SEARCH FOR A NEARLY DEGENERATE LEPTON DOUBLET (L-,L 0 )t

We have searched for a heavy charged lepton with an associated neutrino of nearly the same mass in e+e- annihilation data taken with the Mark II detector at a center of-mass energy of 29 GeV. In order to suppress contamination from conventional two photon reactions, this analysis uses a novel, radiative-tagging technique. Requiring the presence of an isolated, energetic photon allows a search for lepton doublets with mass splittings smaller than that previously accessible to experiment. No evidence for such a new lepton doublet has been found, enabling limits to be placed on allowed mass combinations. Mass splittings as low as 250-400 MeV /c 2 are excluded for charged lepton masses between 500 MeV fc 2 and 10 GeV /c 2•

an isolated, energetic photon as an indication of electromagnetic radiation from the initial-state electron or positron( for very heavy leptons, final state radiation is negligible). Demanding the isolated photon be produced at large angles with respect to the beam axis suppresses the two-photon background far more than it does the heavy lepton signal.
The large suppression can be understood from the following argument. Twophoton cross sections are large because the two virtual photons typically have an invariant mass-squared very near zero, making. them "quasi-real". The emission of an energetic photon from an incoming or outgoing electron, however, ensures that at least one virtual photon must have an invariant mass squared that is large and negative, suppressing the nominal two-photon cross section by many orders of magnitude. There remain backgrounds from two-photon processes with radiation emitted by charged particles created from the coalesced photons, but these backgrounds are quite small and relatively easy to remove through kinematic requirements. The "radiative tag," together with additional topological and kinematic requirements, provides sensitivity to near-degenerate lepton doublets without the necessity of electron or muon identification.
• 4 L--+ L 0 1r- (4) L--+ Lop-(-+ 7r-7ro) In eaeh of these cases, only a single charged particle is emitted from each charged heavy lepton. The branching ratios for these decay modes and others which are important at large flare plotted vs fl in fig. 1 for a charged lepton mass of 10 GeV fc 2 • The branching ratios are very sensitive to {J and relatively insensitive tom_.

PRODUCTION CROSS SECTIONS
For this search, it is necessary to calculate the cross section + -

L+L-)
u(e e -+ 'hAG where 'hAG is a photon satisfying the radiative tag requirements on direction and energy. Lowest-order exact formulas for this cross seetion can be found in ref. 6.
It is necessary, however, to include higher-order radiative corrections, to allow for emission of additional photons during the heavy lepton pair production, photons that are undetected or mistaken for decay products of one of the charged leptons.
We estimate the radiative corrections arising from initial-state radiation and from we find the lowest-order and radiatively corrected cross sections (initial-state radiation only) shown in fig. 2. Final-state radiation is included after event generation through an event-by-event weighting algorithm that depends on the kinematic configuration of the generated charged lepton pair and photon, using the formulas of ref. 6.
The event generator includes the correlations in momenta of decay products from the L-and L +, arising from weak effects in both production and decay. 8 . Formulas may be found in ref. 1.

FINITE LIFETIME EFFECTS
For very low mass differences, the total decay width of the heavy charged lepton becomes small enough that its finite lifetime leads to serious detection inefficiencies.
Because the decay products can originate at a point displaced from the beam collision spot, their extrapolated trajectories are not in general consistent with having passed through that beam spot, a requirement of the Mark II charged-particle trigger. 9 Figure 3 shows the average distance of closest approach to the true beam spot of pions from the decay (4) plotted vs 8 for various values of m-. Since the Mark II trigger efficiency is poorly understood for tracks with impact parameters greater than 5 em, this analysis uses only tracks with smaller impact parameters. From fig. 3, one can see this implies poor sensitivity to lepton doublets with li below::::::: 250 MeV fc 2 •

EVENT SIGNATURES
Since in the nearly degenerate case, single-prong decays predominate, and since in each event two or more neutrinos or antineutrinos are undetected, the characteristic event signature of such heavy lepton pair production is a pair of oppositely charged, acollinear particles, sometimes accompanied by neutral pions. Because the heavy neutrinos carry away most of the available energy, these two tracks have low momenta.
The additional requirement of an isolated, energetic photon leads to a distinct event ·signature with low backgrounds, as discussed in the next section . .,.,

DATA SAMPLE
We use e+e-annihilation data taken at v'S=29 GeV with the Mark II detector at PEP in the detector's "preupgrade" configuration. Although our earlier study 1 was based on a sample of 205.1±3.0 pb-1 , ~uch of that data was taken with reduced main-drift-chamber high voltage, leading to poorer triggering and track reconstruction efficiencies. Since the analysis presented here is quite sensitive to uncertainties in those efficiencies, we choose to use only a sample of data (104.0±1.6 pb-1 ) taken after the main drift chamber returned to full chamber voltage.

EXPECTED BACKGROUNDS
A number of backgrounds were considered in this analysis from both annihilation and two-photon processes. Only four were found to be appreciable: The dominant background comes from e + e---+ r+T-"'f. This background has been determined from Monte Carlo 1 simulation ofT pair production, including initialstate radiation. As in the heavy lepton simulation, final-state radiation is included through an event-by-event weighting algorithm.

e+ e---+ e+ e-r+r-
In general, two-photon backgrounds are a major concern. Besides events with radiation from the electron or positron, which are largely suppressed by fiducial requirements on the tagging photon, there remain backgrounds due to final-state radiation emitted by particles formed by the coalesced photons. In addition, there ate backgrounds from photons produced in the decay of neutral pions. Most of these backgrounds can be removed by requiring that the event's missing momentum transverse to the beam direction be relatively large, since two-photon events typically are characterized by small missing transverse momenta.
An exception, however, is the background from e + e--+ e + e-r+ T-, which naturally has large missing momentum because of the undetected neutrinos produced.
The tagging photon in this background arises mainly from the decay 1r 0 -+ "Y"Y, where one photon has too little energy to be detected, and where the 1r 0 is produced in the \' 8 decay sequence: In annihilation production of tau pairs, the analogous background from T decays to the p are negligible since the Lorentz boost of the high-energy r's preclude the detected photons from satisfying isolation requirements. The background from e + e:.. --+ e + e-r+r-has been simulated with a Monte Carlo program, 10 using the double equivalent photon approximation. 11 3. e + e---+ e + e-7r+7ro1r-1r 0 A small background is expected from the process e + e---+ e + e-7r+1r 0 1r-7ro, where both 1r 0 's decay into photon pairs, and where one photon satisfies the tagging requirements while at least one other photon escapes detection through a gap in the electromagnetic calorimeter acceptance, giving rise to large missing momentum. This process has been simulated with the same Monte Carlo program 10 used for thee+ e---+ e + e-r+r-background, where the cross section has been normalized according to measurements by the JADE and ARGUS experiments. 12 • 13 · + --4. e e --+ qq"'f Accurately predicting backgrounds from hadronic event production is quite difficult. One reason is that the LUND Monte Carlo program 14 used to simulate quarkantiquark production and subsequent "hadronization" has not been verified to the level of accuracy necessary in treating events with only two charged tracks. Another difficulty is that interactions of neutral hadrons in the Mark II electromagnetic are not simulated in this analysis. Although such simulations can be performed, we cannot directly verify their accuracy from the data. For these reasons, the estimate presented below for hadronic backgrounds is not used in setting limits on new heavy lepton production. This is a conservative choice, since inclusion of additional background estimates would improve derived upper limits on production cross sections.

SELECTION OF SIGNATURE EVENTS
As described earlier, we search for events with two acollinear charged particles . . ~ ./. 9 and at least one isolated, energetic photon. In order to ensure very high ·trigger efficiency, thereby reducing dependence upon Monte Carlo trigger simulation, each reconstructed charged track must satisfy stringent requirements: 1) The track momentum must make an angle greater than 45° with respect to either beam direction.
2) The momentum transverse to the beam (p.t) must be greater than 150 MeV.
3) There must be a signal from both photomultiplier tubes of the TOF counter in the track's projected path. In addition, the measured flight time ~ust be in the range 0-12 ns.
4) The track must have at least 10 associated drift chamber signals (out of a possible 23), and at least one of those signals must come from one of the four inner layers of the vertex chamber.
5) The x 2 per degree of freedom calculated from the helical track fit to the drift chamber signals must be less than 5.
6) The impact parameter of the track with respect to the beam collision point in the plane transverse to the beam direction must be less than 5 c~. From measurement of Kg decays in two photon events from the data, we also find a trigger inefficiency that depends upon the angle between a particle's initial direction of motion at production and the direction of that production point with respect to the beam collision point. To reduce sensitivity to this inefficiency, we place a requirement on a variable that depends on the particle's transverse momentum, its .charge, and the location of its point of closest approach to the beam axis. More detail can be found in ref. 15.
In addition to these fiducial and track quality requirements, the tracks must have a total measured moment urn less than 4 Ge V / c, and any energy in the electromagnetic calorimeter associated with the track must' be less than 4 GeV. These requirements select events with low visible energy, filtering out backgrounds from radiative T pair production and from mismeasured radiative Bhabha and p. pair production.
In order to reduce backgrounds from 1r 0 decays, we require the tagging photon ....: I 10 to be isolated both from charged tracks and from other detected photons. To ensure reliable Monte Carlo simulation of calorimeter response, we also require that the photon satisfy tight fiducial requirements: 1) The measured energy must be at least 1 Ge V 2) The photon polar angle()"'! with respect to the beam must satisfy I cos 0"' 11 ~ 0.66.
3) The photon's azimuth direction must be at least 3° away from the center of the nearest crack between calorimeter modules.
4) The total reconstructed energy deposition in the calorimeter within 30° of the photon must be less than 150 MeV. 6) The angle between the photon and nearest charged track momentum must be at least 45°.
If more than one photon in an event satisfies the tagging requirements, the photon with the least total nearby( within 30°) neutral calorimetry energy is taken as the tag.
If more than one eligible photon has no nearby neutral energy, the most energetic is taken as the tag.
Additional requirements are imposed on the topology of each candidate event, designed both to suppress various backgrounds and to ensure reliable measurement.
Because charged tracks passing near one another may induce a signal on the same drift chamber wire or on neighboring wires, creating confusion during track reconstruction, we impose cuts on the minimum opening angle between the two allowed charged tracks. In the plane transverse to the beam, the opening angle must be at least 5. 7°, and in 3 dimensions must be at least 20•.
We also impose cuts on the maximum opening angle between the two tracks. In order to suppress backgrounds from two-photon processes where the tagged photon candidate production is unrelated to the charged particle productions( e.g, cosmic ray coincidences, to be discussed later), we require the acoplanarity (180° minus the opening angle in the transverse plane) be greater than 1.1 o. In order to suppress further the backgrounds from radiative r pair and radiative Bhabha production, we require the opening angle between the tracks in 3 dimensions be less than 160°.
In order to suppress radiative r pair production accompanied by decays involving one or more 1r 0 's, the total neutral energy of the event, excluding the contribution from the tagging photon, must be less than 2 GeV. As discussed earlier, two-photon backgrounds typically have low missing transverse momentum. Hence, we require the missing transverse momentum of the event be greater than 1 GeV /c. Similarly, the direction of the total detected momentum must make an angle greater than 45° with respect to the beam axis. These last two requirements also suppress events with very hard initial-state radiation along one of the beam directionsc Because energetic photons can escape detection through gaps in azimuth between calorimeter modules, leading to apparent missing tran~verse momentum, we also require that the missing transverse momentum point at least 3° away from the center of the nearest gap. Two-photon processes sometimes produce at low angles an electron or positron that can be detected by the SAT system. Such events are enhanced relative to untagged events by the above requirements of missing transverse momentum in the central detector. Similarly, hard initial-state radiation can produce a photon detectable with the SAT calorimeter. In order to suppress such backgrounds, werequire the total SAT detected energy be less than 8 GeV. In addition, if one of the plastic scintillators placed in front of the SAT calorimeters detects a charged particle in coincidence with a measured calorimeter energy greater than 200 MeV, the event is discarded.
Another background, peculiar to this analysis, comes from a cosmic-ray muon inducing an electromagnetic shower in the calorimeter, in coincidence with an electronc 12 positron interaction that produces two charged particles in the central detector. The cosmic ray shower (due to a "knock-on" electron) is reconstructed and misinterpreted as a photon, since typically there is no charged track leading from the beam collision point to the shower region. An example of such an event is shown in fig. 4, where the dashed line indicates the deduced trajectory of the muon that caused the false photon shower.
In order to remove these events, we veto any event that is flagged by one or more

NUMERICAL RESULTS
After all selection cuts, 14 events remain from 104 pb-1 of data. Table I shows the estimated backgrounds from the four processes discussed earlier. Ignoring the estimate for hadronic backgrounds for reasons discussed above, we expect a total of 12.3±1.7 e~ents from conventional processes, consistent with what we observe in the data. Figure 5 shows the distribution in tagging photon energy for the data(plotted points) and for the sum of the first three backgrounds(histogram). Figure 6 shows· the distribution i'n invariant mass of the two charged particles for both data and background. Figure 7 shows the distribution in reconstructed charged track momen-, ' tum(two entries/event) for both data and estimated background. We see no significant deviations between the data and estimated background for these ot any other distributions we have examined.
As a further check, we have applied an algorithm 16 that identifies electrons and pions with 60-90% efficiency and misidentification probabilities less than 15% for tracks with low momenta. Based upon energy deposition and shower shape in the ""' t calorimeter and upon measured charged particle flight times, the algorithm was developed and checked with data taken with the Mark II detector at SPEAR at v'S=3.1 GeV. Table II shows that there is good agreement between the data and estimated backgrounds(shown in parentheses) in the pattern of identified particle combinations.

LIMITS ON NEW LEPTON PAIRS
Having found no significant evidence for a new heavy lepton doublet, we next There are in general many approaches to setting limits on new heavy lepton production. For example, one can compare shapes or total numbers of events between data and the sum of expected backgrounds and a hypothetical heavy lepton signal for one or more distributions such as those in figures 5-7. We take the simplest and somewhat conservative approach of comparing only total numbers of events.
Since the number of surviving events in this analysis is quite low, it is necessary to apply techniques based on Poisson statistics. We define the integrated joint probability P(,\,Nn) for observing Nn or fewer events, given a Monte Carlo estimate ,\ with error UA, according to the following formula: where AB ± UB is the expectation value of the background alone and AT± ur is the expectation value of the background plus the signal. This expression gives a lower, more conservative confidence level than 1-P(.\r,ur,No).
Tables III-VI show the expectation values and errors of the 86 Monte Carlo heavy lepton samples generated for this analysis, along with the confidence levels for exclusion derived from formulas (9) and (10). Most of the lepton doublets for which Monte Carlo samples were generated can be excluded with greater than 99% confidence, although none with 8=200 MeV /c 2 can be excluded with that confidence. Interpolation between these points in the (m-,8) plane yields contours of exclusion at fixed confidence levels, Within the two contours shown in fig. 8 we exclude heavy lepton doublets with ~reater than 95% and 99% confidence. We are limited in sensitivity at high charged lepton masses because production rates for charged fermion-antifermion pairs fall rapidly as the fermion mass-energy approaches the beam energy. As discussed earlier, we are limited at low 8 by effects due to the finite lifetime of the heavy charged lepton. At mass differences much above 1 GeV fc 2 , heavy lepton events have larger visible energies than permitted in this analysis.
This analysis extends our limits on heavy lepton doublet production to a region of smaller 8 than attained in our previous analysis 1 because the radiative tag precludes the necessity for electron or muon identification and for associated high visible energies. On the other hand, the new requirement of an isolated, energetic photon aggravates mass suppression effects, giving much-reduced sensitivity at very heavy lepton masses.

CONCLUSIONS
In conclusion, we have found no evidence for a nearly degenerate heavy lepton doublet (L-,L 0 ) in our 29-GeV annihilation data and have excluded this possibility for mass splittings (8) Table Captions   Table I. Expected backgrounds to candidate events in 104 pb-1 • Note that the last background{radiative quark-antiquark production) is not included in the total and is not used in setting limits on new heavy lepton production.