
G. GRAMMER, Jr.
Physics Department, University of Illinois, Urbana, lllinois 61801, USA
Received 20 December 1977
We have observed events of the form e + + e - --, e + + e - and e+ + e - ~ ~+ + # - in which
there are no other detected particles and there is substantial missing energy; and which cannot be explained by conventional electromagnetic interactions. We show that these events
can be explained as the decay products from the pair production, e+ + e - --*r + + r - , of a
new charged lepton, r -+, of mass ~1800 MeV/c2. Some properties of these events are
presented. In particular, this production cross section is inconsistent with the r being an
electron-related paralepton.
1. Introduction
In the past two years substantial evidence has been found [ 1 - 5 ] for the existence
of a new charged particle called the Z . This particle has a mass [4,5] o f ~ 1 8 0 0
MeV/c2; decays predominantly through the weak interactions, and all its known
properties are consistent with being a lepton. That is, the ~'± appears to be a point
particle having no strong interactions, but having electrodynamic and weak interactions.
* Work supported by the Department of Energy.
** Fellow of Deutsche Forschungsgemeinschaft.
* Permanent address: Laboratori Nazionali, Frascati, Rome, Italy.
189
F.B. Heile et al. / A n o m a l o u s e +e - a n d ~+t~- events
190
Part of the evidence for the r's existence consists of events of the form
e ~ + e - -*e -+ +/a ~ + missing energy,
(1)
in which no other charged or neutral particles are detected. The only simple explanation [1,4,5 ] for these events, called e/a events hereafter, is that they come from the
production and decay sequence
e + + e - --*r + + r ~re*Ve v ~ p - ~ u ,
(2)
or the charged conjugate reaction. These leptonic decays of the r and the nature of
the assumed associated neutrinos, v r, are discussed in sect. 2. Since the r + and r decays are independent, if this explanation of the e,u events is correct, the following
reactions must also occur:
e++e --~r + + rVTe+IJe Pr e - ~e ,
(3)
e÷ +e- ~r ÷ + r--
+
-
-
-
Vrld Pp. Prld l)tl.
(4)
Therefore ee and/4u events,
e + + e - --* e + + e - + missing energy
(5a)
e ÷ + e - -+/l + + ~ - + missing energy,
(5b)
which are analogous to the e/a events must also occur. Indeed, on much more general
grounds such ee and/2/z events must occur, regardless of the nature o f the r, if we
simply assume that:
(i) the e/a events are real;
(ii) the e and/a come from the decays of different particles called r's;
(iii) the r's are pair produced;
(iv) the decays o f the r+r - pair are independent o f each other.
Therefore it is crucial that such ee and/a/~ events exist if the new particle explanation o f the e/~ events is correct. This paper reports:
(i) that such ee and tzta events have been found;
(ii) that their production cross section is consistent with the production cross
section of the e/a events if the 7- is n o t a paralepton;
(iii) that their properties are consistent with the properties of the e# events.
These results are based on data acquired using the SLAC-LBL Magnetic Detector
F.B. Heile et aL / Anomalous e+e-and ta+tz - events
191
at the Stanford Linear Accelerator Center's SPEAR e+e - Colliding Beams Facility.
The study of these ee and ~ events is much more difficult than the study of the
e/a events because there are purely electromagnetic processes with relatively large
cross sections that lead to events of the form of the reactions in eq. (5). For example,
the two-virtual-photon processes [6]
e + + e - -+e + + e - +e + + e - ,
e÷+e - - + / a + + / a - + e + + e - ,
(6)
can contaminate the reactions in eq. (5) if the second e+e - pair is not detected. Such
backgrounds are discussed in sect. 5.
The apparatus is described in sect. 3 and the data analysis is presented in sect. 4.
The results and conclusions are given in sect. 6.
2. Theory
The body of theoretical work on leptons, on their relations to quarks, and on
gauge theories has grown rapidly in the past few years. Refs. [7-9] provide some
introduction to these general theoretical questions concerning leptons. However, in
this section we shall present only a few simple ideas related to our immediate interest,
namely that the ee and ~ events come from a charged heavy lepton whose dominant
decay modes are thru the weak interactions. Hence we consider three types of leptons
in which the electromagnetic decay modes are forbidden or strongly suppressed.
2.1. Sequential heavy leptons
It is possible that the electron and muons are the smallest mass members of a
sequence of charged leptons each having a unique lepton number and a unique asso-
ciated neutrino:
e-+
Pe, ve
T±
VT, V7
(7)
The consequence of the unique lepton numbers and complete lepton number conservation is that the electromagnetic decays
r - ?+ e - +~,,
r - # u - +3',
(8)
192
F.B. Heile et al. / Anomalous e+e - a n d t~+t~- events
Table 1
Predicted branching ratios for a r - sequential charged heavy lepton with a mass 1.9 GeV/c 2, an
associated neutrino mass of 0.0, and V - A coupling
Decay mode
Branching ratio
Number of
charged particles
in final state
v r e - ve
VrU-V-~
vr~rvrK vrp-
0.20
0.20
1
1
urK'-
vrA ~vr(hadron continuum)-
O. 11
1
0.01
1
0.22
0.01
0.07
1
1
1,3
0.18
1,3, 5
The predictions are based on refs. [10,11 ] as discussed in ref. [5 l- The hadron continuum
branching ratio assumes a threshold at 1.2 GeV for production of ~d quark pairs whose f'mal-state
interaction leads to the hadron continuum.
are forbidden and all decays are thru the weak interactions. The purely leptonic
decays are then
T--~Vr+e--
+ffe,
r - -~ vr + ta- + vu •
(9)
Depending on the mass of the r, m r , there may also be hadronic decay modes such as
T-
"-> I) T -I- T T - '
r-
-'v,+u-
+rr + +u-
.
(10)
Although we shall not use it explicitly in this paper, we note that by using conventional
weak-interaction theory and some measurements from known weak interactions the
decay widths and lifetimes of the sequential heavy lepton can be calculated. Table 1
gives the relative decay rates for a 1.9 GeV/c 2 r using V - A coupling and mvr = 0.0
(m~, is the mass of the v,). This yields a lifetime of 2.7 X 10 -13 s [5,10,11].
2.2. Paraleptons
A paralepton [12], following the n o t a t i o n o f Llewellyn Smith [7], has the l e p t o n
n u m b e r of the oppositely charged e or/a. (We formerly called these gauge-theory leptons.) Explicitly the E + has the lepton n u m b e r o f the e - with leptonic-decay modes
E + -~ e + + Ve + r e ,
( 1 1 a)
193
F.B. Heile et at/Anomalous e+e-and u +u - events
E - ~ e - + ~e + ~ e ,
(lib)
E + -+ gt+ + vu + Ve ,
(12a)
E - - + U - + ~u + ~e,
(12b)
and hadronic-decay modes
E + ~ ve + hadrons,
E - ~ ~e + hadrons.
(13)
Clearly the electromagnetic-decay modes are forbidden. A muon-associated paralepton, M ±, can also be defined, but the lower limit on its mass [13] set by muon-neutrino experiments eliminates it from consideration here.
2.3. Ortholeptons [7]
Suc h charged heavy leptons have the same lepton number as the same-charge e
or/a. We define the e ° - to have the lepton number of the e - and the t t * - to have
the lepton number of the/a-. We also call these particles excited electrons or muons.
We expect that their dominant decay will be electromagnetic
e*-* -+ e± + 7,
/a*± -+/l~ + 7
(14)
and so such particles would not be of interest here. However, as discussed by Low
[14] the coupling at the e*e'r and/~*/a7 vertices must be of the form
(e/M) ~ , , ou~ q,e f ~ ,
(15)
where M is an arbitrary mass. By making M very large the electromagnetic decays
can be suppressed and the weak interaction decays allowed to be dominant.
2.4. Comparison o f leptonic-decay rates
If all three types of leptons are assugned V - A coupling dnd all neutrino masses = O,
for sequential leptons and ortholeptons:
r(r- ~ Vre-~e) = 1
r ( r - - , vT~- ~.)
(15a)
'
where r is the decay width to the indicated mode. But for paraleptons with V -- A
coupling and all left-handed neutrinos
P(E- -+e- +re +re)
-2,
r ( E - - + u - + ~, + ~e)
(15b)
because there is constructive interference of the two diagrams which give the e - decay
mode [ 15 ]. (For further discussion see subsect. 6.3.)
194
b:B. H e i l e e t al. / A n o m a l o u s e+ e - a n d
ta+~ - e v e n t s
Fig. 1. Feynman diagram for production of r pairs by one-photon exchange.
2.5. Production cross section
We limit our considerations to the 7- being a spin@ Dirac point particle. Then the
total production cross section thru one-photon exchange, fig. 1, is
Or+r - -
2na2~3(3 - 32)
3s
(16)
Here ~ is the velocity of the r and a is the fine structure constant.
3. Apparatus and experimental method
3.1. S P E A R e+e- colliding beams facility
In the SPEAR e+e - colliding beams facility, fig. 2, the e ÷ and e - have equal and
opposite momenta. Hence the total momentum of an e+e - collision is zero and the
total energy is
Ec.m. = 2Eb ,
2
where/z" b is the energy in each beam. We also use s = Ee.m..
SPEAR operates in the
energy range of 2 ~< Ee.m. <~ 8 GeV. The rate at which events are produced from a
reaction having a cross section o is given by
rate(events/s) = o(cm 2) L(cm -2 s - i ) .
(17)
L is called the luminosity. In SPEAR there is just one bunch of electrons and one
bunch of positrons moving in opposite directions. Hence the luminosity is given by
L =N2f/A ,
(18)
where N is the number of e ~ or e - in a bunch, f is the number of bunch collisions
per second per interaction region, and A is the cross-sectional area of a bunch in cm 2.
The instantaneous luminosity at SPEAR at the beginning of a fill is given approxima-
F.B. Heile et al. / Anomalous e+e - a n d t~+tz - events
E
X
P
E
M
R
IE
N
T
A
LPIT\\
195
~///~'~~
/
,.J
c3
c]c
z
co
'~~~
ylN S
E
P
T
N
U
M
F
'L
(E
C
T
O
R
)
INJECTION
e~,
//;'.
Fig. 2. Layout of the SPEAR e+e - colliding beams facility. This experiment was carried out in
the experimental pit at the bottom of the figure: the west pit.
tely by ( E b / 1 . 8 ) 4 10 30 c m - 2 s - I f o r E b ~< 3 GeV, and is about 10 31 cm --z s - l for
E b > 3 GeV.
This experiment operated in the west pit interaction area of SPEAR (fig. 2).
3.2. D e t e c t o r
A drawing of the detector is shown in fig. 3. The magnetic field is provided by a
solenoidal coil 3.6 m long and 3.3 m in diameter. The field of approximately 4 kG is
longitudinal to the beam axis and is uniform to about -+2%.
We will start at the interaction region and describe in turn each element through
which a produced particle passes. The beam pipe has a mean radius of 8 cm and is
made of 0.15 mm thick corrugated stainless steel. The average effective thickness, due
to the corrugations, is 0.20 mm.
Around the beam pipe are four semi-cylindrical scintillators forming two nesting
196
F.B. Heile et al. / Anomalous e+e-and t~+~- events
MUONSPARKC H A M B E R S ~
FLUXR E T U R N ~
SHOWERC O U N T E R S ~ ~
COIL
ENDCAP-~7
?~
~
~ _ _ ~TRIGGERCOUNTERS
SPARK
CHAMBERS
SOLENOID
"--VACI.MMCHAMBER
LUMINK)SITY
MONITOR
Fig. 3. An exploded view of the detector.
cylinders at 11 and 13 cm radii. These counters are each 7 mm thick and 36 cm long.
They are part of the trigger and serve primarily to reduce triggers from cosmic rays.
There are two cylindrical proportional chambers around the beam pipe at 17 and
22 cm radii. Each consists of 512 sense wires parallel to the beam axis and cathode
strips perpendicular to the beam axis. These chambers were installed in January 1975.
They have no direct effect on the analysis of data presented in this paper.
The main tracking elements of the detector are four modules of concentric cylindrical magnetostrictive spark chambers at radii of 66, 91, 111 and 135 cm. Each
module consists of four cylinders of wires with the wires set at +2 °, - 2 °, +4 ° and
- 4 ° with respect to the beam axis. The tracking algorithms require sparks in three of
the four modules and thus the angular acceptance is normally defined by the 2.68 m
length of the third chamber. Neglecting the finite length of the interaction regions
and the curvature of tracks in the magnetic field, these chambers track particles over
0.70 × 47r sr solid angle. The rms momentum resolution for a 1 GeV/c track is about
15 MeV/c. Because of the high degree of redundancy (three out of four modules, two
out of four wires per module required) these chambers are highly efficient in tracking
particles. The inefficiency has been estimated at 1% per track or less. The structural
F.B. Heile et al. / Anomalous e+e - and ~ +t~- events
197
support for the chambers consists of six 6 mm wall, 5 cm diameter, aluminum posts
at a radius of 79 cm, and a 1.3 cm thick aluminum cylinder at a radius of 1.49 m.
These support posts can be major sources of multiple scattering; for this reason the
analysis programs normally require that at least two particles in each event do not
pass through a support post so that a good vertex for the event can be found. These
posts subtend about 6% of the solid angle so this requirement reduces the effective
solid angle of the detector somewhat. The data have been corrected for this.
Immediately beyond the aluminum cylinder supporting the spark chambers is a
cylindrical array of 48 2.5 cm thick plastic scintillator trigger counters. They are
2.61 m long and are viewed by 5 cm photomultiplier tubes from both ends. They
are-part of the trigger and provide time-of-flight information with an rms resolution
of about 0.5 ns. This is sufficient to separate pions from kaons up to a momentum of
600 MeV/c and kaons from protons up to a momentum of 1100 MeV/c. The solid
angle subtended by these counters is 0.65 × 41r st.
Next a particle will pass through the 9 cm aluminum solenoid coil and enter a
cylindrical array of 24 lead-plastic scintillator shower counters. The 3.10 m long
counters are made of five layers, each layer containing 6.4 mm of lead and 6.4 mm
of scintillator. The counters are viewed from each end by a 13 cm photomultiplier
tube. They are part of the trigger and have the primary function of discriminating
between electrons and hadrons. They also have been used to a limited extent to
detect photons.
Beyond the shower counters are a 20 cm thick iron flux return and one or two
planar magnetostrictive wire speak chambers to detect muons. The flux return is an
adequate hadron filter for our purposes [16].
3.3. Trigger
The trigger rate of the magnetic detector is limited to a few triggers per second
by the time required to recharge the spark chamber pulsing system. To achieve this
low a trigger rate it has been found necessary to require a pipe counter and two sets
of trigger counters with associated shower counters to fire. The shower counters are
set to fire on minimum ionizing particles. No special trigger was used for the ee, p/l,
or e/a events; they were simply acquired as part of the general data acquisition.
3.4. Data a c q u i s i t i o n
Data were acquired over a three year period ending in 1976. The integrated luminosity upon which this paper is based is
fLdt~.
16pb -l = 1.6X 1037 c m - 2 .
The Ee.m. range was 4.0 to 7.8 GeV. Since the data were acquired while the experiment was run for other purposes the data is spread unevenly over the Ec.m. range.
F.B. tleile et al. /Anomalous e+e - a n d u +tz - events
198
The main data blocks are:
Ecan. = 3.9 to 4.6 GeV,
fLdt
= 3.7 p b - ~ ,
Ec.m. = 4.8 GeV,
fLdt
= 0.9 pb - I ,
E¢.m. = 5.8 to 7.8 GeV,
fLdt
= 10.8 pb - I .
3.5. S e l e c t i o n o f electrons
The corrected shower counter pulse height, Hc, is defined in units such that for an
electron of momentum p
(Hc(P)) ~ 100 p ,
(19)
where p is in GeV/c. We defined as electrons all particles with
H c (p) > 50,
(20a)
p > 0.65 G e V / c .
(20b)
We used this fixed lower limit rather than a p-dependent limit for three reasons.
(a) The pulse height distribution for a fixed p is rather broad:
OHc/H c ~ 0.6~X/p,
p in G e V / c .
(21 )
(b) During the three years of data acquisition various changes were made in the
shower counter operating conditions and some degeneration o f the scintillator surface
in the counters may have occurred. Hence the ratio of the corrected pulse height Hc
to the raw pulse height changed with time and several recalibrations of the ratio were
made to preserve, eq. (19). These recalibrations used collinear e+e - events produced
by Bhabha scattering. Nevertheless eq. (19) could not be maintained precisely.
(c) Eq. (19a) is only approximate, there are nonlinearities in the relations of He(p)
to p below 1 GeV/c and above 2 or 2.5 GeV/c. For these reasons a fixed lower limit
in He(P) was easier to use, and losses and corrections easier to evaluate.
The lower limit on p of 0.65 GeV/c was used to reduce the loss of electrons whose
H c was below 50 (see subsect. 4.4).
3.6. S e l e c t i o n o f m u o n s
Muons are sought by looking for sparks in the muon detector chambers (fig. 3)
accessible to a particle. Accessible means that the particle had the proper angle and
sufficient momentum to reach that chamber. Since a muon will multiple scatter in
the iron and other material, we define d u as the measured distance between a muonproduced spark in a muon chamber and the position of the projected muon track in
that chamber. We define o u as one standard deviation due to the multiple scattering
F.B. tteile et al. / A nomalous e +e - a n d ~ +t~- events
199
expected in that distance, and we define the ratio
Du = d~/o u .
(22)
Muons were then defined by:
spark with IDul < 4,
p > 0.65 GeV/c,
~c < 50.
(23)
We note that an e is defined first, hence ifHc > 50 a particle is called an e even if
IDol < 4.
3. 7. E v e n t s e l e c t i o n
We selected all e+e -,/~+/~- and for comparison purposes e;/a ± events with the following properties.
(i) There are two and only two charged particles detected.
(ii) Each particle is an e or a ta as defined in eqs. (20) and (23), in particular
Pl > 0.65 GeV/c and P2 > 0.65 GeV/c.
(iii) The particles have opposite electric charge.
(iv) There are no photons detected. The efficiency for photon detection is close
to 100% for photon energies above 200 MeV but falls to zero when the photon energy
is 20 or 30 MeV.
(v) The coplanarity angle, 0cool, is greater than 20 ° where
cos 0copl = - ( n l X n + ) . ( n 2 × n + ) / ( I n l × n+lln2 X n+l).
(24)
Here n~, n 2 and n+ are unit vectors in the direction of motion of particle 1, particle 2
and the incident e ÷ beam respectively. This cut eliminates the very large number of
coplanar e+e - ~ e+e - and e+e - ~/a+/a - events.
(vi) The missing mass squared, m2m, is greater than 2.0 (GeV/c2) 2. Here
m2m = (fc.m. - El -- E2) 2 - (Pl +P2) 2 ,
(25)
where Ei, Pi are the energy and three-momentum of particle i.
(vii) An angular cut of I cos Oil <~ 0.6 is also used, where Oi is the angle between
particle i and the e ÷ beam direction. This cut was more severe than was used in our
other e±/l ~ studies and reduces the number of events somewhat. It was made in order
to provide a very well defined angular acceptance for electrodynamic-process background calculation.
3. 8. B a c k g r o u n d - e v e n t s e l e c t i o n
For background studies we collected all other 2-prong events in which all criteria
ofsubsect. 3.7 except (ii) were met and in which both particles had p > 0 . 6 5 GeV/c.
200
F.B. Heile et al. / Anomalous e+e - a n d ~ +~ - events
Such events contain one or two particles which are n e i t h e r e ' s n o r a ' s . We call these
particles:
h (for hadron)
i f a m u o n c h a m b e r was accessible,
x (for hadron or m u o n )
if a m u o n c h a m b e r was n o t accessible.
(26)
For most o f the e x p e r i m e n t we did not have c o m p l e t e coverage o f m u o n chambers,
but we always had c o m p l e t e coverage by the electron-defining shower counters.
Hence there can be h a d r o n - m u o n ambiguities but there are no hadron-electron ambiguities.
4. Data analysis
4.1. U n c o r r e c t e d data
Table 2 gives the numbers of events in 5Ec.m. ranges for the uncorrected data. If
there were no anomalous sources o f leptons, no hadron decays to leptons and no misidentification o f particles we would see only ee,/J~ and hh events. However, we k n o w
that the r produces e/~ events. Therefore m o r e generally we should see ee, gt~, e/~ and
hh events. We obviously see other types o f events due partly to particle misidentification and also due perhaps to other decay m o d e s o f the r (subsect. 2.1). Our n e x t task
is to consider this misidentification problem.
Table 2
Number of raw events
Ec.m. range 3.9-4.3
(GeV)
Event type
ee
e#
eh
ex
u~
~h
ux
hh
hx
xx
tot~
Data set
4.3-4.8
4.8-6.8
6.8-7.4
3.9-4.8
All
events
2
2
2
2
1
9
15
11
I0
13
15
14
3
18
3
18
10
12
13
19
13
23
3
10
3
47
48
28
31
30
21
36
7
18
6
70
44
32
38
37
14
36
14
20
12
18
26
18
9
13
12
11
7
4
4
162
143
101
101
112
75
120
34
70
28
111
124
272
317
122
946
The data in the fifth column were obtained in the first year of the detector operation. These data
will be analyzed separately from the later data in the first four columns because of different
operating conditions.
201
F.B. Helle et al. / Anomalous e +e - a n d ~ +~ - events
4.2. M i s i d e n t i f i c a t i o n p r o b a b i l i t i e s
Some e's selected by the cuts in eq. (20) may be hadrons which have interacted in
the shower counter giving Hc > 50. Other e's may come from Ket3 decay and hence
constitute a background for e's from r decay. Similarly, some of the/a's will not be
muons since a hadron can punch through the iron and simulate a muon. Hence to
determine the actual number of ee's, t~/a's or e#'s we will have to correct for these and
all other possible misidentifications. To do this correction we need to know the probability that a particle that is actually an e, g, or h will be classified as an e,/a, h or x.
We will call this probability Pi-~n where i is one of e,/a, or h, and n is one of e,/a, h
or
X.
The two largest and most important misidentification probabilities are Ph-,e and
Ph--,~. These were determined by assuming that every prong in a three- or more-pronge(
event was actually a hadron. Hence by counting how many of these prongs would
have been classified as either an e or a # we arrive at Ph--,e and Ph-~u as the ratio of
the numbers of e's and p's to the total number of hadrons respectively. This is momentum-dependent, and the determination was done in different m o m e n t u m bins and the
results folded with the hadron m o m e n t u m spectrum observed in our two-prong events
to arrive at the probabilities shown in table 3. Note that P h - e and Ph---~, are actually
upper bounds since they include not only the effects o f hadronic decay, interaction,
and punch through, but also include any direct lepton production (from charmed
particles or the r) in the three- or more-prong events as an event where a hadron is
misidentified. Therefore we are overestimating Ph-,e and Ph--,~.
Another fairly large misidentification probability is Pe--,h which is caused by a
fluctuation o f the electron's shower pulse height below our cut. Obviously this is
momentum-dependent since a low-momentum electron will have a much higher chance
of being misidentified as a hadron. This probability was calculated by using radiative
Table 3
The misidentification probabilities Pa--*b described in the text
.........................
Ec.m. range
(GeV)
Data set
3.9-4.3
4.3-4.8
4.8-6.8
6.8-7.4
3.9-4.8
2
2
2
2
1
Pe-~
Pe--~h
Pe-*x
Pta---*e
P/~h
P~a---*x
~0.002
0.098
0.0002
0.001
0.014
0.30
~0.002
0.125
0.0003
0.001
0.011
0.30
~0.002
0.097
0.0002
0.001
0.019
0.30
~0.002
0.107
0.0002
0.001
0.022
0.30
~0.002
0.149
0.0002
0.001
0.045
0.14
Ph--*e
0.16
0.33
0.26
0.30
0.19
Ph~
Ph-~x
0.14
0.30
0.14
0.30
0.14
0.30
0.15
0.30
0.18
0.15
202
F.B. Heile et al. / Anomalous e+e-and tz+~ - events
Bhabha events as a source o f known electrons at different energies. Then in each
momentum bin the ratio of electrons with showers below the cut to all electrons in
that bin gives Pe--,h for that momentum. This was folded with the observed momentum
distribution of electrons in our sample to give the actual Pe--,h shown in table 3.
At various times some of the muon chambers were removed, and in addition there
are gaps between the muon chambers where the muon detection efficiency decreases,
therefore the category x consists of tracks with Hc < 50 that are heading for these
areas. Thus P u ~ x and Ph-,x are equal to the fraction of the solid angle without muon
detection. Also
Pe--, x = Pe--,h Ph--,x,
(27)
Pe--,~, = 0.01Pe--,h(1 -- Ph--,x),
(28)
where the 0.01 in eq. (28) is the probability that an e will give a spark with IO~l < 4
in a muon chamber. Finally P ~ h is given by our muon chamber inefficiency as measured by collinear muons and we estimate 0.001 for Pu_~e.
4. 3. Correction o f data f o r misiden tification-general
Using the P's in table 3 we must now correct the raw data in table 2. An exact
procedure requires knowledge of the decay modes of the r, and perhaps other new
particles, which can produce eh and/ah events. For example, the production of a r + r pair can yield such events if one ~- decays into an e or/a and the other r decays semileptonically into a charged hadron, a neutrino, and either no photons or no detected
photons.
However, at present we do not know what relative numbers of real eh a n d / l h
events to expect. Therefore we have used three different methods to correct the raw
data in table 2. These methods are as follows.
M e t h o d I. We assume that the r + r - pair produces only ee, ~a, and e/a events, and
perhaps hh events. We assume that all backgrounds are hh events. Hence we assume
there are no actual eh or gth events. This method uses a ×2 minimization procedure.
M e t h o d H. We allow in addition to the actual ee, gtp, egt and hh events of Method I,
actual eh and p.h events. These might come from r + r - decays or be background events.
However, we assume on the basis o f p - e universality that the number of actual eh events
equals the number of actual gth events. This assumption is used to reduce the magnitude of the errors resulting from the minimization procedure which we use.
M e t h o d IlL Here we allow actual ee, gt/l, egt, hh, eh, and gh events with no restriction on the relation of the number of eh to the number o f p h events. This method
uses a matrix-inversion procedure so that it also tests for the number of actual ex, gtx,
hx and xx events; numbers which by the definition of x should be consistent with zero
within these errors.
F.B. Heile et al. / Anomalous e+e-and u +ta- events
203
4.4. Event misidentification correction using method I
We assume that only real ee, Or, eia, and hh events exist.
We define:
No (i])
-- the n u m b e r o f observed events o f type i, ],
Na(nm ) = the actual n u m b e r o f events o f type n, m,
Np (i])
= the predicted n u m b e r o f events o f the type i, ] derived from Pi-.h
and Na(nm),
where i,] = e, ia, h, x and n, m = e, ia, h.
We then m i n i m i z e
X 2 = ~ [(No(i])- Np(ij)]2/No(i])
i,]
(29)
with respect to Na(nm). For example, if only Na(ee), Na0a#) and Na(hh) are allowed
to be non-zero,
Np(eU) = 2Na(ee)Pe-ePe--, u + 2NaO#a)Pv-.ePu-, u + 2Na(hh)Ph-.eeh-. u .
(30)
If we assume that the only actual events allowed are ee's, Via's, and hh's, we find that
we cannot obtain a satisfactory m i n i m u m ×2. In fact the category o f observed events
that is the m o s t inconsistent with the predicted events are the eia's, with the eia's observed being consistently a b o u t 4 to 5 standard deviations above the e v ' s predicted.
This o f course agrees with the conclusions o f our previous papers on eia events [1 ].
Table 4
Number of events corrected for misidentification using method I, but not corrected for triggering
inefficiencies (electromagnetic background) or acceptances
Event type
e~
ee
~
hh
total
Ec.m. range
(GeV)
3.9-4.3
4.3-4.8
4.8-6.8
6.8-7.4
3.9-4.8
Data set
2
2
2
2
1
29*7
14±6
27*6
41,11
111
21,7
25± 7
42+-7
36+-7
124
76±11
58+- 10
62+-10
76,18
272
59+-13
77+- 11
70±11
111+-20
317
39+-8
26±7
24+-7
33+-i2
122
The errors are statistical. In this and aU following tables the event numbers are rounded off to the
nearest event to simplify the tables but calculations were carried out using an additional significant figure.
204
F.B. Helle et al. / Anomalous e +e-and ~ +~ - events
Therefore we see that we must expand our class of allowed actual events to include
ee's,/ap's, hh's, and e/a's. When this is done we find that we do get reasonable X2 and
that all ten classes of observed events agree with the predicted events. The results are
shown in table 4.
4.5. E v e n t misidentification correction using m e t h o d H
This method uses the same procedure as method I except that the allowed actual
event types are ee,/a/a, e/a, hh, eh and gh and we require Na(eh) = Na(/ah).
4.6. E v e n t misidentification correction using m e t h o d III
We define two 1 × 10 column matrices: D which gives the number of observed
events, and'A which gives the number of actual events. Specifically:
D =
No(ee)
~(ee) 1
/o(e.)
~(e/a)[
No(eh)
Na(eh)~
No(ex)
' Na(ex) I
No01.)
No(/ah)
No(~X)
No(hh)
No(hx)
A =
N0(xx)
N~0~)
N,0~h)
N~(hh)
Na(hx)
Na(xX).
(31 a)
Then D and A are related by a 10 X 10 matrix M:
D =MA,
(31b)
where, for example, the elements of M are given by
Mee_.,e. = 2Pe_+epe_.,. ,
Mee~ ,e = Pe2---,
e,
Me~eu =ee--+ee.-. +Pe-.e#--'e •
(32)
We then invert the matrix M to yield
A = M -1D.
(33)
F.B. Heile et aL /Anomalous e +e-and ~ +# - events
205
Table 5
Number of events corrected for misidentification using method I11, but not corrected for triggering
inefficiencies, electromagnetic background, or acceptance
Ec.m. range
(GeV)
3.9-4.3
4.3.-4.8
4.8-6.8
6.8-7.4
3.9-4.8
Data set
2
2
2
2
1
7±4
12±8
20 t 12
-4±5
19±8
40 ± 16
-9+-8
9 -+ 10
22+- 14
-5±2
16±13
-8±11
13 t 39
4±9
30-+11
49 ± 27
0-+ 11
19 ± 22
5± 17
-4±2
46±13
54±17
33 -+ 33
0±10
54±13
46 ± 26
2-+13
34 ± 22
10± 18
-7-+3
85±21
69±21
-31 +- 50
12±14
80±16
-23 ± 27
0±14
122 ± 42
3± 22
0±4
19-+7
29±9
21 ± 15
3±4
16±6
10 ± 12
7±5
16 ± 12
-2± 7
3±2
317
122
Event type
ee
eu
eh
ex
tz~
~uh
~x
hh
hx
xx
total
111
.
.
.
.
.
.
.
.
.
.
.
.
.
124
.
.
.
.
.
.
.
.
.
272
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
The errors are statistical.
Taking D from table 2 and calculating M from table 3, we find A for the five sets
of data, table 5. Since there is no constraint on the elements o f matrix A , negative
numbers m a y , and do, appear. A pleasing aspect o f this m e t h o d is that all values o f
Na(eX), N a ~ x ) , Na(hx), and Na(xX) are consistent with zero within their errors. This
is as it should be, because x is a designation for an observed-particle type, and an
actual-particle type can only be e, It or h. The consistency ofNa(eX), NaOaX), Na(hx)
and Na(xx) with zero means that our misidentification probabilities, Pi~u, are correct
within the statistical errors o f this analysis.
4. 7. Correction f o r inefficiencies
Before we can subtract the electromagnetic-processes background we must correct
our events for any detection inefficiencies. The hardware trigger requires that there be
two shower counters latched. F o r a m u o n track we measure a latching efficiency o f
94% whereas for electrons we assume the efficiency is 100%. In the software we
impose a time-of-flight cut which will t h r o w out 1% o f our tracks. The software trackfinding efficiency is 98%. And from a study o f very coil±near Bhabha and mu-pair
events with the m o m e n t u m o f each track very close to the beam energy, we conclude
that an electron track has an 8% chance o f having an extra shower c o u n t e r latching
but that a m u o n has only a 2.5% chance. Since we require that our events have no
extra shower counters latched, we must include this as an inefficiency. N o w then we
multiply all o f these together we find that we are 83% efficient for electrons and 83%
206
F.B. Heile et al. / Anomalous e+ e - a n d u +ta- events
efficient for muons. Thus on a per-event basis we are 69% efficient. This correction
applies to the data from all the methods. Next we need to know the backgrounds
from purely electrodynamic processes.
5. The background from purely electromagnetic processes
There are two different types of purely electromagnetic processes that can survive
our experimental cuts and mimic an anomalous dilepton event. An example of the
first type is
e+ + e - ~ e
++e-+7+7,
(34)
which we call a two-real-photon process since there are two photons in the final state.
An example of the second type is
e++e -oe
++e- +V++/a-,
(35)
which we call a two-virtual-photon process since there are two virtual photon lines in
the Feynman diagram. The cross section for each of these processes is integrated over
the following phase space for the two leptons that enter the detector (see subsects.
3.6 and 3.7).
P 1 > 0.65,
P2 > 0.65 GeV,
Icos 011 < 0 . 6 ,
Icos 02 I < 0.6,
m2m > 2 (GeV/c2) 2 ,
0coot > 20 ° .
(36)
In addition, cylindrical symmetry about the beam direction is assumed. The phase
space permitted for the additional leptons or photons will be discussed in the following subsections.
5.1.7~o-virtual-photon
processes
The diagrams for the two-virtual-photon process are shown in fig. 4 for the case of
e+e - ~ e+e-ju÷/a -. The evaluation of these diagrams requires a seven-dimensional
phase-space integration of a complicated matrix element. This was accomplished by
the use of a program written by Grammer and Kinoshito [6] which integrates the
exact matrix element over our phase space. The initial electron and positron were
required to not enter the detector i.e. Icos 01 > 0.6.
The results of these calculations are shown in table 6 for the case of ee or ~ final
states. The cross sections computed by the program are actually equal but radiative
corrections have been applied to the ee case. A study of the momentum spectrum of
the ee's led to an estimate of approximately a 10% correction per electron track to
account for the probability that an electron would radiate to below the 0.65 GeV
momentum cut.
F.B. Helle et al. / Anomalous e+e-and ~+~- events
e+
207
.e +
detected
particles
e
e
e+
_ e+
defected
particles
e
e
Fig. 4. F e y n m a n diagrams for the two-virtual-photon process e+e - ~ e+e-ta+u - .
This is the lowest-order purely electromagnetic process that could give e±/a+ events.
Our calculations and a calculation by Zipse [17] show that this cross section is negligible (less than a picobarn). This is also confirmed by the experimental data [1 ] since
one would expect an equal number of charge = +2 e/a events as charged = 0 e# events,
whereas the data shows almost no charge = -+2 eg events.
Table 6
Calculated purely electrorn'agnetic contributions to the observed e+e - and the tJ+g - cross sections
e+e -
Data
set
Ec.m.
range
(GeV)
Average
Ec.m.
(GeV)
e+e - (e+e - )
~ +~l (e+e - )
e+e-('r'r)
z+z-('rr)
2
2
2
2
1
3.9-4.3
4.3--4.8
4.8 - 6 . 8
6.8 - 7 . 4
3.9 - 4 . 8
4.1
4.4
6.2
7.2
4.5
1.5
1.9
4.4
5.8
2.0
1.9
2.4
5.4
7.2
2.5
3.2
3.6
4.4
4.3
3.6
0.25
0.30
0.36
0.35
0.30
The cross sections are in pb and are calculated for the kinematic cuts in eq. (35). The particles in
the parenthesis in the final state are not observed.
208
F.B. Helle e t al. / A n o m a l o u s e + e - a n d t~+g - e v e n t s
e+
e+
e
e
e (F.)
/e-
e
~e- (/z-)
Fig. 5. Some F e y n m a n diagrams for the two-real-photon processes e*e -
e+e-~%c+e - ~ ~+~-~.
5.2. Two-real-photon processes
Typical diagrams for the two-real-photon process are shown in fig. 5. Because of
the much larger number of diagrams in this case compared to the two-virtual-photon
case it is impractical to attempt an exact calculation. The approximation we used is
to make an exact calculation for one of the photons and a peaking approximation for
the other photon. The constraint that the missing mass squared be greater than 2.0
(GeV/c2) 2 ensures that the be some lower limit to the energy of the peaking photon
thus avoiding infrared problems.
First let us consider the case e÷e - ~ e + e - 7 7 . The program of Berends, Gastmans
and Gaemers [18] was used to calculate the exact cross section for e+e - ~ e + e - 7 .
With the help of Gaemers the program was modified so that the exact single-photon
cross section was multiplied by the following factor for the peaking photon:
2~
In
- 1
In Wmax
COmax ~Omin +
(37)
The sum is over the initial- and final-state leptons with Pi the momentum of the lepton. The beam energy is E and COmax, (,Omin are the maximum and minimum energies
of the peaking photon respectively. As we sum over each lepton, C.Omin is the minimum
energy that a photon could have and still produce a missing mass squared greater than
2.0 (GeV/c2) 2. For the two initial leptons we set (~max equal to the energy o f the
extra photon; for the two final leptons we use the minimum of either the extra pho-
209
F.B. Heile et al. / A nomalous e +e - a n d t~+U- events
ton e n e r g y or Pi - Pmin- A n d if at a n y t i m e 6Omin is g r e a t e r t h a n 6Omax, t h a t t e r m in
the s u m is set e q u a l t o zero. T h e results we o b t a i n e d are s h o w n in t a b l e 6.
6. Results a n d discussion
6.1. C o r r e c t e d n u m b e r s o f e v e n t s
Table 7 gives the n u m b e r s o f events c o r r e c t e d for m i s i d e n t i f i c a t i o n using m e t h o d I,
c o r r e c t e d for triggering inefficiencies, a n d c o r r e c t e d for the p u r e l y e l e c t r o d y n a m i c
b a c k g r o u n d s in t a b l e 5. T h e ee a n d e/a events are also c o r r e c t e d for e l e c t r o n losses due
to r a d i a t i o n b y the e l e c t r o n ; w h i c h result o n t h e average in t h e n u m b e r o f ee e v e n t s
b e i n g m u l t i p l i e d b y 1.23 a n d the n u m b e r o f e/~ e v e n t s b e i n g m u l t i p l i e d b y 1.11. T h e
n u m b e r o f e v e n t s a n d cross s e c t i o n s in table 7 are n o t c o r r e c t e d for the k i n e m a t i c
cuts:
Icos 0 1 1 < 0 . 6 ,
ICOS 021 < 0 . 6 ,
P t > 0.65 G e V / c ,
P2 > 0.65 G e V / c ,
0 c o # > 20 ° ,
m2m > 2 . 0 ( G e V / c ) 2 .
(37)
Table 7
Using method I, the corrected numbers of events Neta, Nee, N ~ , and Nhh; their ratios; and the
observed cross sections, Oe~, Oee, and alarm, in pb
Ec.m. range 3.9-4.3
(GeV)
4.3-4.8
4.8-6.8
6.8-7.4
3.9-4.8
All events
Data set
2
2
2
2
1
1,2
Luminosity
(pb - ! )
1.88
1.81
4.49
6.85
1.85
16.88
Neu
46±11
13 ± 10
35 ± 9
60±16
0.29 ± 0.22
0.76 -* 0.26
24.7 -* 5.6
7.1 ± 5.2
18.7 ± 4.8
34±10
33 ± 12
56 ± 10
52±17
0.96 ± 0.44
1.62 ± 0.57
18.9 ± 5.8
18.1 ± 6.4
30.7 -* 5.6
121±18
55 ± 18
64 ± 14
111±26
0.45 ± 0.16
0.53 ± 0.14
27.0 ± 4.1
12.3 ± 3.9
14.3 ± 3.2
95±21
52 -* 20
49 ± 16
162±30
0.55 ± 0.24
0.52 ± 0.20
13.8 ± 3.1
7.6 ± 2.9
7.2 ± 2.3
62±13
34 -* 12
29 ± 9
48±18
0.55 ± 0.22
0.47 -+ 0.18
33.7 ± 6.9
18.5 ± 6.4
15.7 -* 5.1
358-*34
187 ± 33
233 ± 27
433±49
0.52 ± 0.10
0.65 ± 0.10
Nee
Nt~~
Nhh
Nee/Nep"
N~JNet a
Oeu
Oee
%~t
The numbers and cross sections are corrected for the purely electromagnetic backgrounds in
table 6 and for misidentification losses and triggering efficiencies. They are not corrected for the
kinematic cuts in eq. (37). The errors are statistical.
F.B. Heile et al. / A n o m a l o u s e +e - a n d ~ +~ - events
210
Table 8
Using m e t h o d ii, the corrected n u m b e r s of events, and the ratios Nee/Net ~ and N~tz/Net ~
Ec.m. range
(GeV)
3.9-4.3
4.3-4.8
4.8-6.8
6.8-7.4
3.9-4.8
All events
Data set
2
2
2
2
1
1, 2
Neta
Nee
N/~
Nhh
Neh
24"-11
3-*7
25 -* 9
21 ± 11
39 ± 14
39 -* 14
0.12 ± 0.31
1.06 -* 0.63
84*-25
36±18
46 -* 15
30 -* 23
74 -* 36
74 -* 36
0.43 -* 0.24
0.55 ± 0.24
101-.24
64±19
50 -* 16
144 ± 45
1 ± 37
1 ± 37
0.64 -* 0.24
0.49 ± 0.19
46"-13
25±10
21 -* 8
17 -* 12
31 *- 16
31 -* 16
0.54 -* 0.27
0.46 ± 0.22
263-*40
146-.31
183 *- 27
213 ± 56
195 -* 59
195 -+ 59
0.56 -* 0.14
0.70 -* 0.15
Nub
Neo/Ne~
N~tJNe~
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
8-+12
18±11
41 ± 10
1 ± 17
50 ± 18
50-+ 18
4.9 ± 6.3
5.9 ± 8.5
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
The n u m b e r s are corrected for the purely electromagnetic background in table 6 and for misidentification losses and triggering efficiencies. They are not corrected for the kinematic cuts in eq.
(37). The errors are statistical.
We shall n o t c o r r e c t f o r t h e s e c u t s h e r e , b u t t o o r i e n t t h e r e a d e r w e n o t e t h a t f o r
e v e n t s c o m i n g f r o m r + r - d e c a y s t h e s e c u t s r e s u l t in a 15 t o 2 0 % a c c e p t a n c e .
T h e c r o s s s e c t i o n s in t a b l e 7 are g i v e n t o a l l o w t h e r e a d e r t o c o m p a r e t h e m d i r e c t l y
w i t h t h e p u r e l y e l e c t r o m a g n e t i c c o n t r i b u t i o n s in t a b l e 6; r e m e m b e r i n g t h a t t h e l a t t e r
c r o s s s e c t i o n s h a v e a l r e a d y b e e n s u b t r a c t e d t o y i e l d t h e c r o s s s e c t i o n s in t a b l e 7. In
f u t u r e t a b l e s , h o w e v e r , w e shall o n l y p r e s e n t t h e n u m b e r s o f e v e n t s , s i n c e t h a t is all
Table 9
Using m e t h o d III, the corrected n u m b e r s of events and their ratios
Ec.m. range
(GeV)
.
.
.
.
.
.
.
.
.
.
4.3-4.8
3.9-4.3
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
4.8-6.8
6.8 -7.4
3.9-4.8
All events
.
Data set
2
2
2
2
1
1,2
Ne~
Nee
N~t~
Nhh + N h x + N x x
Neh + Nex
N~h + N~x
20-+ 12
2±8
24 ± 12
38-*25
22-* 18
45 ± 27
0.12 -* 0.39
1.19 ± 0.93
- 1 1 ± 17
16 ± 24
38 -+ 16
29±41
25±58
72 -* 42
87±28
32 ± 23
52 ± 19
55±41
47~49
70 ± 41
0.37 i 0.29
0.60 ± 0.29
110± 34
66 ± 37
64 ± 23
183±69
-26±76
- 3 4 ± 43
0.60 ± 0.38
0.58 ± 0.27
4 6 ± 15
2 1 ± 12
19±9
2 5 ± 18
35±23
2 4 ± 18
0.46 ± 0.30
0.41 ± 0.24
2 5 2 ± 51
137±52
197-* 37
330±95
103± 111
177±80
0.54 ± 0.23
0.78 ± 0.22
Nee/Net a
N~u/Net a
The n u m b e r s are corrected for the purely electromagnetic backgrounds in table 6 and for misidentification losses and triggering efficiencies. They are not corrected for the kinematic cuts in eq. (37).
The errors are statistical.
F.B. Heile et al. / Anomalous e+e-and u+tz- events
211
we need to calculate ratios. Incidentally, the observed Oeg cross sections which appear
in table 7 are larger than those which have been published in our papers [1,2] because
the latter are not corrected for any losses or trigger inefficiencies. Also there are statistical differences because the latter cross sections are based on a larger data sample.
The corrected numbers of events using methods II and III are given in tables 8 and
9, respectively.
Looking at tables 7, 8 and 9, we conclude that irrespective of the method:
(i) anomalous ee and/aV events have been found in e+e - annihilations;
(ii) the observed cross sections are of the same order of magnitude as that of the
anomalous e~u events. This of course is what we expect from our explanation of the
e/a events being produced by the pair-production process e÷e - ~ r ÷ r - .
In comparing all event numbers in the tables we see that methods II and III give very
similar values for Neu, Nee, and N ~ . But method I (table 7) gives about 30% higher
values. This is because the setting ofNeh = N~h = 0 in method I redistributes these
events into the other categories.
6.2. Nee/Net ~ and Nuu/Ne~ ratios
Table 10 lists the Nee/Nel a and Nuv/Nev ratios from the three methods. Before
considering these ratios we discuss the systematic errors. Those systematic errors
which can equal or exceed the statistical errors have the following sources:
(a) the subtraction of backgrounds from misidentification of hadrons as e's or/a's
has systematic errors because of our empirical method for finding Ph--,e and Ph~u ;
(b) the correction for muon losses due to P ~ h and Pu~x has some uncertainties;
(c) the correction for electron losses due to Pe~h and to the loss of e's because
they radiate has uncertainties, particularly when the e momentum is near the 0.65
GeV/c cut;
(d) there are uncertainties in the calculation of the purely electromagnetic backgrounds, particularly in the calculation of e÷e - ~ e ÷ e - e ÷ e - and e+e - ~ e+e-TT.
Table I 1 gives the maximum systematic errors in the ratios.
Returning to table 10, we see that all the methods give the same ratios within
their statistical errors; therefore it fortunately doesn't matter what set of ratios we
use. We say fortunate because we have no sure way to know what method is correct.
Table 10
Ratios of corrected numbers of events
Method
Nee/N e~t
N ~JNet ~
I
II
II1
0.52 ---0.10
0.56 ± 0.14
0.54 ± 0.23
0.65 ± 0.10
0.70 ± 0.15
0.78 ± 0.22
The error is statistical.
212
F.B. Heile et al. / Anomalous e+e - and ~ +t~- events
Table 11
The maximum systematic errors are given
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Nee/Net~
.
.
N~/Ne~
Systematic error due to
background subtractions
50.07
-*0.09
Systematic error due to
~-Ioss correction
-*0.06
~0.11
Systematic error due to
e-loss correction
-*0.08
-~0.09
Systematic error due to
subtraction of purely
electromagnetic background
,-0.10
-0.15
±0.08
Total systematic errors
+(3.16
if combined in quadrature
-0.19
Value of ratio with statistical
error (one standard deviation)
from method ii
sO. 19
0.56 ± 0.14
0.70 ± 0.15
The relative signs indicate the correlation between the effect of the systematic errors on the two
ratios, except in the total error. For convenience we have also listed the ratio values and their
statistical error from method Ii.
However, for the r e m a i n i n g parts o f this p a p e r we shall use m e t h o d ll's values, on the
a r g u m e n t t h a t m e t h o d I is t o o restrictive a n d t h a t m e t h o d III gives the same results
as m e t h o d II, b u t w i t h larger errors.
6.3. Comparison with the heavy-lepton hypothesis
We use the e x p e r i m e n t a l values
Nee/Nez = 0 . 5 6 + 0 . 1 4 + o.16
--
-
0 . 1 9
)
N z J N e u = 0 . 7 0 ± 0.15 ± 0 . 1 9 .
(38)
Here the first error is one s t a n d a r d deviation statistical e r r o r a n d the s e c o n d e r r o r is
the m a x i m u m s y s t e m a t i c e r r o r (see table 11).
F r o m eq. ( 1 5 a ) we find t h a t for a s e q u e n t i a l l e p t o n or a n o r t h o l e p t o n :
Nee/Neu = 0 . 5 ,
Nt~u/Neu = 0 . 5 .
(39a)
F o r an e-related p a r a l e p t o n w i t h o u r k i n e m a t i c cuts (eqs. ( 3 7 ) ) eq. ( 1 5 b ) is slightly
F.B. Helle et al. / Anomalous e+e-and t~+t~- events
213
changed [19] and we obtain for V - A coupling and all left-handed neutrinos
Nee/Neu = 0.86,
Nuu/Neu = 0.29.
(39b)
Comparison o f eq. (39) with eq. (38) shows that our results are consistent with eq.
(39a) but.are inconsistent with eq. (39b). If we use zero systematic errors the probability of the values in eq. (38) fitting eq. (39b) is 6.3 × 1 0 - s ; if we use the maximum
systematic errors that probability reduces to 1.1 × 10 -2. Hence our third conclusion
is:
(iii) the r can be a sequential lepton or ortholepton. It cannot be an E-type paralepton with V - A coupling and all left-handed neutrinos from our data *.
For a/a-related paralepton, theory demands
Nee/Neu = 0.29,
Nuu/Neu = 0 . 8 6 .
(39c)
This is inconsistent with the values in eq. (38) but not as inconsistent as is the erelated paralepton hypothesis. However the r being a/a-related paralepton with normal
coupling is already ruled out by muon-neutrino experiments (subsect. 2.2).
6.4. Comparative properties o f the ee, pda and e/a events
Fig. 6 gives the r distribution (formerly called the p distribution [1,2]) of the
momenta, where
r-
p-
0.65
0 ~<r ~< 1 ,
(40)
Pmax - 0.65'
is a momentum scaling variable which allows us to combine data with different Ec.m.
values. These data are not corrected for purely electromagnetic backgrounds (sect. 5
and table 6), but they are corrected for hadronic backgrounds. Our limited statistics
and r-dependent systematic errors make it unprofitable for us to attempt to quantitatively correct the r distributions for the electromagnetic background bin by bin. To
make a rough comparison we fit the e/a distributions with the r curve expected for a
heavy lepton with mr = 1.9 GeV/c 2, mvr = 0.0, and V - A coupling. (The fit is obtained by adjusting the leptonic branching ratio.) The same curve multiplied by 0.5
is then drawn in the ee and/a/a distributions. We see that within statistics the ee's and
/a/a's are higher in every r bin, which is what we expect from the purely electromagnetic background which has not been subtracted. We conclude:
(iv) the total r distributions for the ee and/a/a events can contain the r distribution
expected from the r.
We expect that the purely electromagnetic processes ee ~ eeee and ee ~ ee/a/a will
* Rosen [20] has discussed the more general case in which a paralepton is not restricted to V - A
coupling and all left-handed neutrinos. In some of these more general cases our data does not
exclude the r - having the same lepton number as the e÷.
214
F.B. Heile et al. / A n o m a l o u s e + e - a n d i~+~ - events
I
3.0
1
-
2.5 ~
I
All
ee
I
Ec.m.
I
ekz
t
I
(0)
/
/~/z
1.5
,.o
÷ ÷
0
1
Ec.m. < 4.8 GeV
ee
ta
=
(b)
L e,,
2.5
2.0
t,x,,
riO
1.5
h
O
rr
1.0
taJ
0D
D 0.5
Z
0
Ec.m ~_4.8 GeV
2.0
(c)
~
1.5
~
LO
.~
0.5
~
0
0
0.5
0
0.5
0
0.5
I.O
r
Fig. 6. The r distributions for ee, eu and ~,u events for: (a) all Ec.m., (b) Ec.m. < 4.8 GeV, (c)
/:'c~m. < 4.8 GeV (c) Ec.m. :~ 4.8 GeV. To facilitate comparisons the numbers of events in each
energy range are normalized so that the area under the e/~ data curve is 1.0. The distributions are
corrected for hadronic background, but not for the background from the purely electromagnetic
processes: ee ~ eeee, eet~u, ee'r3,, ~u~'r. See the text for an explanation of the curves.
F.B. Heile et ak / Anomalous e+e-and ta+ta- events
215
c o n t r i b u t e a p e a k in t h e r d i s t r i b u t i o n as r ~ 0. We see s u c h a p e a k c l e a r l y in all t h e
d i s t r i b u t i o n s , in t h e Ec.m. ~ 4 . 8 ee d i s t r i b u t i o n s ; b u t n o t in t h e Ee.m. < 4 . 8 ee
d i s t r i b u t i o n . We b e l i e v e this a b s e n c e o f a p e a k in t h e last case is d u e t o i n s u f f i c i e n t
4.0
I
I
I
I
Ec.m.<4.8 GeV
'(a) I!
5.5
ee
e~
~;" I~'
Ec.m. __.4.8 GeV
(b)
5.0
2.5
~" 2.0
w
1.5
1.0
4o!
0.5
0
3.5
ee
I
~z/z
e/~
3.0
2.5
U3
I-->
w
2.0
1.5
1.0
0.5
0
]j
0
-I
0
-I
0
COSOcoII
Fig. 7. The cos 0ooll distributions for ee, et~ and #ta events for: (a) Ec.m. < 4.8 GeV, (b) Ec.m.
4.8 GeV. To facilitate comparisons the numbers of events in each energy range are normalized so
that the area under the eta data curve is 1.0. The distributions are not corrected for the purely
electromagnetic processes: ee ~ eeee, eetata, ee3"r and tata~r'r. See the text for an explanation of
the stepped lines.
216
b:B. Helle et al. / A n o m a l o u s e + e - a n d t~+~ - events
correction for e losses near the 0.65 GeV/c momentum cutoff. The relevant systematic error in table 11 is large enough to allow for this uncorrected loss; but we have
not adjusted the e-loss correction to give such a peak because that would beg the question.
Fig. 7 gives the cos 0con distributions [1,2] where
COS 0coil = -- (191 " P 2 ) / ( I p l l [p2I) •
(41)
Note that when the particles are moving in exactly opposite directions, Pl = - P 2 ,
0con = 0 and cos 0coil = + 1. As in the r-distribution case we do not attempt to correct for the electromagnetic backgrounds. The stepped line is a fit to the e~u cos 0coil
distribution for a heavy lepton with mr = 1.9 GeV/c 2, mvr = 0.0 and V - A coupling.
The stepped lines in the ee and/4u distributions are obtained by multiplying the,e/a
line by 0.5. We conclude:
(v) the ee and/l/a cos 0coll distributions can contain the cos 0coil distribution
expected from the 7. The excess events in the cos 0coil > 0.6 bins are what is expected
from the electromagnetic backgrounds ee ~ eeee, ee/a/a, eeT"r,/a/173,.
6.5. Conclusions
Conclusions ( i ) - ( v ) taken together say that all the data which we have on anomalous ee and/a/l events is consistent with the r being a mass ~1800 M e V / c 2 charged
lepton; and it can be either a sequential lepton or an ortholepton.
We are very grateful to K.J.F. Gaemers for his help with the calculations of the
electromagnetic backgrounds. He is writing a separate paper on these calculations.
We are also very grateful to P. Lepage for his help with these calculations.
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