First observation and branching fraction and decay parameter measurements of the weak radiative decay Ξ 0 → Λ e + e −

The weak radiative decay Ξ 0 → Λ e + e − has been detected for the ﬁrst time. We ﬁnd 412 candidates in the signal region, with an estimated background of 15 ± 5 events. We determine the branching fraction B (Ξ 0 → Λ e + e − ) = [7 . 6 ± 0 . 4(stat) ± 0 . 4(syst) ± 0 . 2(norm)] × 10 − 6 , consistent with an internal bremsstrahlung process, and the decay asymmetry parameter α ΞΛ ee = − 0 . 8 ± 0 . 2, consistent with that of Ξ 0 → Λ γ . The charge conjugate reaction Ξ 0 → Λ e + e − has also been observed.


Introduction
Since the discovery of hyperons, their (weak) radiative decays have held particular interest [1,2].Still, the precise nature of the decays themselves remains an open question [3,4].
Reliable techniques to predict branching ratios remain elusive.Furthermore, because SU(3) symmetry is broken only weakly in this regime, weak radiative decays should approximately conserve parity [5].Consequently, the asymmetries of decay angular distributions should be small.However, results from experiments indicate a relatively large (negative) asymmetry in every mode investigated [6].A number of models have been proposed to explain this apparent discrepancy [7].Experimental results tend to favor pole models or models based on chiral perturbation theory, which correctly find the sign of the asymmetry.Recently, a resolution of at least part of the puzzle has been offered [8].
When the NA48 Collaboration undertook investigations with a high-intensity K 0 S beam in 2002, trigger strategies for identifying radiative hyperon decays were included from the outset.The production over the full course of the run of more than 3 × 10 9 neutral cascades, Ξ 0 (1315), offered NA48 unmatched sensitivity for the study of such decays. 1his Letter details the measurement with these data of the weak radiative hyperon decay Ξ 0 → Λe + e − .This is the first measurement of this decay channel.If one assumes an inner bremsstrahlung-like mechanism producing the e + e − pairs, the expected rate for this process may be estimated naively assuming the (virtual) photon converts internally (Dalitz decay) or by using the machinery of QED as carried out in rate predictions for Σ 0 → Λe + e − [1,2].The results give a range from about 1/182 to 1/160 of the rate of Ξ 0 → Λγ, or (6.4 − 7.3) × 10 −6 .Such a process should exhibit a decay asymmetry like that in Ξ 0 → Λγ.

Data
The signal was sought among events containing one Λ (which decayed in-flight to a high-momentum proton and a much lower momentum π − ), one electron, and one positron, all in time.An additional in-time photon was required for the normalization channel, (Ξ 0 → Λπ 0 , π 0 → e + e − γ), a relatively abundant process whose final state is similar to that of the signal and which was selected via the same trigger tree as the signal channel.

Beam line and detector
The NA48 beam line was designed to produce and transport both K 0 L and K 0 S beams simultaneously [9].For the 2002 run, in order to increase dramatically the intensity of the K 0 S beam, the K 0 L target was removed and the K 0 L beamline blocked, the proton flux on the K 0 S target was greatly increased, and a 24 mm platinum absorber was placed after the Be target to reduce the photon flux in the neutral beam.An additional sweeping magnet was installed across the 5.2-meter long collimator, which, tilted at 4.2 mrad relative to the incoming proton beam, selected a beam of long-lived neutral particles (γ, n, K 0 , Λ, and Ξ 0 ).In each 4.8 s spill, occurring every 16.2 s, ∼ 5 × 10 10 protons impinged on the target.Approximately 2 × 10 4 Ξ 0 s, with momenta between 60 and 220 GeV/c, decayed in the fiducial volume downstream of the collimator each spill.
The detector for the 2002 run was identical to that used for NA48's measurement of direct CP-violation [9], except that the tagging counter immediately after the last collimator was removed.
The neutral beam exited the final collimation into an evacuated tank, approximately 90 m in length, terminated by a Kevlar window 0.3% of a radiation length thick.The detector was arrayed immediately downstream of this window.
A magnetic spectrometer followed the decay volume.It consisted of four drift chambers, two before and two after an analyzing magnet which provided a transverse momentum kick of 265 MeV/c in the horizontal plane.The chambers were identical, with two planes of sense wires in each of four orientations (x, y, u, v), vertical, horizontal, and at ±45 • .The u and v wires of the third chamber were the only ones left un-instrumented.Track-time resolution was about 1.4 ns.Space-point resolution was approximately 150 µm in each projection, and the momentum resolution (with p in GeV/c) was σ p /p = 0.48% ⊕ 0.015% × p.The resulting m π + π − resolution in K 0 S → π + π − decays was 3 MeV/c 2 .
A liquid krypton calorimeter (LKr) detected and measured the energy and position of electromagnetic showers.Its active region was divided transversely into approximately 2 cm × 2 cm cells, and its depth was 27 radiation lengths.Its single-shower time resolution was less than 300 ps; its transverse position resolution was better than 1.3 mm for a single photon of energy greater than 20 GeV; and its energy resolution [10] was σ(E)/E = 3.2%/ √ E ⊕9%/E ⊕0.42%,where E is in GeV.The resulting m γγ resolution in π 0 → γγ decays was approximately 1 MeV/c 2 .
The sensitive region of the electromagnetic calorimeter primarily constrained the fiducial volume of the experiment.Seven rings of scintillation counters bounded, in projection, the edges of this acceptance region, and the last two rings acted as trigger vetoes of extraneous activity.
A scintillator hodoscope, comprised of segmented horizontal and vertical strips arranged in four quadrants and located between the downstream end of the spectrometer and the upstream face of the calorimeter served as a zeroth-level charged-track trigger.Beyond the electromagnetic calorimeter stood an ironscintillator sandwich hadron calorimeter and three layers of muon counters, each shielded by an iron wall.
The entire detector array was sampled every 25 ns.An event trigger initiated a readout of information within a 200 ns window around the trigger time.In this way, time sidebands allowed investigations of accidental activity.
The experiment employed a multi-level trigger designed to maximize flexibility while minimizing pile-up, dead-time losses, and the collection of uninteresting events.To be included in the present analysis, events passed the lowest level hardware trigger if a horizontal-vertical coincidence occurred in at least one quadrant of the scintillator hodoscope, there were no in-time hits in the veto rings, at least three views in the first drift chamber registered more than two hits (as required in the case of more than one track), and either the energy in the electromagnetic calorimeter exceeded 15 GeV or the total energy in the electromagnetic and hadron calorimeters exceeded 30 GeV.The next level trigger required more than one track to have passed through the spectrometer forming one or more good vertices2 .The highest level trigger, an offline software cull, passed events in which a two-track invariant mass was consistent with that of a Λ and contained at least one high-energy cluster in the calorimeter not associated with either track forming the Λ.
A downscaled sample of minimum bias events was collected concurrently with the physics data.Complete trigger information was available for these events, so trigger efficiencies could be measured.The relative fraction of events containing all signal final state particles that passed the required triggers was sig trig = (96.5 ± 0.2)%, while the relative fraction of normalization events was norm trig = (97.1 ± 0.2)%.

Event selection criteria
From events passing all trigger levels, those containing exactly four charged tracks, two of each charge sign, that passed well within the fiducial volumes of the first and fourth drift chambers were kept for further analysis.
Signal event simulation showed that 99% of final state pions, electrons, and positrons had momenta of less than 30 GeV/c.A track with momentum greater than 3 GeV/c and associated shower energy within 5% of this momentum was identified as an electron or positron, depending on charge.A positive track whose momentum was greater than 30 GeV/c and either had no associated electromagnetic shower or the shower energy to momentum ratio was less than 0.8 was identified as a proton.If no such track was found, or if there were not both an electron and a positron identified, the event was abandoned.If the final track had a momentum greater than 4 GeV/c, but not more than 1/3.7 that of the proton track, it was identified as a pion.Otherwise, the event was abandoned.
The tracks associated with the proton and pion had to be separated by at least 5 cm in the first drift chamber and their detection times had to be within 2 ns.If not, the event was abandoned.The distance-of-closest-approach (doca) of the two tracks when projected back towards the target was required to be less than 2.2 cm, and the longitudinal position of this doca had to lie between 4 and 40 meters down stream of the target for the event to be further considered.The momentum vectors of the two tracks were projected, with respect to a reference frame centered on the beam axis, from their positions in the first drift chamber onto the face of the LKr.These projections were weighted by the relativistic energies of the particles associated with the respective tracks, added vectorially, and then normalized to the energy sum of the two particles.The result, a quantity called the center of gravity (COG), had to be greater than 8 cm to ensure that a parent of the two tracks was unlikely to have been directly produced in the target.The COG of a directly produced particle should be small.The invariant mass of surviving proton and pion candidate pairs was calculated.If the result differed from the nominal mass of the Λ by more than 3 MeV/c 2 (approximately 3σ), the event was abandoned.
The electron and positron tracks had to have times within 2 ns and a spatial separation in the first drift chamber of at least 2.5 cm.The latter requirement rejects conversions in the Kevlar window.Any unassociated shower in the calorimeter with energy above 1.5 GeV disqualified the event as a signal candidate.
A shower of between 3 and 120 GeV in the electromagnetic calorimeter was considered a photon candidate for the normalization channel if it was unassociated with any track, centered within the fiducial volume of the detector at least 5 cm from a dead cell, and isolated from any other shower.
Finally, for both signal and normalization channels, the event COG, which ideally would be 0 (see above), had to be equal to or less than 6 cm.
A signal (normalization) region was defined as 2σ either side of the nominal Λe + e − (γ) invariant mass, where σ m = 1 MeV/c 2 .For the Λ, the pπ invariant mass was used.Selection from the entire data set according to these criteria resulted in 412 signal candidates and 29522 normalization events reconstructed.

Acceptance and reconstruction efficiency
The product of geometrical acceptance (A) and selection criteria efficiency ( ) was determined with a Monte Carlo simulation.Nearly 10 5 signal-like events were generated according to a two-body model of a Λ and a virtual photon.The model included the decay parameter α = −0.78,found for the decay Ξ 0 → Λγ [11], and a 1/m 2 ee energy distribution for the converting photon, as would be the case for inner conversion.In this way, the model was intended to represent inner bremsstrahlung production.Generated events were stepped through a GEANT simulation of the NA48 detector and analyzed as real data, with the result: (A × ) sig = (2.69 ± 0.05)%.For the normalization channel, about 160 × 10 6 events (about 7× the measured flux) were generated with the latest PDG values for the decay parameters incorporated [6].The result of the detector simulation and reconstruction was (A × ) norm = (0.1251 ± 0.0003)%.Radiative corrections, using PHOTOS [12], were included, as was a Ξ 0 polarization of −10% for signal generation. 3

Background
Two sources of background were identified: physics and accidentally in-time combinations.

Physics backgrounds
The Ξ 0 decays predominantly to Λπ 0 .If the π 0 Dalitz-decays, and the photon goes undetected, the final state is that of the signal.Similarly, if the π 0 decays via the double-Dalitz mechanism, and an electron and a positron go undetected, the final state is again that of the signal.Finally, the π 0 → e + e − decay results in an irreducible background, but its rate is very small.Simulations of each of these channels at about seven times the flux lead to estimates of 4.6 ± 0.8, 0.1 ± 0.1, and 1.2 ± 0.4 events, respectively, infiltrating the signal region.

Kaon decays
The flux of neutral kaons was an order of magnitude larger than that of the Ξ 0 .The decay K 0 S → π + π − e + e − has a branching fraction of 4.7 × 10 −5 .If one of the pions met the requirements of a proton in this analysis, and the resulting m pπ ≈ m Λ , then this process would mimic the signal.Simulation with twice the flux of such events demonstrated that an explicit mass cut | m ππee − m K 0 S |> 0.015 GeV/c 2 eliminated essentially any trace of this background with negligible impact on signal-finding efficiency.The decay chain K 0 L → π + π − π 0 , π 0 → e + e − γ, has a product branching ratio of about 1.5 × 10 −3 .The K 0 L lifetime and their typical momentum of 80 GeV/c mean that about 4% of them decay in the experiment's decay volume.For these to become a background to the Λee signal, a pion would have to be mistaken as a proton and the invariant mass of it combined with that of the other pion would have to be close to that of the Λ.In addition, the photon would have to go undetected.Because of this last condition, an explicit kaon mass cut would be ineffective in reducing the background.On the other hand, the efficiency for this chain appearing in the signal region is correspondingly reduced and the COG is smeared out.We estimate on the basis of Monte Carlo simulation that 2 ± 2 such events will populate the signal region.

Accidentally in-time combinations
We estimated the contamination by accidental coincidences four ways: (1) Running the same analysis on the data, but requiring that the final-state leptons have the same charge.(2) Requiring that at least one track or shower be between 10 and 20 ns out-of-time and scaling appropriately.These approaches, which are not independent, yielded between 1 and 9 events in the signal region; we take the number to be 7 ± 5 events.In conclusion, combining the physics backgrounds with those attributed to accidentals and combinatorics, the estimated number of background events in the signal region is 15 ± 5 [see Table 1 for a of the background estimation].
The background contamination of the normalization sample was estimated from the tails of the m eeγ spectrum, which peaks sharply at m π 0 .Including a linear extrapolation under the mass peak, the number was estimated to be 428 ± 258.
The total number of Ξ 0 produced during the run was estimated by fully reconstructing Ξ 0 → Λπ 0 , π 0 → e + e − γ events without a longitudinal vertex position cut and using the equation From the entire data set, 29522 such events were reconstructed.After background subtraction, this gives an integrated flux of The first uncertainty is due to statistics, and the second is from branching fraction uncertainties, primarily that on B(π 0 → e + e − γ).
Table 2 Quantities that entered into Ξ 0 flux calculations.
No. of events in signal region 29552 Estimated no. of background events 428 ± 258 At the end of the analysis, 412 events were found in the signal region [see Figure 2].

3-body MC
Fig. 3. Reconstructed m ee spectra from data (points), 1/m 2 ee (solid line), 2-body flat (dashed line), and 3-body phase space (dotted line).The distributions from simulated data have been normalized to contain the same number of events in the signal region of the data, without background subtraction.

m ee spectrum
The associated m ee distribution is consistent with a 1/m 2 ee shape [see Figure 3], and we consider only this model (presumably inner bremsstrahlung) in determining of the branching fraction, including systematic uncertainties.

Branching fraction
Given the background estimate, efficiencies, and flux discussed above, and the PDG Λ → pπ − branching ratio [see Table 3], the branching ratio for Ξ 0 → Λe + e − is determined to be where the uncertainty here is statistical only.A check for Ξ 0 → Λe + e − found a clear peak of 24 events, of which, roughly, as many as 7 may be background, in the invariant mass plot.This number is consistent with the Ξ 0 branching fraction and relative Ξ 0 and Ξ 0 production rates.The production mechanism, kinematics and backgrounds of the Ξ 0 , however, differ from those of the Ξ 0 , and no further consideration of this charge-conjugate channel is given here.

Systematic uncertainties
Analysis selection criteria were varied when looking at the data and when determining reconstruction efficiencies.The branching fraction result was most sensitive to the treatment of the reconstructed Ξ 0 vertex and backgrounds from the Ξ 0 → Λπ 0 channel in relation to m ee .No cut was placed on the longitudinal position of the Ξ 0 vertex.Requirements varying the minimum longitudinal position of the vertex in 6-m intervals beginning before the target (to account for resolution effects) resulted in branching fraction changes of between 0.2% and 3%.We assign the highest variation (±3%) as a systematic error.
It was possible to eliminate nearly all physics backgrounds by excluding signal events with 0.100 GeV/c 2 < m ee < 0.135 GeV/c 2 , which, according to signal Monte Carlo, reduces the reconstruction efficiency by 5%.Cutting this region from the final data sample, and recalculating the branching ratio, results in a shift of 1.8%, which was included symmetrically as a systematic uncertainty.These, along with smaller variations in the branching fraction resulting from other modifications of the selection criteria, were added in quadrature to give a systematic uncertainty of ±3.6% on the branching fraction.
We conservatively assign a relative ±1% uncertainty on the determination of the background to account for correlations in methods for estimating accidentally in-time events.
The branching fraction differed by about 1% when signal and normalization modes were simulated with and without radiative corrections, and we include this difference symmetrically as a systematic uncertainty.
For the A × determinations, the Ξ 0 polarization of simulated events was set to −10%.Samples of simulated data, generated with the polarization varied between 0% and −20% (±10%), were used to recalculate the branching fraction vary.The largest variation among these trials was 2.7%, and this variation is taken symmetrically as a systematic uncertainty.
The decay asymmetry used in generating simulated signal events was that of the process Ξ 0 → Λγ [11].Our measurement, discussed below, is in agreement with this value, but with a 25% uncertainty.Varying our simulation within this 25% range changed the branching fraction by at most 2.5%, and this is symmetrically assigned to systematic uncertainty.
The determination of the trigger efficiency and Ξ 0 flux were discussed above.The difference between trigger efficiencies for signal and normalization channels is taken as an uncertainty, affecting the branching ratio by 0.6%.An alternative, less direct, calculation of the flux was statistically consistent with the one described above.The two differed by 1.9%, and we conservatively include, symmetrically, this amount as a systematic uncertainty.

Asymmetry parameter
The angular distribution of the proton relative to the Ξ 0 line of flight in the Λ rest frame is given by [6]: The cos θ pΞ spectrum from signal events was corrected by subtracting scaled backgrounds from the side-band regions indicated in Figure 1 and by dividing, bin-by-bin, the acceptance as determined from a Ξ 0 → Λe + e − simulation where the spectrum was generated to be flat in cos θ pΞ .A two-parameter fit to this corrected spectrum gives the product of asymmetry parameters α ΞΛee α , where α is the asymmetry parameter for the decay Λ → pπ − .This latter was taken to be α = 0.642±0.013[6].The fit (over the interval −0.8 < cos θ pΞ < 1) [see Figure 4] to the data yields, α ΞΛee = −0.8± 0.2 This is consistent with the latest published value of α ΞΛγ = −0.78±0.18(stat)±0.06(syst) [11].
The existence of the charge conjugate reaction Ξ 0 → Λe + e − , has been confirmed.

( 3 )
Taking events with m pπ values between 7 and 10 standard deviations from the central value (m Λ ) and computing m Λee .(4) Defining two "side-band" regions, one along each axis in COG-versusm Λee space [see, in Figure 1, the hatched rectangles at high COG and high mass; each region has the same "area" as the signal region, the open rectangle in the figure].

Fig. 1 .
Fig. 1.COG versus m Λee after all other selection criteria were imposed.The three hatched boxes are side-band regions.The signal region is the open box at low COG around m Ξ 0 .The side-band regions at high mass-low COG and high COG were used to estimate accidental and combinatoric backgrounds in the signal region.All three side-band regions were used in the subtraction of background under the decay-angle distribution (see text).

Fig. 2 .
Fig. 2. m Λee after all selection criteria.Arrows indicate signal region.Stacked in various hatchings (see legend) are the estimated sources of background.

Table 3
Quantities that entered into branching fraction calculations.

Table 4
Sources of systematic uncertainty on the branching fraction.