and S. WORM[(h)]
(BNL E888 Collaboration)
(1) Brookhaven National Laboratory, Upton, NY 11973
(2) University of California, Irvine, California 92717
(3) University of California, Los Angeles, California 90024
(4) Princeton University, Princeton, NJ 08544
(5) Stanford University, Stanford, California 94309
(6) Temple University, Philadelphia, Pennsylvania 19122
(7) University of Texas at Austin, Austin, Texas 78712
(8) College of William and Mary, Williamsburg, Virginia 23187
We have searched for a neutral H dibaryon decaying via and . Our search has yielded two candidate events from which we set an upper limit on the H production cross section. Normalizing to the inclusive production cross section, we find at 90% C.L., for an H of mass 2.15 GeV/.
The theory of quantum chromodynamics imposes no specific limitation on the number of quarks composing hadrons other than that they form color singlet states. Although only qqq and states have been observed, other combinations can form color singlets. Jaffe has proposed that a six-quark state uuddss may have sufficient color-magnetic binding to be stable against strong decay. Such a state, which Jaffe named H, would decay weakly, and the resultant long lifetime would allow the possibility of observing such particles in neutral beams. Theoretical estimates of have varied widely, ranging from a deeply bound state with <2.10 GeV/ to a slightly unbound state with near the threshold, 2.23 GeV/. In this mass range the H would decay almost exclusively to , , and . Several previous experiments have searched for H's but with no compelling success. The search described here is sensitive to H's having mass and lifetime in a previously unexplored range.
We have searched for and decays by looking in a neutral beam for decays in which the momentum vector does not point back to the production target. The experiment, E888, was performed in the B5 beamline of the Alternating Gradient Synchotron (AGS) of Brookhaven National Laboratory. A second phase of the experiment searched for long-lived H's by using a diffractive dissociation technique. The detector used for the decay search (Fig. 1) was essentially that used for the E791 rare kaon decay experiment and has been described in detail elsewhere.
Figure 1: The E888 detector and beamline.
In brief, a neutral beam was produced using the 24 GeV/c proton beam from the AGS incident on a 1.4 interaction length Cu target. The targeting angle was 48 mr. After passing through a series of collimators and two successive sweeping magnets, the neutral beam entered a 10 m long vacuum decay tank within which candidate 's decayed. Downstream of the tank was a two arm spectrometer consisting of two magnets with approximately equal and opposite impulses and 5 drift chamber (DC) stations located before, after, and in between the magnets. Downstream of the spectrometer on each side of the beam were a pair of trigger scintillator hodoscopes (TSCs), a threshold Cherenkov counter (CER), a lead-glass array (PbG), 0.91 m of iron to filter out hadrons, a muon-detecting hodoscope (MHO), and a muon rangefinder (MRG) consisting of marble and aluminum slabs interspersed with streamer tubes. For the first half of the run the Cherenkov counters were filled with a He-N mixture (n = 1.000114) to identify electrons; for the second half the left-side counter was filled with freon (n = 1.0011) to identify protons from (due to lack of light). Only the left counter was used for this purpose as the soft pion from decay is accepted only when on the right; when it is on the left, the first magnet bends it back across the beamline and it is not reconstructed. The lead-glass array (PbG) consisted of two layers: a layer of front blocks 3.3 radiation lengths (r.l.) deep and a layer of back blocks 10.5 r.l.\ deep. The PbG was used to identify electrons by comparing the total energy deposited () with the track's momentum. A minimum bias trigger was defined as a coincidence between all 4 TSC counters and signals from the 3 most upstream DC stations. A Level 1 trigger (L1) was formed by putting minimum bias triggers in coincidence with veto signals from the Cherenkov counters and muon hodoscope. All events passing L1 were passed to a Level 3 software trigger which used hit information from the first 3 DC stations to calculate an approximate two-body mass. Events with <1.131 GeV/ were written to tape.
Offline, all events containing two opposite-sign tracks forming a loose vertex were kinematically fit and subjected to the following cuts: there could be at most one extra track-associated hit or one missing hit in the ten DC planes which measure the x (bending) view of each track; the 's per degree of freedom resulting from the track and vertex fits had to be of good quality; the vertex had to be within the decay tank and downstream of the fringe field of the last sweeper magnet; both tracks had to be accepted by CER, PbG, MHO, and MRG detectors and have p>1 GeV/c; neither track could intersect significant material such as the flange of the vacuum window; to reject background from , had to be ; and to reject background from resulting from secondary interactions, had to be >4 times the mass resolution of decays (1.55 MeV/).
Events passing these cuts were subjected to particle identification criteria in order to reject background from () and () decays. To reject electrons, we require that there be no track-associated Cherenkov hit and that tracks with p>2 GeV/c (<2 GeV/c) have (<0.52). The low momentum track on the right side of the detector was required to deposit <0.66 in the front PbG blocks. To reject muons which passed the MHO veto in the trigger, we cut events with a hit in the MRG which was consistent with the projection of a track and which corresponded to at least 65% of the expected range of a muon with that track's momentum.
Lambda candidates were selected by requiring that be less than 4 times the mass resolution of decays (0.55 MeV/). The data was then divided into two streams: a normalization stream consisting of 's which project back to the production target, and a signal stream consisting of 's which do not. The former were selected by requiring that the square of the collinearity angle be less than 1.5 mrad, where is the angle between the reconstructed momentum vector and a line connecting the production target with the decay vertex. This sample contains negligible background. The signal sample was selected by requiring that >145 MeV/c, where is the momentum transverse to the line connecting the production target with the decay vertex. This cut value was chosen to eliminate decays, which have a kinematic endpoint of 135 MeV/c. The distribution of 's from two-body decays exhibit an approximate Jacobian peak (not exact because the vertex is the 's) with an endpoint which depends upon . A large fraction of high- 's were found to project back to a collimator located just upstream of the decay tank. We thus required that the point in our beamline to which a projects back be located downstream of this collimator: m.
A signal region for H candidates was defined by the criteria MeV/c and , where is the distance in proper lifetimes between the decay vertex and the nearest material (beamline element) to which the momentum vector projects back. The cut rejects decays which survive the CER, PbG, MHO, and MRG vetoes due to detector inefficiency, while the cut rejects 's which originate from collimators, flanges, and other beamline elements. All cuts were determined without looking at events in the signal region, in order that our final limit on H's be unbiased. After fixing cuts we looked in the signal region and observed two events. The estimated background is 0.15 events from 's originating from beamline elements, and <0.21 events from decays (all as the is too high for ). The former is estimated by studying the distribution of 's originating from a ``hot'' flange located immediately upstream of 9.65 m. The latter is estimated by first counting the number of final events cut because the low-momentum track had (these are electrons); this is then multiplied by the ratio of the number of electrons passing PbG analysis cuts to the number having , as determined from a sample of decays. The vs. plot for the final high- sample is shown in Fig. 2. In this figure the Cherenkov veto for the freon counter is not imposed. A band of decays is visible at MeV/c which results from the MeV/c cut and the cut; this latter cut constrains from above. 's which originate from beamline elements are visible at low . For the freon subset, when we require that there be no signal in the left Cherenkov counter, all but two decays are eliminated while all 's at low remain.
Figure 2: vs. for the high- sample. The signal region is denoted by dashed lines. The band of events from =145 to 150 MeV/c are decays; the leftmost edge is due to a cut, while the rightmost edge is due to a lower cut on .
Figure 3: vs. for the final high- sample. The two events in the signal region are circled. The cluster of events at GeV/c, GeV/ are consistent with Monte Carlo simulated decays. There is a third event which is well-separated from the decays and which lies just outside the signal region; the 3 separated events are consistent with decay if GeV/.
Also visible in Fig. 2 are our two candidates, which have of 187 and 191 MeV/c and of 6.7 and 9.4. The values correspond to a Jacobian peak from decay if GeV/. The probability for a decay to have such high is extremely small, as it is kinematically forbidden for a decay to have both and MeV/c (Fig. 3). The probability for a decay to look like these events is also very small, as the PbG response for the electron candidate tracks is very uncharacteristic of electrons: = 0.44 and 0.27, and for both events = 0 (Fig. 4). This response is typical of pions from decay. To investigate background from neutrons in the beam interacting with residual gas molecules in the decay tank, we recorded and analyzed a sample of data equivalent to 1% of the total sample with the decay tank vacuum spoiled by a factor . This sample yielded one event in the signal region, implying a background level in the rest of the data of 0.04 events. We also studied potential background from decays where the originates from a beamline element; from Monte Carlo simulation and the number of 's observed originating from beamline elements, we estimate a background of less than 0.10 events. The total background estimate from known sources is less than 0.50 events. The probability of 0.50 events fluctuating up to two or more events is 0.090; if such a fluctuation occurred, it is remarkable that the of the events is so similar.
Figure 4: (PbG) vs. for: a) the low momentum track of 's from the final high- sample with only the PbG cuts relaxed, and b) low momentum electrons from decay. In (a), the tracks from the two events in the signal region are circled. There are 4.7 times as many events in (b) as in (a).
Figure 5: 90% C.L. upper limits on the H production cross section as a function of or (see Ref. ). The dashed contour corresponds to an H lifetime half that given on the top scale.
A 90% C.L. upper limit on the H production cross section can be
expressed in terms of the inclusive production cross section
where is the number of 's originating from the target, and are geometric acceptances for 's originating from the target and from H decays, respectively, and are branching ratios, is the inclusive production cross section, and is the factor which multiplies the single-event sensitivity to give the value of which has a 10% chance of producing 2 detected events. Here we conservatively assume no background and take . The acceptance accounts for the fact that 's from H's must project back to a restricted region of the beamline. Since decays are common to both signal and normalization channels, all trigger and detection efficiencies divide out of Eq. (1).
The acceptances and were determined from Monte Carlo simulation using several different estimates of the production momentum spectra. For the H simulation, a central production spectrum was used with a broad peak at . A spectrum corresponding to a coalescence model for H production  resulted in a limit on about 50% lower. We quote here the more conservative limit resulting from the central production spectrum. The inclusive production spectrum was taken from a measurement by Abe et al.; comparison with our data shows very good agreement.
The acceptance also depends crucially on H lifetime.
Here we assume the relationship between and
, , and
calculated by Donoghue et al., and
obtain 90% C.L. upper limits on
function of . Our acceptance is maximum
for ns and becomes small for
ns due to
the m cut. Our limits for
plotted in Fig. 5.
For GeV/, Jaffe's original prediction,
From Abe et al., mb/sr, so b/sr. For GeV/, consistent with the observed , the acceptance is lower and the two candidate events correspond to a differential cross section of b/sr. The authors of Ref.  note that may be shorter than their predicted value by up to a factor of two; this would increase our acceptance for GeV/ and decrease our acceptance for greater than this value. The resultant 90% C.L. upper limits are plotted as the dashed contour in Fig. 5. If we assume that the invariant cross section has the form , then our limit (2) corresponds to nb for a wide range of parameters B and C.
There are few theoretical predictions of the H production cross section. Cousins and Klein predict a differential cross section of 100 b/sr for p-Cu interactions at our targeting angle based on a coalescence model. Cole et al. considers and coalescence and predicts for p-Cu collisions at AGS energies; taking the inelastic cross section to be 780 mb gives b. Rotondo considers only coalescence and predicts a total cross section at Fermilab energies of 1.2 b.
We are indebted to the E791 and E871 collaborations, which built or supported most of the apparatus used here. We thank V.L.Fitch for much encouragement, and S. Black, K. Schenk, and N. Mar for their help in various stages of this work. We gratefully acknowledge the strong support of BNL, in particular R. Brown, A. Pendzick, the AGS staff, and the C.C.D. We also thank the SLAC computing division and the Princeton C.I.T., where all the data was reconstructed. This work was supported in part by the U.S. Department of Energy, the National Science Foundation, and the R.A. Welch Foundation.