Observation of anomalous production of muon pairs in e+e− annihilation into four-lepton final states

Volume 244, number 3,4

PHYSICS LETTERS B

26 July 1990

Observation of anomalous production of muon pairs in e + e - annihilation into four-lepton final states AMY Collaboration Y.H. Ho a, y. Kurihara b, T. Omori b, p. Auchincloss a, D. Blanis a, A. Bodek ~, H. Budd ~, M. Dickson a, S. Eno a, C.A. Fry a,b, H. Harada ~, B.J. Kim ~, Y.K. Kim a, T. Kumita a, T. Mori a, S.L. Olsen a,c, N.M. Shaw a, A. Sill ~, E.H. Thorndike ~, K. Ueno a, C. Velissaris ~, G. Watts ~, H.W. Zheng ~, K. Abe b, y . Fujii b, y. Higashi b, S.K. Kim b, A. Maki b, T. Nozaki b, H. Sagawa b, y. Sakai b, y. Sugimoto b, y . Takaiwa b, S. Terada b, R. Walker b,a, R. Imlay d, P. Kirk d, j. Lim d, R.R. McNeil d, W. Metcalf a, S.S. Myung d, C.P. Cheng e, p. Gu e, j. Li e, Y.K. Li e, M.H. Ye e, Y.C. Zhu ~, A. Abashian g, K. Gotow g, K.P. Hu g, E.H. Low g, M.E. Mattson g, L. Piilonen ~, K.L. Sterner g, S. Lusin f C. Rosenfeld f, A.T.M. Wang f, S. Wilson f, M. Frautschi h, H. Kagan h, R. Kass h, C.G. Trahern h, R.E. Breedon i,b, G.N. Kim i.b, Winston Ko i, R.L. Lander i, K. Maeshima ~, R.L. Malchow i, J.R. Smith ~, D. Stuart ~, F. Kajino J, D. Perticone k, R. Poling k, T. Thomas k, y. Ishi ~, K. Miyano ~, H. Miyata ~, T. Sasaki ~, Y. Yamashita m, A. Bacala n,o, j. Liu n, I.H. Park n, F. Sannes ", S. Schnetzer n, R. Stone n, j. Vinson n, H. Ichinose P, S. Kobayashi P, A. Murakami P, J.S. Kang q, H.J. Kim q, M.H. Lee q, D.H. Han r, E.J. Kim r, D. Son r, T. Kojima s, S. Matsumoto s, R. Tanaka s, y . Yamagishi s, T. Yasuda ~, T. Ishizuka t and K. Ohta t a b c d e f g h

University of Rochester, N Y 14627, USA KEK, National Laboratory for High Energy Physics, lbaraki 305, Japan Tsukuba University, Ibaraki 305, Japan Louisiana State University, Baton Rouge, LA 70803, USA Institute of High Energy Physics, Beijing 100039, PR China University of South Carolina, Columbia, SC 29208, USA Virginia Polytechnic Institute andState University, Blacksburg, VA 24061, USA Ohio State University, Colombus, OH 43210, USA University of California, Davis, CA 95616, USA J Konan University, Kobe 658, Japan k University of Minnesota, Minneapolis, M N 55455, USA Niigata University, Niigata 950-21, Japan m Nihon Dental College, Niigata 951, Japan " Rutgers University, Piscataway, NJ 08854, USA o University of the Philippines, Quezon City, 3004, Philippines P Saga University, Saga 840, Japan q Korea University, Seoul 136-701, ROK r KyungpookNational University, Taegu 702-701, ROK Chuo University, Tokyo 112, Japan t Saitama University, Urawa 338, Japan

Received 26 February 1990

We report results of a study of four-lepton final states produced in e+e - collisions at center-of-mass energies from 50 to 61.4 GeV using the AMY detector at the TRISTAN collider. For the cases where two or three charged tracks are produced at large angles relative to the beam direction, the cross sections agree with QED. However, we observe an excess of e+e---,e+e-la+~t events with four tracks at wide angles and with dimuon mass less than 1.0 GeV/c 2. 0370-2693/90/$ 03.50 © 1990 - Elsevier Science Publishers B.V. ( North-Holland )

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F o r discussion and analysis we partition the e + e - ~ e + e - ~ + ~ - events according to observed charged topology into untagged, single-tag, and double-tag subsamples. F o r untagged kinematics, both o f the final e r a n d e - are unobserved in the detector because they emerge at a small angle relative to the b e a m axis where detector coverage is incomplete. If one or both o f the final electrons emerge at an angle large enough for detection, the event is respectively a single-tag or double-tag event. The ~+ and ~ - are m e a s u r e d in all cases. This subdivision by topology is convenient for d a t a analysis and, m o r e importantly, reflects the radically different relative contributions o f the groups o f F e y n m a n graphs to the different kinematic regimes. Table 1 shows these relative contributions, excluding interference, for the kinematic cuts a d o p t e d for our analysis. F o r both e + e - e + e - and e+e-~t+~t - final states, we obtain resuits for the untagged and single-tag cases that are consistent with Q E D predictions. The double-tag e + e - e + e - rate is likewise consistent. F o r the doubletag e+e-tx+~t - process, however, the Q E D expectation is 1.9 events in our data, and we observe seven. If this discrepancy is statistical, the probability is 0.34%. In five o f the seven events the invariant mass o f the m u o n pair is less than 1.0 G e V / c 2. We would not detect a similar excess in the e + e - e + e - reaction because we suppress the radiative Bhabha background by excluding events with e r e - pairs o f low invariant mass. A detailed description of the A M Y detector is given in ref. [2 ]. In brief, the m o m e n t a o f charged particles are d e t e r m i n e d from their curvature in a 3.0 T magnetic field. The trajectories are m e a s u r e d in a strawtube vertex chamber and an open-cell cylindrical drift

In this letter we present m e a s u r e d p r o d u c t i o n rates for the e + e - ~ e + e - e r e - a n d e r e - ~ e + e - ~ r l . t processes and c o m p a r e t h e m with the p r e d i c t i o n o f q u a n t u m electrodynamics ( Q E D ) . The d a t a sample, corresponding to an integrated luminosity o f 33.8 p b - l at center-of-mass energies from 50 to 61.4 GeV, was o b t a i n e d with the A M Y detector at the TRIST A N e+e - collider o f the Japanese N a t i o n a l Laboratory for High Energy Physics ( K E K ) . The lowest o r d e r F e y n m a n diagrams that contribute to these processes can be classified into four groups: multiperipheral, bremsstrahlung, annihilation, and conversion as shown in fig. 1. The Q E D expectation is that these d i a g r a m s a n d their radiative corrections should account for the observed cross sections to high precision. Previous studies o f the processes e r e ---, e r e - ~ + £ - ( ~ = e , or ~t) at the lower energies o f the PEP and P E T R A colliders have shown no discrepancies with Q E D [ 1 ]. + e

~

r

e+ r e+

l-e-

e(a)

(c)

Multiperipheral

Annihilation

I

e(b)

e-

Bremsstrahlung

(d)

26 July 1990

Conversion

Fig. 1. The four classes of lowest-order Feynman graphs for the reaction e+e--~e+e-~+~-: (a) multiperipheral, (b) bremmstrahlung, (c) annihilation, and (d) conversion.

Table 1 RelatiVe contribution (in percent) to the cross sections for the four-lepton processes under various experimental tagging conditions (by requiring the number of visible tracks above 20 ° ). The interference between the different Feynman groups is not included. Contribution (%)

untagged (2 tracks) single-tag (3 tracks) double-tag (4 tracks)

574

multi-peripheral

bremsstrahlung

annihilation

conversion

~ 100 ~ 83 ~ 10

~ 0 ~17 ~80

~0 ~0 ~4

~0 ~0 ~6

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chamber (CDC). A cylindrical electromagnetic calorimeter (SHC), also within the magnetic field volume, covers the angular range Icos01 <0.743, and endcap calorimeters cover the angular ranges 0.777 < l cos 01 < 0.899 (RSC) and 0.899 < l c o s 01 < 0.966 (PTC). The number of Bhabha events (e+e ---, e+e - ) observed in the PTC, appropriately scaled, is our measure of integrated luminosity. The SHC, RSC, and PTC are the principal tools for electron identification. To qualify as an electron in the untagged sample a track must have an SHC energy E and a CDC momentum p such that 0.7 2.0 GeV this criterion is 91% efficient. For the single and doubletag samples the electron criteria are less restrictive: E/p> 0.5 or E > 5.0 GeV where E may be measured in the PTC or RSC as well as the SHC. For p > 1.0 GeV/c these criteria are 98% efficient. The probability that a charged pion is misidentified as an electron is about 13% at 1.0 GeV/c and drops to 0.2% at 5 GeV/c. We identify tracks measured in the CDC as muons when they penetrate the SHC and the iron flux return yoke, a total of about nine nuclear interaction lengths at 90 ° . Four layers of planar drift chambers at the outer surface of the yoke measure the exit location of penetrating tracks, and an adjacent layer of scintillation counters measures the transit time relative to beam-crossing time. These detector elements cover the solid angle Icos 01 <0.74. To suppress contamination from cosmic rays we require the scintillator time to be consistent with a track produced at the beam crossing. For muons with momentum above 3.0 GeV/c and within the fiducial cuts of the muon detection system, the muon identification efficiency is about 83%. In hadronic events, misidentification of charged pions and kaons as muons occurs at the respective rates of -~ 1.3%/p(GeV/c) and = 6%/p, primarily as a result of decay-in-flight. For the sample of untagged events, muons are required to have p > 2.0 GeV/c. For the single and double-tag samples the corresponding cut is p > 2.5 GeV/c. In the case that an event has one muon identified by penetration through the yoke (positive identification), minimum energy deposition in a calorimeter, i.e. El p < 0.5, is sufficient to confirm that a second track is also a muon. In the selection of single and double-tag events these tracks may have momentum as low as

26 July 1990

1.0 GeV/c, i.e., well below the cut used for positive identification. Potentially serious backgrounds arise from the processes e+e - --.e+e-7 and e+e - --. ~t+la-7 followed by pair conversion of the 7 in the beam pipe. We suppress these events by the requirement that the invariant mass of any e+e - pair exceeds 1.0 GeV/c 2. We forego an analogous cut on the invariant mass of muon pairs. It would by superfluous because less than 10 - 4 of "J' conversions in the beam pipe produce a ~t+~t- pair. The contamination expected from this process is much less than one event in any of our three topological samples. Previous analysis of four-lepton final states have treated the muons and the electrons symmetrically in this regard [ 1 ]. The selection criteria for the untagged event samples are as follows. The event must have exactly two oppositely charged tracks each with p > 2.0 GeV/c. At least one of these must be positively identified as an electron or muon. If exactly one track is positively identified as a muon, the other track must have El p < 0.5. Events with back-to-back tracks are rejected by the requirements that the acollinearity angle exceeds 10 °. This requirement suppresses contamination from radiative Bhabha events, e+e - -+x+x-, and cosmic rays. Finally we require that the missing energy Emiss exceeds the net missing momentum IPmiss I by more than x//s/2 for the e+e-e÷e - final state and by more than 0.8x/s/2 for the e+e-kt+lx- final state. This criterion suppresses contamination from e+e---,~+~- 7 where the 7 is unobserved, in which case Emiss = [Pmissl. We observe 651 examples of e+e - - , e + e - e + e -, and the expected contamination is 14.7 from tau pairs and 4.0 from e+e-7 final states. We observe 587 examples of untagged e+e ---, e+e-la+la-, and the contamination expected in this sample is 11.7 events, all from tau pairs. To qualify for the single-tag sample, events must have at least one positively identified track in the solid angle Icos01 <0.707 with momentum p~>2.5 GeV/ c. Two additional tracks must have Icos 01 ~<0.906, p>~ 1.0 GeV/c, and satisfy the criteria for electron or muon identification. In addition the single-tag events pass a 1-C kinematic fit assuming one missing particle with the fitted direction of the missing particle

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within 25 ° of the beam axis [ 3 ] ~. Events in the double-tag sample have at least one positively identified e or ~t in the solid angle Icos/91 ~<0.707 with m o m e n t u m p > 2.5 GeV/c. A second track must be an electron, be in the solid angle Icos01 ~<0.707, a n d have m o m e n t u m p > 1.0 GeV/c. A third track must have Icos 01 ~<0.906 a n d satisfy electron or m u o n identification criteria. The fourth track need only have Icos01 ~<0.906 and p>~0.3 GeV/c. The double-tag events pass a 4-C kinematic fit applied to the four observed charged tracks and assuming no missing particles in the final state [ 3 ] ~. Finally we scanned graphic reconstructions of the surviving events. As a result we rejected twelve single-tag and four doubletag candidates, all to them because the event reconstruction software had produced two tracks from the hits left by a single particle. The n u m b e r of events observed were 15 and 1 for the e + e - e + e - single and double-tag samples a n d 13 and 7 for the respective e + e - l a + t a - samples. One event in the double-tag e + e - ~t+ ~t- sample that passes all of the requirements contains a 5.1 GeV photon that is 15 ° from the e track ~2. We interpret this photon as final-state radiation from the electron. These events have a rather distinct topology and are highly constrained; the ex-

al The cuts on the Z2 of the fit were adjusted so that (70-90)% of simulated single and double-tag events would be retained. The ~2 of a typical simulated background event is at least an order of magnitude larger than the cuts. ~2 This is event number 7 in table 3. The 5.1 GeV photon is near the e- track. This track's measured momentum of 2 I. l GeV/ c is boosted to 27.4 GeV/c by the fitting program.

26 July 1990

pected c o n t a m i n a t i o n in these samples is listed in table 2. For both the single and double-tag cases it is less than one event. To obtain the predictions of QED for these fourlepton processes, we ran several i n d e p e n d e n t Monte Carlo event generators. Two of these, both by Berends, Daverveldt, and Kleiss ( B D K ) , use the same general methods but are tailored for the single-tag and double-tag kinematics [ 4 ] ~3. The B D K codes incorporate all four groups of F e y n m a n graphs a n d allow fully for their interference. The code for double-tag kinematics also incorporates Z exchange in some of the graphs. The generator by Vermaseren incorporates only the multiperipheral and bremsstrahlung graphs [ 6 ]. One generator by K u r o d a uses only the multiperipheral and bremsstrahlung graphs [7]. A second generator by Kuroda, which incorporates only the conversion and a n n i h i l a t i o n diagrams, supplements the Vermaseren calculation for the double-tag kinematics [ 8 ]. The cross sections we obtain for the groups of F e y n m a n graphs taken separately are consistent a m o n g the various generators. For the doubletag kinematics, the sum of results from the K u r o d a and Vermaseren codes, which does not include important interference terms, is greater than the B D K result. In the case of e + e - p . + B - events, the difference is 15%, a n d the net c o n t r i b u t i o n of all the interference terms between the groups of graphs is - 15%. We extract events from the B D K generator, enter these in a simulation code for our detector, and use ~3 Thecode forsingle.tage+e-~t+~t- events was discussedin ref. [ 5 ]; the code for the double-tag events was obtained from J. Hilgart at CERN.

Table 2 Numbers of events observed in AMY and the corresponding results from QED event generators with integrated luminosity of 33.8 pb- ~. For single and double-tag events, the cross sections are calculated at x/s= 56 GeV. The BDK calculation includes all four groups of Feynman graphs and their mutual interference, which is destructive for the double-tag events. The Vermaserenand Kuroda calculations only include the multiperipheral and bremsstrahlung graphs.

untagged single-tag double-tag

576

Event type

Observed

e÷e-e+e e+e-la+l.te+e-e+e e+e-~t+kte+e-e÷e e÷e-p.+ B-

651 587 15 13 1 7

BDK

15.8 _+0.3 1.36_+0.04 1.93 _+0.02

Vermaseren

14.7 +0.7 16.0 _+0.2 1.40_+0.04 1.91 _+0.03

Kuroda

Estimated background

680_+22 635_+21

18.7 11.7 <0.9 <0.5 ~0 ~0

Volume 244, number 3,4

0

> r~ 3 ~

PHYSICS LETTERS B

26 July 1990

a) U n t a g g e d e e e e S a m p l e

b) U n t a g g e d ee/z/z S a m p l e

: ....

....

I ....

i ....

i ....

I ....

i ....

i ....

I ....

I ....

102

101

r~

I00 z

i0-I

,

,I,,,,I,,,,I

5

0

....

10

I,,,,

15

I t

20

0

5

10

Mee(GeV/e s)

15

20

25

M~(GeV/J)

Fig. 2. (a) dN/dM~ for the untagged e+e---,e+e---,e+e-e+e -, and (b) dN/dM,~ for the untagged e+e-~e+e-~t+~t- reactions. The curves are the QED predictions for the selections cuts described in the text. a

Single-tag eeee Sample

'"

i . . . . . . . .

b) S i n g l e - t a g ee/z/.z S a m p l e i

I ....

i

i

i

i

i

t

I

i

F

i

0

4

3

z Q)

Z 0

,,

0

i,

I,,,

I0

20 30 M i n i m u m Mo~(GeV/c z)

i

0

i0

20

30

40

M~(GeV/c ~)

Fig. 3. (a) dN/dM~for the single-tag e4-e- --,e4-e-e+e-, and (b) dN/dM~,for the single-tag e 4- e- ~ e 4- e-I~ 4- i1_ reactions. The curve are the QED predictions for the selection cuts described in the text. the s i m u l a t i o n results to correct for d e t e c t o r accept a n c e a n d efficiency ~4. T h e n u m b e r s o f e v e n t s w h i c h *~ In the double-tag e+e-lx+~t - case, for example, we generated 400 000 events with 0>/20 ° for all four tracks. Of these, we simulated the 9951 events that had all tracks with p>_-0.3 GeV/ c, Me+c- >/0.5 GeV/c 2, and at least one ~t directed at the ~t identification system (0/> 43 ° ). Of these, 3435 pass all of the selection criteria.

the Q E D codes p r e d i c t for o u r i n t e g r a t e d l u m i n o s i t y are listed t o g e t h e r w i t h o u r d a t a in table 2. In figs. 2a and 2b we show the distributions o f ~ + ~ i n v a r i a n t m a s s for the u n t a g g e d samples. T h e c u r v e s in these figures are the d i s t r i b u t i o n s p r o d u c e d f r o m the Q E D e v e n t g e n e r a t o r ( K u r o d a ) a n d are in g o o d a g r e e m e n t w i t h the o b s e r v a t i o n s . In figs. 3 a n d 4 we p r e s e n t the c o r r e s p o n d i n g i n v a r i a n t m a s s d i s t r i b u 577

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(ions for the single-tag a n d double-tag samples. F o r the single-tag e + e - e + e - final states only the smallest e+e - invariant mass in each event is included. We observed just one double-tag e + e - e + e - event, and its m i n i m u m e÷e - invariant mass is 1.83 G e V / c 2. The data are in good agreement with Q E D predictions, shown as solid curves, except for the doubletag e + e - p + ~ t - sample, fig. 4. In this case there is a significant excess o f events at small ~t+~t- invariant mass. If, following the protocol o f previous analyses [ 1 ], we consider only events with kt+~t - opening angle greater than 10 ° or M o o > 1.0 G e V / c 2, then we respectively retain one or two events, which is consistent with the corresponding Q E D prediction o f 1.2 events. In our experiment, however, we see no justification for placing a lower limit on Moo. The e + e - n + n - final state, like e+e-~t+p. - and unlike e + e - e + e - , is not susceptible to background from c o n v e r t e d 7's. We e x a m i n e d this channel to see if it exhibits an excess o f double-tag low mass n ÷ n - events like the double-tag e+e-~t+~t - events. Since in the double-tag sample, the bremsstrahlung graph is expected to d o m i n a t e , the ratio o f rates for p r o d u c t i o n o f n + n - a n d p.+p- can be estimated reliably using the vector d o m i n a n c e m o d e l [9]. Using tabulated data [ 10 ] on the reaction e + e - - , n + n - for center-ofmass energies below 1 GeV, where p (770) resonance d o m i n a t e s the cross section, we estimate the exDouble-tag

d"

ee/z/z S a m p l e

3.0

0 (9

0

(9 >

2.5 2.0 1.5 1.0 0.5 0.0 0.1

0.5

1

5

10

M ~ ( G e V / c 2) Fig. 4. dN/dM~,, for the double-tag e+e ~e+e-la+p_ - reaction. The curve is the QED prediction for the selection cuts described in the text.

578

26 July 1990

pected n u m b e r o f e + e - n + n - events in our d a t a with M ~ < 1.0 G e V / c 2 a n d kinematics similar to the double-tag e + e - p + p - events to be 1.0. We use the same selection criteria for e + e - n + n - final states as for double-tag e+e-ja+~t - events except that in lieu o f a positively identified m u o n we require a positively identified hadron, i.e., a track in the solid angle ]cos 01 < 0.707 with p > 2.5 G e V / c , E / p < 0.5, and no associated hits in the m u o n detection system. W i t h these criteria, the acceptance and efficiency for the e + e - n + n - and e + e - ~ t + g - final states are virtually the same. No events pass the e + e - n + n - selection criteria. The absence o f any observed e + e - n + n - events and the good muon identification properties o f the A M Y detector rules out the possibility that the excess e+e-rt+~t - events are in fact cases o f e + e - - e + e - + ( h a d r o n s ) where h a d r o n s have been misidentified as muons. If the source o f the excess events were the reaction e+e - - - , e + e - q - - , e + e - p+ ~ - 7, we would expect to see a large rate for e + e - - e + e - q - e + e - 7 7 which is ~ 103 times more probable. O u r observed rate for e+e-Y7 final states is in good agreement with Q E D expectations for d o u b l y - r a d i a t i v e Bhabha scattering and shows no evidence for e + e - q final states [ 11 ]. The same logic rules out e + e - - - , e + e - q ' - , e + e - r t + g - 7 , as a possible explanation o f the excess events. Details o f the kinematics o f the seven e + e - g + g events are given in table 3. F o r four o f these events Moo is consistent with 300 M e V / c 2. The events are dispersed a m o n g the different center-of-mass energies as indicated in the table. We have constructed the distributions o f IPo+ + P o - I / E b . . . . and the angle between the vectorpo+ + P o - and the direction o f the nearest electron. F o r neither distribution is there a clear discrepancy in shape with the Q E D predictions. We have, however, noticed one peculiarity in this channel besides the excess n u m b e r o f events. The distribution o f cos 0oo, where 0 , , is the polar angle o f Po + + P o - , heavily favors the direction o f the incident e +, ( ( c o s 0oo) = - 0.46 + 0.25 ), whereas the expectation from Q E D is that this distribution is symmetric about cos 0oo = 0. In summary, using a 33.8 p b - ] sample o f e + e - collisions, spanning center-of-mass energies from 50 to 61.4 GeV, we have studied properties o f the reactions e + e - - - , e + e - ~ + ~ - , where ~+~- can be either

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Table 3 Fitted values of the kinematic variables for the double-tag e +e-Ix + ~t- events. , ~ and p are in units of GeV, and 0 and q~are in degrees. #

x/s[GeV]

p[GeV]

1 2 3 4 5 6 7

50.0 52.0 56.0 56.0 57.0 60.0 60.8

1 2 3 4 5 6 7

~t

Ix+

e-

e +

0[deg]

0[deg]

25.0 25.5 27.1 27.9 26.8 25.9 27.4

52.8 69.0 48.2 56.3 60.7 97.4 82.4

287.5 194.8 208.3 120.9 23.2 346.6 110.9

50.0 52.0 56.0 56.0 57.0 60.0 60.8

13.7 6.9 14.3 1.2 18.5 25.3 25.4

123.1 137.0 144.3 145.8 104.5 82.6 85.6

105.7 10.7 3.8 312.2 186.6 169.4 278.9

1 2 3 4 5 6 7

50.0 52.0 56.0 56.0 57.0 60.0 60.8

4.7 12.0 9.9 3.0 3.1 4.6 1.9

132.2 104.0 116.8 125.8 134.1 87.8 133.7

109.9 15.7 43.4 293.2 242.9 31.1 359.0

1 2 3 4 5 6 7

50.0 52.0 56.0 56.0 57.0 60.0 60.8

6.6 7.6 4.6 23.8 8.7 4.3 6.1

132.1 99.1 115.0 122.3 137.3 91.3 133.9

110.0 15.9 44.6 301.5 242.0 193.4 355.4

e + e - o r ~t+~t - . A n o r d e r 0/4 Q E D calculations is m g o o d a g r e e m e n t w i t h the results for the case w h e r e o n l y t w o or three final state particles are o b s e r v e d in the detector. In the case w h e r e all final state particles are o b s e r v e d at large o p e n i n g angle, we see an excess o f e + e - ~ e + e - ~ t + ~ t - events. T h e e v e n t s cluster at small ~t+la - i n v a r i a n t mass, n e a r M , , _~ 300 M e V / c 2, a n d t h e y are a s y m m e t r i c in the d i s t r i b u t i o n o f the polar angle o f the ~t+ la-pair. T h e statistical p r o b a b i l i t y o f o b s e r v i n g such an excess is a f r a c t i o n o f a percent. A m o r e d e t a i l e d d e s c r i p t i o n o f this m e a s u r e m e n t is g i v e n in ref. [ 12 ]. We wish to t h a n k R. Kleiss, M. K u r o d a , S. K a w a b a t a , a n d J. V e r m a s e r e n for useful discussions a n d for assistance w i t h calculating the Q E D cross

26 July 1990

sections. We t h a n k the T R I S T A N s t a f f for the excellent o p e r a t i o n o f the storage ring. In a d d i t i o n we ack n o w l e d g e the strong s u p p o r t a n d e n t h u s i a s t i c assist a n c e p r o v i d e d by the staffs o f o u r h o m e institutions. T h i s w o r k has b e e n s u p p o r t e d by the J a p a n M i n i s t r y o f Educations, Science a n d Culture ( M o n b u s h o ) and Society for the P r o m o t i o n o f Science, the U S D e p a r t m e n t o f Energy a n d N a t i o n a l Science F o u n d a t i o n , the K o r e a n Science and E n g i n e e r i n g F o u n d a t i o n a n d M i n i s t r y o f E d u c a t i o n , a n d the A c a d e m i a Sinica o f the P e o p l e ' s R e p u b l i c o f China.

References [ 1] A. Petradza, Ph.D. thesis, University of Michigan (1989), unpublished; CELLO Collab., H.-J. Behrend et al., Z. Phys. C 43 (1989) 1; JADE Collab., W. Barrel et al., Z. Phys. C 30 (1986) 545; MARK-J Collab., B. Adeva et al., Phys. Rev. D 38 (1988) 2665; PLUTO Collab., Ch. Berger et al., Z. Phys. C 27 (1985) 249. [ 2 ] AMY Collab., T. Kumita et al., Measurement of R for e+eannihilation at TRISTAN, KEK preprint 89-188, submitted to Phys. Rev. D; see also: AMY Collab., H. Sagawa et al., Phys. Rev. Len. 60 (1988) 93; AMY Collab., S. Igarashi et al., Phys. Rev. Lett. 60 (1988) 2359. [ 3 ] O.I. Dahl et al., SQUAW, LBL Group-A note P- 126 ( 1968 ), unpublished. [4] F.A. Berends, P.H. Daverveldt and R. Kleiss, Phys. Len. B 148 (1984) 489. [ 5 ] F.A. Berends, P.H. Daverveldt and R. Kleiss, Comput. Phys. Commun. 40 (1986) 309. [ 6 ] J.A.M. Vermaseren, in: Proc. Intern. Workshop on photonphoton collisions (Amiens, 1980), eds. G. Cochard and P. Kessler (Springer, Berlin); Nucl. Phys. B 229 (1983) 347. [7] M. Kuroda, Meiji Gakuin University (Tokyo) Res. J. 424 (1988) 27. [ 8 ] M. Kuroda, Meiji Gakuin University preprint MGU-DP 7 ( 1988 ), unpublished. [ 9 ] G.J. Gounaries and J.J. Sakurai, Phys. Rev. Lett. 41 ( 1968 ) 244. [ 10 ] J. Lefrancois, in: Proc. Intern. Symp. on Electron and photon interactions at high energies, 1971 (Laboratory for Nuclear Science, Cornell, Ithaca, NY, 1971 ); see also G.J. Feldman and M.L. Perl, Phys. Rep. 19 (1975) 233. [ l l ] A M Y Collab., S.K. Kim et al., Phys. Lett. B 223 (1989) 476. [ 12] Y.H. Ho, Ph.D. thesis, University of Rochester (1990), unpublished. 579